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HSC Science (Electronics) 12th Board ExamMaharashtra State Board
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# Solution - The Cartesian Equations of Line Are 3x -1 = 6y + 2 = 1 - z. Find the Vector Equation of Line. - HSC Science (Electronics) 12th Board Exam - Mathematics and Statistics

#### Question

The Cartesian equations of line are 3x -1 = 6y + 2 = 1 - z. Find the vector equation of line.

#### Solution

Given equations of the line are:
3x -1 = 6y +2 = 1 - z
Rewriting the above equation, we have,

3(x-1/3)=6(y+2/6)=-(z-1)

((x-1/3))/(1/3)=((y+1/3))/(1/6)=((z-1))/-1 ....(1)

Now consider the general equation of the line:

(x-a)/l=(y-b)/m=(z-c)/n...(2)

where, l,m and n are the direction ratios of the line and the point (a,b,c) lies on the line.
Compare the equation (1), with the general equation (2),

we have l=1/3, m=1/6 and n=-1

Also, a=1/3, b=-1/3 and c=1

This shows that the given line passes through (1/3, -1/3, 1)

Therefore, the given line passes through the point having

position vector bara=1/3hati-i/3hatj+hatk and is parallel to the
vector barb=1/3hati+1/6hatj-hatk

So its vector equation is

barr=(1/3hati-1/3hatj+hatk)+lambda(1/3hati+1/6hatj-hatk)

Is there an error in this question or solution?

#### APPEARS IN

2014-2015 (March) (with solutions)
Question 1.2.4 | 2 marks

#### Reference Material

Solution for question: The Cartesian Equations of Line Are 3x -1 = 6y + 2 = 1 - z. Find the Vector Equation of Line. concept: Equation of a Line in Space. For the courses HSC Science (Electronics), HSC Science (Computer Science), HSC Science (General) , HSC Arts
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# If two dice are rolled simultaneously, find the probability of the following events. Event A: The sum of the digits on the upper faces is at least 10 - Algebra

Sum

If two dice are rolled simultaneously, find the probability of the following events.

Event A: The sum of the digits on the upper faces is at least 10

#### Solution

Sample space,

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6),

(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6),

(3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6),

(4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6),

(5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6),

(6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

∴ n(S) = 36

Let A be the event that the sum of the digits on the upper faces is at least 10.

∴ A = {(4, 6), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

∴ n(A) = 6

∴ P(A) = ("n"("A"))/("n"("S"))

= 6/36

∴ P(A) = 1/6

Concept: Probability of an Event
Is there an error in this question or solution?

format: plain


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## All functions

example_ct_data

Example Ct value data

example_gp_partab

Example Gaussian Process prior parameter table

example_seir_incidence

True simulated SEIR incidence

example_seir_partab

Example SEIR model parameter table

likelihood_detectable()

Likelihood for using proportion detectable only

p_a()

Function to give probability of observing x given age a and the viral kinetics curve

plot_distribution_fits()

Plot distribution fits

plot_posterior_density()

Plot posterior density

plot_prob_infection()

Plot probability of infection

predicted_distribution_fits()

Predicted distribution fits

prop_detectable_single()

Probability of having a detectable Ct for a given time since infection

reverse_gp_model()

Given a vector of daily infection probabilities, converts this to the input expected by the Gaussian process model

simulate_observations_wrapper()

Simulate full line list data

simulate_reporting()

Subset line list data by testing strategy. Options:

1. Sample a random fraction of the population if the only argument is frac_report

2. Sample some random fraction of the population at a subset of time points, specified by timevarying_prob

3. Observe symptomatic individuals with some fixed probability, frac_report if symptomatic is TRUE

4. Observe symptomatic individuals with some time-varying probability, timevarying_prob, if symptomatic is TRUE INPUTS:

1. individuals: the full line list from the simulation, returned by virosolver::simulate_observations_wrapper

2. solve_times: vector of times at which individuals can be reported

3. frac_report: the overall fraction/probability of individuals who are reported

4. timevarying_prob: a tibble with variables t and prob. This gives the probability of being reported on day t

5. symptomatic: if TRUE, then individuals are reported after developing symptoms. If FALSE, then we take a random cross-section OUTPUTS:

6. A tibble with line list data for individuals who were observed

7. A plot of incidence for both observed individuals and the entire simulated population

8. Plot growth rate of cases/infections in the entire population and observed population

simulate_viral_loads_wrapper()

Simulate observed Ct values for the line list dataset. NOTE this differs to virosolver::simulate_viral_loads, as this function only solves the viral kinetics model for the observation time INPUTS: 1. linelist: the line list for observed individuals 2. kinetics_pars: vector of named parameters for the viral kinetics model OUTPUTS: 1. A tibble with the line list data and the viral load/ct/observed ct at the time of sampled


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# !FTL

!FTL, an Articulation-Invariant Stroke Gesture Recognizer with Controllable Position, Scale, and Rotation Invariances. Nearest neighbor classifiers recognize stroke gestures by computing a (dis)similarity between a candidate gesture and a training set based on points, which may require normalization, resampling, and rotation to a reference before processing. To eliminate this expensive preprocessing, this paper introduces a vector-between-vectors recognition where a gesture is defined by a vector based on geometric algebra and performs recognition by computing a novel Local Shape Distance (LSD) between vectors. We mathematically prove the LSD position, scale, and rotation invariance, thus eliminating the preprocessing. To demonstrate the viability of this approach, we instantiate LSD for n=2 to compare !FTL, a 2D stroke-gesture recognizer with respect to $1 and$P, two state-of-the-art gesture recognizers, on a gesture set typically used for benchmarking. !FTL benefits from a recognition rate similar to $P, but a significant smaller execution time and a lower algorithmic complexity.$

## References in zbMATH (referenced in 1 article )

Showing result 1 of 1.
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FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT.
FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT. FOR THE WORK ENVIRONMENT & THE ENVIRONMENT ENVIRONMENT.

Our Mission

Great office furniture is built to last.
But 99% of it ends up in landfill.
Let’s break this cycle together.

# HOW IT WORKS

## SHOP

By location, furniture type, timeframe, quantity, color, finish, material, and manufacturer.

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Product is reviewed and approved within 24 hours.

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Upload the product content to our platform.

## PRODUCT ID

A Reseat ID is assigned to track its life-cycle & backstory.

## ENJOY

Give the furniture a 2nd life-cycle.

## New Listings

Our Story

All furniture has a unique backstory.
It’s something that we celebrate, and frankly, are a bit obsessed with.

But how did we — that’s me, Brandi, and my husband Eric — get here? That’s a story with its own twists and turns.

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Ready to get your assets into the circular economy? Reseat is here to help! Our easy-to-use- platform makes it simple to list your products and get them in front of interested buyers.

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# Quest:Hillshire quests

WARNING: This page contains Quest spoilers. ~ Solutions ~ Table ~ List ~ All ~ Category ~

Highlight to view quest spoilers.

## Hillshire quests

Walking inside Hillshire requires a pass (see Hillshire Tourist) or bypassing the troll at the entry of town.

#### "Hillshire Tourist", in which you visited scenic Hillshire. (Quest level 2)

Go to the campsite on the road northwest from Pekan Ford, and search the ashes. Take the tarnished ring from the circle of stones and go to Hillshire by going northwest then northeast at the junction outside the tourism office. Give the tarnished ring to the bridge troll and he will give you a pass to enter Hillshire.

#### "Occult Apprentice", in which you became more knowledgeable in magical control. (Quest level 7)

REQUIRED SKILLS/BONUSES NEEDED (Below scores CONFIRMED. Minimum bonus may be less.)
*Magic.methods.physical.evoking (feather) - 79 bonus
*Magic.methods.elemental.fire (book) - 121 bonus
*Magic.methods.mental.channeling (spider Ice cube)- 183 bonus (may be up to 20 points lower)
*Magic.spell.misc (spider Ice cube)- between 134 and 138 bonus
*Magic.methods.mental.animating (bottle of alcohol) - 181 bonus

REQUIRED ITEMS
*Feather - available from corpses of birds. Also available in a pillow south from main quest room.
*Book - available in various shops.
*Spider Ice Cube - available in Krazzander's, Ankh-Morpork.
*Bottle of Alcohol - must be a bottle, not a glass.  Beware that most bars and restaurants don't sell alcohol in bottles.

The quest is in northwestern Hillshire, in the Wizards house. Go upstairs and then north (if the door is not open, say friend). You then meet a wizard who asks if you'd like to be an apprentice. Say yes. He will tell you to retrieve the above items, in potentially varying order. Read the scroll he tells you to read for each item, then perform the following actions in line with the appropriate item.

Feather - Drop feather, then lift feather.
Book - Drop book, then force book to combust.
Cube - Drop the cube and cast Flizzlofrob's Morphogenic Resonator at cube.
Alcohol - Drop bottle, then induce weather from bottle.


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# Quick Calculation 3.8

A First Course in String Theory

.

Show that this condition fixes uniquely $\displaystyle{\alpha = \gamma = 1/2}$, and $\displaystyle{\beta = - 3/2}$, thus reproducing the result in (3.90).

~~~

Eq. (3.93):

$\displaystyle{l_P = (G)^\alpha (c)^\beta (\hbar)^\gamma}$

.

$\displaystyle{l_P = \left( \frac{l_p^3}{m_p t_P^2} \right)^\alpha \left( \frac{l_P}{t_P} \right)^\beta \left( \frac{m_P l_P^2}{t_P} \right)^\gamma}$

.

\displaystyle{\begin{aligned} 3 \alpha + \beta + 2\gamma &= 1 \\ -\alpha + \gamma &= 0 \\ - 2 \alpha - \beta - \gamma &= 0 \\ \end{aligned}}

.

var('a b c')

solve([3*a+b+2*c==1, -a+c==0, -2*a-b-c==0], a, b, c)

.

\displaystyle{\begin{aligned} \alpha &= \frac{1}{2} \\ \\ \beta &= \frac{-3}{2} \\ \\ \gamma &= \frac{1}{2} \\ \\ \end{aligned}}

.

Eq. (3.90):

$\displaystyle{l_P = \sqrt{\frac{G \hbar}{c^3}}}$

— Me@2022-06-23 10:46:22 AM

.

.


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Question: data import within the GeneGeneintrR pipline
0
2.6 years ago by
23139904500 wrote:
I was trying very hard to prepare the raw data for the pachage geneinteR. but when i import my data with the sys.data() recommended by the vigenette. the results show there is only "" in my data. whatis the trouble. can sb tell me how to import the .ped file correctly?
modified 2.6 years ago • written 2.6 years ago by 23139904500

> ped<-system.file('中期答辩/inter.ped')
> ped
[1] ""

Before is the code i read the ped file in R.And the result seems so wired.

when I figure out how to load the image file, i will upload my ped file format.


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# Paper on network model of attitudes

Our paper on the Causal Attitude Network (CAN) model was published in Psychological Review (PDF).

In the paper, we introduce the CAN model, which conceptualizes attitudes as networks consisting of interacting evaluative reactions, such as beliefs (e.g., judging a presidential candidate as competent and charismatic), feelings (e.g., feeling proudness and hope about the candidate), and behaviors (e.g., voting for the candidate). Interactions arise through direct causal connections between the evaluative reactions (e.g., feeling hopeful about the candidate because one judges her as competent and charismatic). The CAN model assumes that causal connections between evaluative reactions serve to heighten the consistency of the attitude and we argue that the Ising model’s axiom of energy expenditure reduction represents a formalized account of consistency pressure. Because individuals not only strive for consistency but also for accuracy, network representations of attitudes have to deal with the tradeoff between consistency and accuracy. This tradeoff is likely to lead to a small-world structure and we show that attitude networks indeed have a small-world structure. We also discuss the CAN model’s implication for attitude change and stability. Furthermore, we show that connectivity of attitude networks provides a formalized and parsimonious account of the dynamical differences between strong and weak attitudes.

Dalege, J., Borsboom, D., van Harreveld, F., van den Berg, H., Conner, M., & van der Maas, H. L. J. (2015). Toward a formalized account of attitudes: The Causal Attitude Network (CAN) model. Psychological Review. Advance online publication.

# New network study: what are ‘good’ depression symptoms?

Our new paper “What are ‘good’ depression symptoms? Comparing the centrality of DSM and non-DSM symptoms of depression in a network analysis” was published in the Journal of Affective Disorders (PDF).

In the paper we develop a novel theoretical and empirical framework to answer the question what a “good” symptom is. Traditionally, all depression symptoms are considered somewhat interchangeable indicators of depression, and it’s not clear what a good or clinically relevant symptom is. From the perspective of depression as a network of interacting symptoms, however, important symptoms are those with a large number of strong connections to other symptoms in the dynamic system (i.e. symptoms with a high centrality).

So we went ahead and estimated the network structure of 28 depression symptoms in about 3,500 depressed patients. We found that the 28 symptoms are intertwined with each other in complicated ways (it is not the case that all symptoms have roughly equally strong ties to each other), and symptoms differed substantially in their centrality values. Interestingly, both depression symptoms as listed in the Diagnostic and Statistical Manual of Mental Disorders (DSM) — as well as non-DSM symptoms such as anxiety — were among the most central symptoms.

When we compared the centrality of DSM and non-DSM symptoms, we found that, on average, DSM symptoms are not more central. At least from a network perspective, this raises substantial doubts about the validity of the depression symptoms featured in the DSM. Our findings suggest the value of research focusing on especially central symptoms to increase the accuracy of predicting outcomes such as the course of illness, probability of relapse, and treatment response.

Fried, E., Epskamp, S., Nesse, R. M., Tuerlinckx, F., & Borsboom, D. (in press). What are ‘good’ depression symptoms? Comparing the centrality of DSM and non-DSM symptoms of depression in a network analysis. Journal of Affective Disorders, 189, 314–320. doi:10.1016/j.jad.2015.09.005

# HRQoL Paper published

Recently, our paper “The application of a network approach to health-related quality of life (HRQoL): introducing a new method for assessing hrqol in healthy adults and cancer patients” was published in Quality of Life Research.

The objective of this paper was to introduce a new approach for analyzing Health-Related Quality of Life (HRQoL) data, namely a network model.

The goal of this paper was to introduce the network approach in the analyzation of Health-Related Quality of Life (HRQoL) data. To show that the network approach can aid in the analysis of these kinds of data, we constructed networks of two samples: Dutch cancer patients (N = 485) and Dutch healthy adults (N = 1742). Both completed the 36-item Short Form Health Survey (SF-36), a commonly used instrument across different disease conditions and patient groups [1]. In order to investigate the influence of diagnostic status, we added this binary variable to a third network that was constructed using both samples. The SF-36 consists of 8 sub-scales (domains). We constructed so-called “sub-scale” networks to gain more insight into the dynamics of HRQoL on domain level.

Results showed that the global structure of the SF-36 is dominant in all networks, supporting the validity of questionnaire’s subscales. Furthermore, we found that the network structure of the individual samples were similar with respect to the basic structure (item level), and that the network structure of the individual samples were highly similar not only with respect to the basic structure, but also with respect to the strength of the connections (subscale level). Lastly, centrality analyses revealed that maintaining a daily routine despite one’s physical health predicts HRQoL levels best.

We concluded that the network approach offers an alternative view on Healt-Related Quality of Life. We showed that the HRQoL network is, in its basic structure, similar across samples. Moreover, by using the network approach, we are able to identify important characteristics in the structure, which may inform treatment decisions.

Kossakowski, J. J., Epskamp, S., Kieffer, J. M., Borkulo, C. D. van, Rhemtulla, M., & Borsboom, D. (in press). The Application of a Network Approach to Health-Related Quality of Life: Introducing a New Method for Assessing HRQoL in Healthy Adults and Cancer Patients. Quality of Life Research. DOI: 10.1007/s11136-015-1127-z.

[1] Ware, J. E, Jr, & Sherbourne, C. D. (1992). The MOS 36-item short-form health survey (SF-36): I. Conceptual framework and item selection. Medical Care, 30, 473–483.

# ERC Consolidator grant for the Psychosystems Project

The European Research Council (ERC) has awarded a consolidator grant to Denny Borsboom to support the psychosystems project. The project, which is entitled “Psychosystems: Consolidating Network Approaches to Psychopathology”, is designed to further develop the theory and methodology of networks for mental disorders. The ERC will support the project for five years, allowing us to launch a number of new postdoc and PhD projects.

# Bereavement network paper published

Our new network paper “From Loss to Loneliness: The Relationship Between Bereavement and Depressive Symptoms” was published in the Journal of Abnormal Psychology (PDF).

In the paper we examined 2 competing explanations concerning how spousal bereavement impacts on depression symptoms: a traditional latent variable explanation, in which loss triggers depression which then leads to symptoms; and a network explanation, in which bereavement directly affects particular depression symptoms which then activate other symptoms. We re-analyzed data from the CLOC study, a prospective cohort of 515 individuals, half of which would experienced spousal loss throughout the course of the study (the other half was queried as control group). We modeled the effect of partner loss on depressive symptoms either as an indirect effect through a latent variable, or as a direct effect in a network constructed through a causal search algorithm.

Overall, losing a partner impacted on very specific depression symptoms (e.g., feeling lonely and sad mood), but not on others (e.g., sleep problems). The effect of partner loss on these symptoms was not mediated by a latent variable. The network model indicated that bereavement mainly affected loneliness, which in turn activated other depressive symptoms. The findings support a growing body of literature showing that specific adverse life events differentially affect depressive symptomatology [1-3], and suggest that future studies should examine interventions that directly target such symptoms

[1] Keller, M. C., Neale, M. C., & Kendler, K. S. (2007). Association of different adverse life events with distinct patterns of depressive symptoms. The American Journal of Psychiatry, 164(10), 1521–9. doi:10.1176/appi.ajp.2007.06091564
[2] Cramer, A. O. J., Borsboom, D., Aggen, S. H., & Kendler, K. S. (2013). The pathoplasticity of dysphoric episodes: differential impact of stressful life events on the pattern of depressive symptom inter-correlations. Psychological Medicine, 42(5), 957–65. doi:10.1017/S003329171100211X
[3] Fried, E. I., Nesse, R. M., Guille, C., & Sen, S. (2015). The differential influence of life stress on individual symptoms of depression. Acta Psychiatrica Scandinavica, (6), 1–7. doi:10.1111/acps.12395

# Network Application 0.1

During the last couple of months, I have been working on building a web application (called NetworkApp) that enables users to upload their own data, construct networks and analyze them. Today, version 0.1 of this application has been released.

The NetworkApp has been build with Shiny: a web application framework for R. While R is used to build the web application, the user won’t see this and thus does not need to have any programming skills to use the NetworkApp.

# New paper on depression symptom profiles

Our new study titled “Depression is not a consistent syndrome: An investigation of unique symptom patterns in the STAR*D study” was published in the Journal of Affective Disorders (PDF).

In the paper we examine the degree of heterogeneity of Major Depression (MD). The DSM-5 defines a host of depression symptoms, which are commonly added up to sum-scores that reflect overall depression severity. This implies that depression symptoms are interchangeable indicators of the same underlying condition. It further implies that all patients with MD have the same disorder, justifying the search for things like “depression risk factors” and “depression biomarkers”.

Therefore, we wanted to investigate how much depressed individuals actually differ in their symptoms. Using a conservative strategy to estimate profiles, we identified 1030 unique depression symptom profiles in 3703 depressed patients. 83.9% of these profiles were endorsed by five or fewer subjects, and 48.6% were endorsed by only one single individual.

The results could have shown that most patients fit into a few common patterns, but the most common symptom profile had a frequency of only 1.8%. This substantial symptom variation among individuals with the same diagnosis calls into question the status of MD as a specific consistent syndrome. It stresses the importance of investigating specific symptoms and their dynamic interactions. Sum-scores obfuscate important insights, and the analysis of individual symptoms and their causal associations that is an important part of the ‘Psychosystems Project’ described on this website offers a way forward.

# Network Model Selection Using qgraph 1.3

In this post I will describe some of the new functionality in the 1.3 version of qgraph. The qgraph package is aimed at visualizing correlational structures and, more recently, at visualizing the results of network analysis applied to, in particular but not limited to, psychology. The application of network analysis to psychology has been the core interest of the Psychosystems research group in which the qgraph package has been developed. In version 1.2.4 and 1.2.5 new functions were introduced to compute graph descriptives of weighted graphs and in version 1.3, the visualization techniques are extended with model selection tools for estimating the graph structure. As such, qgraph is no longer just a visualization tool but a full suite of methods for applying network analysis from data to estimating a graph structure and assessing graph descriptives. Version 1.3 is on CRAN now and will be updated on mirrors shortly. To install and check if you have version 1.3 run:

install.packages("qgraph")
packageDescription("qgraph")$Version  Alternatively, you can install the developmental version from GitHub: library("devtools") install_github("sachaepskamp/qgraph")  # Network models In qgraph generally two types of network models can be estimated for multivariate Gaussian data: the correlation network and the partial correlation network. In graph literature a correlation network is typically denoted with bidirectional edges whereas a partial correlation network is typically denoted with undirected edges: In qgraph, bidirectional edges can be plotted but are omitted by default to make the graph clearer. Both the correlation network and the partial correlation network are saturated models if fully connected and degrees of freedom can be obtained by removing edges. Thus, a network model simply means a correlation or partial correlation network in which some edges are set to be equal to zero; model selection means that we attempt to identify which edges should be set to zero. This can be done broadly in three ways: • Thresholding: simply remove all edges that are weaker than some threshold, such as all edges that are not significantly different from zero. • Model search: Continuously estimate models in which some edges are set to zero and stepwise comparisons or an information criterium to decide which model is optimal • LASSO estimation: jointly estimate parameter values and the absence of edges using regularization techniques (more on this below). ## Correlation networks A correlation network is a model for marginal independence relationships; two unconnected nodes imply a marginal independence between two nodes. For instance, the graph above implies the following independence relationship: $A \!\perp\!\!\!\perp C.$ We can use the schur complement to see the relationship between $$A$$ and $$C$$ after conditioning on $$B$$: $\mathrm{Cov}\left( A, C \mid B \right) = \mathrm{Cov}\left( A, C \right) - \mathrm{Cov}\left( A, B \right) \mathrm{Var}\left( B \right)^{-1} \mathrm{Cov}\left(B, C \right) \not= 0,$ Since both covariances with $$B$$ are nonzero and the inverse of a variance is always nonzero for any random variable. Thus, the correlation network above does not only imply a marginal independence, it also implies a conditional dependency relationship: $A \not\!\perp\!\!\!\perp C \mid B.$ Such an induced dependency can only occur in very specific causal structures that might not correspond to our general notion of nodes interacting with each other. In general, we expect that if $$A$$ and $$B$$ are correlated and $$B$$ and $$C$$ are correlated than $$A$$ and $$C$$ are also correlated. In general, we would expect correlation networks to often be saturated, especially when constructing networks based on psychometric tests that are designed to contain correlated items. As such, we generally do not apply model selection to correlation networks. Even though correlation networks are not that interesting from a modeling perspective they are very interesting in the information they portray about the structure of a dataset. Epskamp et al. (2012) described how qgraph and a correlation network of the Big 5 can be used from a psychometric point of view to simply visualize the correlational patterns in the dataset; factors should emerge as clusters of nodes. Cramer et al. (2012) interpreted the same Big 5 network in the context of the network perspective of psychology. Furthermore, correlation networks have also been described and used by Cramer, Borsboom, Aggen and Kendler (2011), Schmittmann et al. (2013) and Ruzzano, Borsboom and Geurts (2014). ## Partial correlation network The partial correlation network is a model for conditional independence relationships. In the above undirected network there is no edge between nodes $$A$$ and $$C$$, which implies that: $A \!\perp\!\!\!\perp C \mid B.$ Thus, the partial covariance between $$A$$ and $$C$$ after conditioning on all other nodes in the network equals zero. Now, by definition, $$\mathrm{Cov}\left( A, C \mid B \right)$$ is equal to zero and thus: $\mathrm{Cov}\left( A, C \right) = \mathrm{Cov}\left( A, B \right) \mathrm{Var}\left( B \right)^{-1} \mathrm{Cov}\left(B, C \right) \not= 0,$ which implies the following marginal relationship: $A \not\!\perp\!\!\!\perp C.$ Therefore, the partial correlation network implies the opposite kind of independence relationships between unconnected nodes; unconnected nodes are conditionally independent but marginally still allowed to correlate. The edges in the network can be understood as pairwise interactions between two nodes This allows us to model interaction effects between pairs of nodes while still allowing all nodes to correlate. Such a network of pairwise interactions is termed a pairwise Markov Random Field (Lauritzen, 1996). If the data is assumed multivariate normally distributed then the model is called a Gaussian Graphical Model, Gaussian Random field, concentration network or partial correlation network; the network structure is then directly related to the inverse of the covariance matrix with zeroes indicating missing edges. We will use the term partial correlation network to describe this class of networks. In a partial correlation network, the strength of edges—the partial correlation between two nodes after conditioning on all other nodes—is directly equivalent to the predictive quality between two nodes that would be obtained in multiple regression. Thus, the strength of an edge can be seen as how well two nodes predict each other; in the above network knowing $$A$$ tells you something about $$B$$ and in turn knowing $$B$$ tells you something about $$C$$. The network can also be seen as large scale mediation analysis, as in the above network the predictive quality of $$A$$ on $$C$$ is mediated by $$B$$. # Network estimation using qgraph We will analyze the BFI dataset from the psych package, of which the correlation network had previously been described on Joel Cadwell’s blog. This dataset contains 25 items on the five central personality traits: openness to Experience, conscientiousness, extroversion, agreeableness and neuroticism. For each trait there are five indicators, such as “make friends easily” for extroversion and “make people feel at ease” for agreeableness. We can load the data into R as follows: library("psych") data(bfi)  We are only interested in the interactions between items of the big five so we only subset the 25 indicators: bfiSub <- bfi[,1:25]  These responses are measured on a five point scale, and thus the assumption of normality is violated by default. As a solution, we compute not the Pearson correlations but the polychoric correlations instead. To do this, we can use the cor_auto() function in qgraph that automatically detects if data looks ordinal and runs the lavCor() function from the lavaan package to compute Pearson, polychoric or polyserial correlations where needed: library("qgraph") bfiCors <- cor_auto(bfiSub)  ## Variables detected as ordinal: A1; A2; A3; A4; A5; C1; C2; C3; C4; C5; E1; E2; E3; E4; E5; N1; N2; N3; N4; N5; O1; O2; O3; O4; O5  To help plot our graph we can also load more information on the meaning of each node: Names <- scan("http://sachaepskamp.com/files/BFIitems.txt",what = "character", sep = "\n") Groups <- rep(c('A','C','E','N','O'),each=5)  Now we can plot the (saturated) correlation network. To do so, we can simply send the correlation matrix to the qgraph() function and use some more arguments to make the plot look good. In addition, we can set graph = "cor" to tell qgraph that the input is, in fact, a correlation matrix (this doesn’t do much other than check if the matrix is positive definite): corGraph <- qgraph(bfiCors, layout = "spring", graph = "cor", nodeNames = Names, groups = Groups, legend.cex = 0.3, cut = 0.3, maximum = 1, minimum = 0, esize = 20, vsize = 5, repulsion = 0.8)  In this network each node represents one of the 25 items in the BFI dataset and edges represent the strength of correlation between them; green edges represent positive correlations, red edges negative correlations and the wider and more saturated an edge the stronger the correlation. The argument layout = "spring" forced qgraph to use a weighted version of the Fruchterman and Reingold (1991) algorithm to place strongly correlated nodes together. The nodeNames, groups and legend.cex arguments controlled the coloring and the legend placed next to the graph, the vsize argument the size of the nodes and the repulsion argument the repulsion ratio used in the Fruchterman-Reingold algorithm. The minimum argument causes all edges with a value below the minimum to not be drawn (these edges are only made invisible but still taken into account when computing graph descriptives), the maximum argument sets an upper bound for the width of edges to scale to and the cut argument splits scaling in saturation and width; edges above the cut value are fully saturated and scale in width whereas edges below the cut value are small and scale in color. By default qgraph will choose these values to optimally plot a graph (see the manual for more details); to know which values qgraph used you could use the argument details = TRUE. The above correlation network overall nicely retrieves the five factor structure; as expected factors emerge as clusters of correlations. To compute the saturated partial correlation network we can set the argument graph = "pcor": pcorGraph <- qgraph(bfiCors, layout = corGraph$layout, graph = "pcor",
nodeNames = Names, groups = Groups, legend.cex = 0.3,
cut = 0.1, maximum = 1, minimum = 0, esize = 20,
vsize = 5)

Now we set the layout argument to be equal to the layout of the correlation network and the cut value to be lower as partial correlations are generally weaker than correlations. We can see that the partial correlation network generally returns the same pattern of interactions but also that some edges—such as between N4 and N1—are much weaker in the partial correlation network than in the correlation network.

## Thresholding

Both the networks shown above are fully saturated; even though some (partial) correlations are so weak they are practically invisible both networks are fully connected. The aim of model selection is to identify which connections are zero, as these values indicate (conditional) independence relationships. A straightforward way of doing this is by thresholding; setting all edges that are not significantly different from zero to be equal to zero.

To use thresholding in qgraph we can use the threshold argument, which works different than minimum in that it removes edges from the network, influencing the network descriptives. The threshold argument can be set to both a value or a string indicating the type of adjustment for multiple tests to be used, which corresponds to the adjust argument of corr.test function in the psych package. In addition to the options psych provides the threshold argument can be set to locfdr to use the local FDR measure provided by the fdrtool package and used in the FDRnetwork function in qgraph. For instance, we can remove all non-significant edges using the Holm correction on the partial correlation network as follows:

holmGraph <- qgraph(bfiCors, layout = corGraph$layout, graph = "pcor", threshold = "holm", sampleSize = nrow(bfi), nodeNames = Names, groups = Groups, legend.cex = 0.3, cut = 0.1, maximum = 1, minimum = 0, esize = 20, vsize = 5)  Which makes the network much cleaner and more interpretable. ## Model search While thresholding can be insightful it is a rather crude way of model selection; we only remove the non-significant edges and do not look at how other edge values change nor at how well the model without certain edges explains the data. To accomplish this we need model selection. We are particularly interested in the question: what model explains the data appropriately while being simple (having few edges). One way to accomplish this is by evaluating all possible models and comparing them on some information criterium—such as the BIC—that weights the likelihood against the sparsity. For a three-node network all possible models are the following: The connections between models indicate nesting relationships; a model with only an edge between $$A$$ and $$B$$ is nested in the model with both edges between $$A$$ and $$B$$ and $$B$$ and $$C$$. The number of possible models is $$2^{p(p-1)/2}$$ with $$p$$ being the amount of nodes in the network. It will be clear that in the case of a three node network it is entirely tractable to estimate $$8$$ models and compare the BIC values but for the case of $$25$$ nodes it becomes much impossible to compare all possible models. Thus, a search is performed to navigate through the model space. We could start at the bottom with the independence model and stepwise move higher to more complicated models by only comparing directly nested models, or start at the top with the saturated model and stepwise move lower to simpler models. The first routine is called step-up estimation and the second routine step-down estimation. The findGraph function in qgraph can be used to search for an optimal (partial) correlation network. This function can be used to do brute search of all models, step-up comparison and step-down comparison. To compare models the Extended Bayesian Information Criterium (EBIC; Foygel & Drton, 2010) is used. By default, the findGraph function will start at the thresholded graph using Holm correction and iterate between step-up and step-down search until an optimal model is found: optGraph <- findGraph(bfiCors, nrow(bfi), type = "pcor") optimalGraph <- qgraph(optGraph, layout = corGraph$layout,
nodeNames = Names, groups = Groups, legend.cex = 0.3,
cut = 0.1, maximum = 1, minimum = 0, esize = 20,
vsize = 5)

## LASSO estimation

Model selection can be a slow process as the amount of variables increases, and the stepwise process might get lost in the model space and not converge to the best model. For example, stepwise up and stepwise down methods often obtain a different model. A well established method for simultaneously estimating parameters and performing model selection on a partial correlation network is to employ the least absolute shrinkage and selection operator (LASSO; Tibshirani, 1996) regularization technique. A particularly fast variant of the LASSO for these kinds of networks is the graphical LASSO which directly estimates the inverse of the covariance matrix (Friedman, Hastie and Tibshirani, 2008) and has been implemented in the R package glasso.

In short, the graphical LASSO estimates not the maximum likelihood solution but a penalized maximum likelihood solution in which the likelihood is penalized for the sum of absolute parameter estimates. Because of this, the graphical LASSO estimates a model that still explains the data well with generally weaker parameter estimates and many parameter estimates of exactly zero. The amount of penalization is specified by a tuning parameter $$\lambda$$. In qgraph, the EBICglasso function can be used to estimate a network using 100 different $$\lambda$$ values and return of these the network that minimizes the extended Bayesian Information Criterium (EBIC; Chen, and Chen, 2008). Such a procedure has been established to accurately recover the network structure (Foygel & Drton, 2010; van Borkulo et al., 2014).

To automatically have qgraph run EBICglasso and estimate the model we need only set graph = "glasso":

glassoGraph <- qgraph(bfiCors, layout = corGraph\$layout,
graph = "glasso", sampleSize = nrow(bfi),
nodeNames = Names, groups = Groups, legend.cex = 0.3,
cut = 0.1, maximum = 1, minimum = 0, esize = 20,
vsize = 5)

This method runs extremely fast and returns a sparse and interpretable network structure. This network shows some interesting properties. For example, neurotocism consists of two distinct clusters, an anxiety and a depression cluster, connected by the item “N3: Have frequent mood swings”. The Conscientiousness item “C5: Waste my time” and the extroversion item “E3: Know how to captivate people” act as a bridging nodes between the different personality trait clusters. Finally, most strong connections make perfectly sense when interpreted as a pairwise interaction.

# Graph descriptives using qgraph

Now that we have estimated the partial correlation network in different ways we can look at how these networks compare in terms of graph descriptives. We are particularly interested in node centrality and clustering. To compare the estimated networks, we can use the centralityPlot and clusteringPlot functions which use ggplot2 to visualize the estimates:

centralityPlot(
list(
saturated = pcorGraph,
threshold = holmGraph,
modelSearch = optimalGraph,
glasso = glassoGraph)
)

We can similarly compare the clustering coefficients:

clusteringPlot(
list(
saturated = pcorGraph,
threshold = holmGraph,
modelSearch = optimalGraph,
glasso = glassoGraph)
)

## Warning: Removed 25 rows containing missing values (geom_point).

We can see that even though the graphs all are highly similar they can differ on centrality and clustering coefficients. However, generally all graphs are somewhat aligned; nodes that are highly central are so across all graphs.

# Four new Ph. D. projects on networks

We are happy to welcome four new Ph.D. researchers into the network community:

• Marie Deserno will investigate determinants of success and problems in Autism, in the context of a project organized by the Academische Werkplaats Autisme. The project is supervised by Hilde Geurts, Sander Begeer, and Denny Borsboom.
• Riet van Bork will investigate methodologies suited to distinguish between network and latent variable explanations of symptom covariation. The project is funded partly by a European Commission Career Integration Grant awarded to Mijke Rhemtulla, who will supervise the project together with Denny Borsboom.
• Jonas Dalege will develop network models for the structure and dynamics of attitudes in a project that involves a collaboration between the Psychological Methods and Social Psychology groups at the University of Amsterdam. The project is supervised by Frenk van Harreveld, Han van der Maas, and Denny Borsboom.
• Merijn Mestdagh will develop time series models for nonlinear networks that involve large number of variables at the K.U. Leuven in a Ph. D. project awarded by the Flemish Organization for Scientific Research (FWO). The project is supervised by Francis Tuerlinckx and Denny Borsboom.

# Three new NWO-Veni projects on networks

A very successful round of 2014 NWO grant applications for network researchers!

Our own Angélique Cramer received a Veni grant to further develop network methodology and apply that to mood disorders:

• Network psychometrics: methods for exposing the architecture and dynamics of mood disorders
Dr A.O.J. (Angélique) Cramer (f), University of Amsterdam – Psychometrics
In the network approach a psychological disorder is a consequence of interactions between symptoms (gloomy and fretting). In this proposal methods to construct and analyse these networks will be further developed. Subsequently the networks of patients with mood disorders will be investigated: for example, can we predict when the patient will experience a relapse?

Hanneke Wigman of Groningen University received a Veni grant to investigate symptom networks in the etiology of psychosis:

• Networks of symptoms in psychosis
Dr J.T.W. (Hanneke) Wigman (f), University Medical Centre Groningen – Psychiatry
The researcher will study the development of psychoses (a lost sense of reality) by describing networks of early symptoms and by examining per person how these symptoms influence each other. This will help to develop personalised treatment recommendations.

Annemarie Kalis of Utrecht University received a Veni grant to investigate the role of mental content in empirical psychological research, one subproject of which is devoted to network models:

• A role for content and mental causation in empirical psychology
Dr A. Kalis (f), Utrecht University – Philosophy
Many mental states have content: our convictions, desires, intentions ‘are all about something’. Empirical psychology, however, scarcely offers space for the notion of content. This project will develop a philosophical analysis that shows how mental content can and should play a role in in empirical psychological research.


text:
# '2-3' or 'two to three' proper use

In the following sentence is the use of '2-3' appropriate for a PowerPoint presentation or should it be 'two to three'?

Research shows that a deaf child tends to produce signs 2-3 months earlier than hearing children’s first spoken words.

Is there a difference in the meanings between these two methods of statement?
Why is one preferred over the other, if it is?

-

## 4 Answers

The en-dash is used for ranges of values, such as "1994–2010," "pp. 183–652."
I find it fine to use the en-dash in such cases in a presentation.

In some cases, it could be convenient not to express a range of values using the en-dash; for example, the Guide for the Use of the International System of Units suggest not to use the en-dash if it could be confused with a subtraction, such as in "an amperage of 2–5 A."

The value of a quantity is expressed as the product of a number and a unit (see Sec. 7.1). Thus, to avoid possible confusion, this Guide takes the position that values of quantities must be written so that it is completely clear to which unit symbols the numerical values of the quantities belong. Also to avoid possible confusion, this Guide strongly recommends that the word “to” be used to indicate a range of values for a quantity instead of a range dash (that is, a long hyphen) because the dash could be misinterpreted as a minus sign. (The first of these recommendations once again recognizes that unit symbols are not like ordinary words or abbreviations but are mathematical entities—see Sec. 7.2.)—The Guide for the use of the International System of Units, page 18.

-
It's hard to see how anyone could interpret "2–5 A" as "2 minus 5 amperes", because (a) although currents can flow either way, amperage is always a measure of their magnitude, not their direction, and (b) even if negative amperages were accepted, they would never be stated in this uncalculated way: it would have to be "an amperage of -3 A". – John Bentin Jun 27 '11 at 6:42
@John Bentin That is what the guide reports. – kiamlaluno Jun 27 '11 at 6:56
@JohnBentin The wall supply voltage, $v$, to a circut is guaranteed to be within 110–120 VAC. The supply is fed through the a transformer with 500 primary windings and two secondary coils of 200 and 300 windings each, giving an output of (*note, a real book would have LaTeX here - the stuf between the '$'s denotes LaTeX)$v_1 = \frac{200}{500} * v = 44–48 VAC$and$v_2 = \frac{300}{500} v = 66–72 VAC$. The resulting voltages are fed into an ideal op-amp subtraction circut, with$v_1$as the negative value. The resulting voltage is then$v_r$=$v_2 - v_1$= 66–72 - 44–48 VAC = 22–24 VAC$. – AJMansfield Apr 20 '13 at 23:14
@JohnBentin Not that any actual professional would do that (the circuit or the notation mistake), but this could easily happen in a low-quality textbook. – AJMansfield Apr 20 '13 at 23:17

The two statements are equivalent. If word count or space is a consideration, use "2–3", preferably with an en dash and not a hyphen. (See this question for more info on dashes and hyphens.) If you were writing something longer, I would suggest using "two to three" or a similar phrase instead; almost all style guides suggest spelling out small numbers, although they differ on the cutoff point.

-

No difference in meaning, it's just that 2-3 is slightly more 'informal'.

If you were reading out the displayed text of the presentation, no-one would think it odd if you said "two or three" rather than "two to three" (I would even prefer that, since I don't like the ungainly homophonic usage).

-

There's nothing wrong with either "two to three" or "2-3" in this case. Either are not preferred above the other. I reckon it's just that "two to three" is more formal only. Nothing else.

-


text:
## Abstract

Understanding the preferences of patients and health professionals is useful for health policy and planning. Discrete choice experiments (DCEs) are a quantitative technique for eliciting preferences that can be used in the absence of revealed preference data. The method involves asking individuals to state their preference over hypothetical alternative scenarios, goods or services. Each alternative is described by several attributes and the responses are used to determine whether preferences are significantly influenced by the attributes and also their relative importance. DCEs are widely used in high-income contexts and are increasingly being applied in low- and middle-income countries to consider a range of policy concerns. This paper aims to provide an introduction to DCEs for policy-makers and researchers with little knowledge of the technique. We outline the stages involved in undertaking a DCE, with an emphasis on the design considerations applicable in a low-income setting.

KEY MESSAGES
• Conducting a discrete choice experiment in a developing country context can involve issues not encountered in developed countries.

• Selection of attributes in key. Although secondary literature can be used to identify an initial set of attributes, in low-income settings additional primary research is almost always necessary to ensure that the final set of attributes is appropriate and valid.

• Pre-testing the questionnaire is likely to be particularly important where there are cultural and language differences between the researchers and study participants, or where the population surveyed has a low level of literacy.

## Introduction

A discrete choice experiment (DCE) is a quantitative technique for eliciting individual preferences. It allows researchers to uncover how individuals value selected attributes of a programme, product or service by asking them to state their choice over different hypothetical alternatives. DCEs have been applied to a range of health policy, planning and resource allocation decisions in high-income settings. These include the elicitation of views on diagnosis, treatment and care (Coast et al.2006; King et al.2007; Lancsar et al.2007; Kjaer and Gyrd-Hansen 2008), access to services (Gerard and Lattimer 2005; Gerard et al.2006; Longo et al.2006) and the employment preferences of health personnel (Scott 2001; Ubach et al.2003; Wordsworth et al.2004).

Although DCEs have been frequently applied in health economic research in high-income countries, there are comparatively few examples of DCEs being used elsewhere. Searches of the published literature identified only four papers that had employed a DCE to consider a health issue in a low- and middle-income country (LMICs) (Hanson et al.2005; Baltussen et al.2006; Christofides et al.2006; Baltussen et al.2007) and a further three papers were identified by undertaking selective searches of the internet (Chomitz et al. 1997; Penn-Kekana et al.2005; Baltussen and Niessen 2006). Moreover, we are aware of several DCEs currently underway in LMICs. These include: an examination of public preferences for maternity services in Ghana (Ternent et al.2006) and an estimation of women's demand for barrier methods for HIV prevention in South Africa (Terris-Prestholt et al.2008a, b). In addition, there are ongoing DCEs to elicit the employment preferences of health workers, including of doctors and nurses in Ethiopia (Hanson and Jack 2007), clinical officers in Tanzania (O Maestad and J Riise Kolstad, personal communication) and several cadres in Malawi, South Africa and Tanzania (C Normand, personal communication). In LMICs, DCEs have been more frequently used outside of the health sector, with academic articles reporting preferences in the agriculture, water, transport and tourism sectors (Baidu-Forson et al.1997; Tiwari and Kawakami 2001; Tano et al.2003; Hope and Garrod 2004). Internet searches also returned several discussion papers, reports and other sources of grey literature that had applied the technique in these settings (Carlsson et al.2005; Porras and Hope 2005). Nonetheless, the use of DCEs in LMICs remains relatively recent.

This paper aims to provide an introduction to the DCE methodology for those working on health issues in low-income countries. We describe the technique, outline the stages involved in its application and emphasize the design considerations pertinent to conducting a DCE in a low-income setting. In discussing the design process, we draw on our experiences of conducting DCEs to elicit patient preferences of hospital services in Zambia (Hanson et al.2005) and employment preferences of health workers in Malawi (Mangham and Hanson, 2008).

## What is a Discrete Choice Experiment?

Techniques for eliciting preferences have primarily emerged from a desire to understand consumer demand for goods and services where it was not possible to use revealed preference data on the actual choices made by individuals. This would arise for products and services not traded on a market, such as for a new product under development and not yet commercially available. Similarly, where there is no variation in the products available (or services provided), it is not possible to isolate the contribution of each product attribute to the overall utility derived from the product.

DCEs require respondents to state their choice over sets of hypothetical alternatives. Each alternative is described by several characteristics, known as attributes, and responses are used to infer the value placed on each attribute. In comparison to other stated preference techniques that require the individual to rank or rate alternatives, a DCE presents a reasonably straightforward task and one which more closely resembles a real-world decision.

The method has its theoretical foundation in random utility theory and relies on the assumptions of economic rationality and utility maximization (Hall et al.2004). In stating a preference the individual is assumed to choose the alternative that yields his/her highest individual benefit, known as utility. Moreover, the utility yielded by an alternative is assumed to depend on the utilities associated with its composing attributes and attribute levels (Lancaster 1966). In other words, Yiq is the utility of individual q for the ith alternative and is assumed to be a function of its attributes:

where Xi is a vector of attributes for the ith alternative accompanied by a set of weights, βi, that establish the relative contribution of each attribute to the utility associated with the ith alternative, and ɛiq is the residual capturing the unobserved variation in the characteristics of different options and any measurement errors.

DCEs are used to determine the significance of the attributes that describe the good or service and the extent to which individuals are willing to trade one attribute for another (Drummond et al.2005). Information on the relative importance of the selected attributes can be useful for those involved in policy decisions and setting resource allocation priorities, and may be designed with that in mind (Baltussen and Niessen 2006; Baltussen et al.2007). For example, a DCE on the employment preferences of registered nurses in Malawi was designed in light of the Malawi government's programme to recruit and retain health personnel, which included salary increases to improve motivation and discourage attrition (Palmer 2006). The results of the DCE showed that remuneration had a significant impact on how nurses viewed their employment, and that they were willing to trade-off pay increases to obtain improvements in non-monetary benefits or working conditions (Mangham and Hanson, 2008).

The method can be used to estimate the marginal valuations of attributes or the willingness to pay (WTP) for a unit change in each attribute estimated (Drummond et al.2005). In comparison with standard techniques, which estimate WTP for the good or service as a whole, this more detailed information on WTP by attribute may be useful, though some evidence suggests that the levels of the cost attribute can affect the estimates (Radcliffe 2000; Drummond et al.2005). DCE results can also be analysed by subgroup and it is possible to consider the extent to which individuals’ characteristics impact on the marginal valuations. For instance, a DCE applied to elicit the patient preferences for hospital quality in Zambia estimated WTP for the different attributes for the whole sample and by socio-economic group. They found the highest willingness to pay was for a thorough, rather than superficial, examination and that the WTP for this attribute in the lowest socio-economic group was only about half that in the highest group.

## How to design a DCE

Discrete choice analysis involves the construction of an experimental design to study the effects of the attribute levels on the stated preference (or dependent variable). The attributes of an experimental design are variables that have two or more fixed levels.

There are several stages to the design of a DCE, which we outline below. In our discussion the design considerations pertinent to conducting a DCE on a health-related issue in a low-income setting are highlighted. We also use examples from our own experience of undertaking DCEs in sub-Saharan Africa, to elicit patient preferences on the quality of hospital services in Zambia (Hanson et al.2005), and the employment preferences of registered nurses in Malawi (Mangham and Hanson, 2008).

### Establishing attributes

The first stage of a DCE involves identifying the attributes relevant to the stated research question and then assigning levels for each of these attributes (Ryan 2001; Hensher et al.2005). Since these attributes and attribute levels describe the hypothetical scenarios under consideration in the DCE, this is a critical aspect of the design. The underlying validity of the study depends, therefore, on the researcher's ability to correctly specify the relevant attributes. Despite the importance of this stage in the design, there is often sparse explanation in the DCE literature of how attributes and levels are established (Coast and Horrocks 2007).

Selecting and defining the attributes requires a good understanding of the target population's perspective and experience (Hall et al.2004; Coast and Horrocks 2007). Researchers working in a different cultural or language setting may find obtaining the necessary depth of understanding a challenge and may want to involve local experts. Policy concerns may also shape the choice of attributes, and it is often advisable to engage local institutions and policy-makers during this preparatory stage (Baltussen and Niessen 2006). For example, in the Malawi study on nurses’ employment preferences, the decision to include an attribute on the provision of government housing was influenced by the Ministry of Health's interest in how the availability and quality of government housing affects the retention of health personnel.

Published and grey literature, such as policy documents and government reports, are a useful starting point for identifying attributes. For example, the literature on the global shortage of health workers (Buchan and Sochalski 2004; Joint Learning Initiative 2004; World Health Organization 2006) provided a background to the Malawi study, while Malawi government policy and programme documents provided detail on the country-specific situation (Buchan and Sochalski 2004; Joint Learning Initiative 2004; World Health Organization 2006; Coast and Horrocks 2007).

It is often necessary, however, to augment secondary sources with primary data to ensure that the DCE is tailored to the study setting. Primary qualitative data were essential for selecting and defining the attributes that registered nurses considered important. Semi-structured interviews were conducted with public sector nurses to obtain information on their current working conditions, preferences, reasons for the shortage of nurses and priorities for reform. The sample included views of nurses based in urban and in rural settings in three geographically distinct districts, working in primary, secondary and tertiary health facilities, and with differing degrees of seniority and experience. Additional interviews were also held with senior officials in the Ministry of Health to obtain their perceptions, policy concerns and remuneration data. In Zambia, qualitative data were collected using focus group discussions on what dimensions of the quality of hospital services were important to individuals when choosing a hospital. In total, 16 separate discussions were held with men and women from two districts, and from different socio-demographic groups: university students, market sellers, residents from high and low density areas (Hanson et al.2005).

In both settings, the discussions were facilitated by a sociologist from a local research institute and were tape recorded, transcribed, translated and supplemented by detailed written notes. Local researchers brought a valuable perspective, knowledge and experience to the design of the DCE. They led the collection of qualitative data, which not only encouraged respondents to be more open, but also allowed them to express themselves in their local languages.

In both studies content analysis was used to obtain possible attributes for the DCE. This involved reading all transcripts and written notes to identify major themes, followed by a more detailed review, during which additional themes and sub-themes emerged. The transcripts were coded manually and relevant extracts recorded in a summary table. Software packages can also assist the coding and retrieval of data, and are particularly useful where the number of interviews is large or for more complex qualitative analysis (Lewando-Hundt et al.1997).

There are no design restrictions on the number of attributes that could be included in a DCE, though in practice most DCEs have contained fewer than 10 to ensure that respondents are able to consider all attributes listed when making their choice (DeShazo and Fermo 2002). The greater the number of attributes, the greater the cognitive difficulty of completing a DCE. With too many attributes, the participants may be encouraged to apply a simple decision rule in which they base their response on a single or subset of attributes. In establishing attributes it is also important to avoid conceptual overlap between two or more of the attributes, known as inter-attribute correlation, since it would prevent the accurate estimation of the main effect of a single attribute on the dependent variable.

In both the Malawi and Zambia studies, six attributes were established that were important to the respondents and were policy relevant. For example, the attributes relating to the quality of hospital services identified in the Zambia study were: (1) the likelihood that the child will receive all the drugs s/he needs at the hospital, (2) the likelihood that the hospital staff will examine the child properly, (3) staff attitudes, (4) cleanliness of the wards and toilets, and (5) the waiting time between arrival at the outpatients department and admission to the ward. In addition a sixth cost attribute was included that covered the costs of the child's examination and treatment. Other issues frequently mentioned by discussants were not included in the DCE because of inter-attribute correlation with the established attributes. They were: the availability of diagnostic services, quality of nursing care, staff dedication and availability of staff (Hanson et al.2005).

In specifying attributes, care should be taken to ensure that definitions are appropriate for the setting and are not ambiguous. For example, the Malawian nurses frequently used the term ‘upgrading’ when referring to obtaining additional professional qualifications. These long-term educational opportunities are distinct from in-service training courses, and in defining the attribute on access to training it was therefore important to use the ‘upgrading’ expression to avoid attribute ambiguity.

### Assigning attribute levels

Once the attributes are established, attribute levels need to be assigned. Typically the levels chosen should reflect the range of situations that respondents might expect to experience, and again qualitative data are valuable. Ensuring the levels are realistic and meaningful will increase the precision of parameter estimates (Hall et al.2004).

In the Malawi study, qualitative data were used to determine base levels that reflected the prevailing working conditions for the public sector registered nurses. Additional levels were then established that represented a reasonable improvement from the base. For ease of cognition we sought to establish no more than three levels for each attribute, initially opting for two levels and then adding a third where there was no single base level. For example, variation in the actual provision of government housing meant both ‘no government housing’ and ‘basic government housing’ were possible base levels. Three levels were also used for the pay attribute as we were interested in the preferences over the magnitude of the pay increase. A net monthly pay of K30,000 Malawi kwacha (approximately US$240) was an average prevailing salary for public sector registered nurses, and two higher levels were included, K40,000 ($320) and K50,000 (\$400). These higher pay levels were similar to those in the private sector and in line with what the interviewed nurses had indicated they would consider a reasonable salary.

### Designing the choice sets

The next stage in the design of a DCE is to generate the hypothetical alternatives and to combine them to create choice sets. A full factorial design can be generated which consists of all possible combinations of the levels of the attributes, and permits estimation of main effects and interactions. A main effect refers to the direct independent effect on the choice variable of the difference in attribute levels (e.g. difference in price). An interaction effect is the effect on the choice variable obtained by varying two or more attribute levels together (e.g. difference in price combined with difference in colour).

In most practical situations it is considered too cost-prohibitive and tedious to have subjects rate all possible combinations in a full factorial design (Kuhfeld 2005). A design with five attributes, each with three levels would, for example, generate 243 possible alternatives (35). Thus, fractional factorial designs are often used to consider a selection of possible alternatives.

In selecting a fractional factorial design, researchers should seek to obtain a design that is both orthogonal and balanced (Huber and Zwerina 1996; Kuhfeld 2005). In orthogonal fractional factorial designs, the parameter estimates in the linear model are uncorrelated, which means that the attributes of the design are statistically independent of each other (Hensher et al.2005; Kuhfeld 2005). A balanced design has each attribute level occurring equally often, and this minimizes the variance in the parameter estimates (Kuhfeld 2005). Fractional factorial designs that are both orthogonal and balanced are known as orthogonal arrays and these can be obtained from design websites such as http://www.research.att.com/~njas/oadir (Burgess and Street 2005). However, orthogonal arrays only exist for certain combinations of attributes and attribute levels (Kuhfeld 2005). For other combinations there will be a trade-off between the degrees of orthogonality and balance. Researchers should select the most efficient design, using a measure known as D-efficiency (Carlsson and Martinsson 2003; Burgess and Street 2005; Kuhfeld 2005; Street et al.2005).

A third property that characterizes efficient choice designs is minimal overlap (Huber and Zwerina 1996; Maddala et al.2003). Each attribute level is only meaningful in comparison to others within the choice set, or in other words no information is obtained on an attribute's value when its levels are the same across all alternatives within a choice set. Researchers should, therefore, seek to minimize the probability that an attribute level repeats itself in each choice set. Finally, Huber and Zwerina (1996) have argued for the importance of utility balance, which refers to balancing the utilities of the alternatives offered in the choice set, though in practice the lack of prior information on the utility of attributes limits the applicability of this criterion (Huber and Zwerina 1996).

The recommended approach to constructing an experimental design continues to evolve (DeShazo and Fermo 2002; Street et al.2005; Adamowicz 2006; Louviere 2006) and ensuring that the generated DCE meets best practice can be a challenge. Consequently, we encourage researchers planning to undertake a DCE to review the latest publications, within and beyond the discipline of health economics. We are also aware that access to the latest information may be an obstacle for those undertaking research in LMICs.

### Generating and pre-testing the questionnaire

The created choice sets form the basis for the DCE questionnaire. The number of choice sets presented to each individual will depend on the size of the fractional factorial design and the strategy employed in designing the choice sets (Street et al.2005). Typically DCEs ask respondents to consider up to 18 choice sets, with 18 representing a practical limit of how many comparisons can be completed before boredom sets in (Hanson et al.2005; Christofides et al.2006). This boredom threshold level is likely to vary, and will depend on the number of choice sets, their complexity and the characteristics of the target population.

In both the Zambia and the Malawi studies we applied a pairwise design, such that respondents were asked to consider a choice set with two alternatives and state their preference for each pair. For illustration, an example of a choice set from the Malawi study is shown in Figure 1. A dichotomous choice has frequently been applied in health services research and the statistical information obtained represents the demand conditional on accepting one of the two scenarios.

Figure 1

Example of a choice set from the study of employment preferences of Malawian registered nurses

Figure 1

Example of a choice set from the study of employment preferences of Malawian registered nurses

In the Malawi study we also asked a second question that introduced a ‘choose neither’ option. This allowed respondents to reject both alternatives and provided data to estimate unconditional demand. In many situations the inclusion of a non-choice option will more closely resemble a real world context, since individuals are not required to make a choice, though these non-choice responses do not provide any information on how individuals trade-off the attribute levels of the available alternatives. In our design, the motivation behind asking both which job they considered superior and which one they would choose was to ascertain the extent to which the personal circumstances of respondents were an explicit constraint in their decision-making. For example, we hypothesized that married women would be more constrained in making their choice over place of work.

The internal consistency of responses can be considered by including one or two choice pairs in which one option is superior to the other on all characteristics. In the Zambia study this assumed that people prefer a lower cost, more thorough examination, a shorter waiting time, and better drug availability, cleanliness and staff attitudes. Individuals that fail to choose the superior hospital job may have misunderstood the task or were unable to provide consistent answers because of problems of communication or translation. While it is useful to know the extent to which individuals respond rationally, Lancsar and Louviere (2006) advise against excluding apparently ‘irrational’ choices from the analysis of DCEs as that may cause statistical bias and/or affect statistical efficiency.

The questionnaire should be clearly presented and contain a standard introduction to the DCE with choice set examples. To minimize any bias caused by the order in which the choice sets occur or the attributes are described, it is good practice to produce several versions of the questionnaire in which choice sets and attributes are presented in different orders (Kjaer et al.2006). Pictures, diagrams and symbols may aid comprehension, and are particularly relevant for conducting a DCE in low-income countries where literacy cannot be assumed. Similarly, in some settings the questionnaire will need to be translated into one or more local languages. For example, picture boards and verbal descriptions were used when eliciting preferences on hospital quality in Zambia and interviews were administered in both Bemba and English (Hanson et al.2005). Finally, it is usual to collect data on socio-economic indicators to allow analysis of the impact of individual characteristics on the choices made.

In preparing the questionnaire it is also important to consider how the DCE will be administered. It is possible for the questionnaire to be self-administered, undertaken in examination conditions (Chomitz et al. 1997) or, as we opted, to have trained fieldworkers administer the questionnaire to respondents individually. In many low-income countries, postal or online surveys will not be feasible because of the infrastructure, and given the lower levels of literacy, there are also likely to be practical advantages to having fieldworkers explain what is asked of consenting respondents and work through examples.

Piloting the questionnaire is a key stage in most survey designs and is particularly relevant when working across cultures and several languages. Moreover, pre-testing provides an opportunity to review several elements of the design process, including the selection and definition of attributes and their levels (Hall et al.2004). This is important given the extensive role of the researcher in the design of the DCE. For example, pre-testing in the Malawi study identified the conceptual overlap between the type of hospital and the typical workload, which led to the rewording of the levels relating to place of work (Mangham and Hanson, 2008). Minor modifications were also made to the definition of the attribute levels for typical workload. Other aspects of the design which should be reviewed during pre-testing include the respondent's understanding of the task, their ease of comprehension and whether the number of choice sets can be managed by the target population (Hall et al.2004).

### Analysing of DCE data

Once the choice sets and questionnaire design are finalized, the DCE questionnaire can be administered to collect data for subsequent analysis. Our discussion on data analysis is restricted to a few key aspects, since the focus of this paper is on how to design a DCE. Furthermore, the same methods for analysing DCE data apply irrespective of the study context and are well documented elsewhere (Louviere et al.2000; Hensher et al.2005).

The analysis of DCE data typically involves regression models that have a dichotomous or polychotomous categorical dependent variable, such as a probit, logit, or multinominal logit specification. In its simplest form, the observed sources of utility can be defined as a linear expression in which each attribute is weighted by a unique parameter to account for that attribute's marginal utility. It is usual to specify the regression model in terms of differences in attribute levels between the choices being analysed:

Moreover, as respondents are asked to consider multiple choice pairs, it cannot be assumed that the error terms are independent and panel data estimation techniques are required. The estimated parameters represent the marginal utility associated with a change in the attribute level in moving from one alternative to the other.

## Discussion

In developing countries the application of DCEs to consider questions of health policy and planning is relatively recent, but appears to be of growing interest (Chomitz et al. 1997; Hanson et al.2005; Penn-Kekana et al.2005; Baltussen et al.2006; Christofides et al.2006; Ternent et al.2006; Mangham and Hanson 2008). Moreover, Baltussen and Niessen (2006) argue that a multi-criteria approach to health priority setting is essential and DCEs, as a technique for undertaking multi-attribute analysis, should be used more routinely to guide resource allocation decisions.

The stages involved in the design of a DCE are the same regardless of study setting: establishing attributes and attribute levels, designing choice sets, and generating and pre-testing the DCE questionnaire. There are, however, some particular challenges in conducting a DCE in a developing country context, and in describing each element of the design we have sought to highlight the additional design considerations. These challenges may relate to working in different cultural or language settings, or surveying populations that have a lower level of literacy or are less accustomed to market research techniques. Many of these challenges will be common across a range of research methodologies and will be familiar to those experienced in undertaking research in LMICs. Nevertheless, we believe that there is merit in considering aspects of the DCE design that may require more attention when the method is to be applied in a low-income setting.

For example, the use of primary data when establishing attributes and attribute levels may be more critical in a low-income setting. The validity of the research findings depends on the analyst's ability to correctly specify the relevant programme, product or service attributes and levels, and this requires a detailed understanding of the target populations’ experience and point of view (Hall et al.2004). Access to relevant information on the policy context or specific health programmes can be a challenge, particularly in developing countries, and the perspectives and concerns of individuals are often poorly articulated. Thus, although secondary literature can be used to identify an initial set of attributes, in low-income settings additional primary research is almost always necessary to ensure that the final set of attributes is appropriate and valid.

Similarly, pre-testing the questionnaire is likely to be even more important in a context where there are cultural and language differences between the researchers and study participants, or where the population surveyed has a lower level of literacy. Pre-testing provides an opportunity to ensure that the information is presented in a comprehensible way, and that the choices are realistic and meaningful. It also provides an opportunity to observe how cognitively demanding the questionnaire is for respondents to complete. Researchers may, for example, need to reduce the number of choice sets reviewed, adjust the number of attributes in each alternative or include pictorial information and verbal descriptions. Such amendments should help to ensure that responses are a better reflection of individual preferences and improve the precision in the parameter estimates.

Given some of these additional challenges of designing a DCE for a low-income country, it is reasonable to ask whether a research methodology that was originally developed to understand demand for consumer products in high-income countries readily translates to questions of public policy and health resource allocation in low-income countries. Our experience, and that from the literature, suggests that participants are able to state their preferences over health service provision and areas for policy reform (Chomitz et al. 1997; Hanson et al.2005; Penn-Kekana et al.2005; Baltussen et al.2006; Christofides et al.2006; Ternent et al.2006; Mangham and Hanson, 2008). The results also suggest that the preferences are reasoned and deliberate. For instance, the internal consistency of responses was high in both the Zambia and Malawi studies, from which we inferred that the vast majority of individuals were making rational choices. Similarly, the theoretical validity of the valuations, which is assessed by determining whether the estimated coefficients are of the anticipated sign, found that the results were consistent with prior expectations.

DCEs that elicit preferences on the provision of health services or strategies for policy reform should be useful for health policy-makers and planners involved in identifying priorities for resource allocation. Although the task of choosing between alternative scenarios is reasonably straightforward to comprehend, some elements of the design are complex. It will be important, therefore, that researchers are able to communicate the research findings and policy implications in a way that can be easily understood.

DCEs, and other stated preference techniques, also have the advantage that they are a means of obtaining preferences on situations that are not traded explicitly in markets, as is often the case with health care, or have public good characteristics, such as a vaccination programme (Pokhrel 2006). Similarly, their ability to be used in situations that are purely hypothetical means that it is possible to elicit preferences over potential policy reform or health system changes prior to their implementation. Moreover, as the design of DCEs is controlled and the attributes are varied systematically, it is straightforward to identify the effect of an attribute on the choice variable (Baltussen and Niessen 2006; Pokhrel 2006).

As the benefits of the DCEs become more widely understood we expect the technique to be increasingly applied to health policy and planning questions in developing countries. We hope this paper provides a useful introduction for those wanting to gain a better understanding of the methodology and the process of designing a DCE.

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text:
시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 0 0 0 0.000%

## 문제

Curiosity is equipped with quite a lot of high-tech hardware in order to perform analysis of Mars surface in location. (It’s kind of hard to imagine sending rocks back from Mars.) One of the ways in which scientists try to infer which chemical elements are contained in a particular sample is to heat or burn them, and observe which frequencies of light are emitted. Different elements have characteristic spectra, and one can then see which combinations of elements would produce the observed spectrum.

We model this as follows: there are n possible frequencies, 1 ≤ n ≤ 100, and m elements that we suspect may occur on Mars (1 ≤ m ≤ 12). For each of the m elements that could possibly be in the sample, we are told at which frequencies they emit light: this is a bit vector of n zeros or ones. Similarly, the sample is described by such an n-bit vector. We assume that if element i occurs in the sample in any quantity, then all of its frequencies will be observed. If multiple elements produce the same frequency, we of course still observe that frequency — there is no cancellation. For each sample, you are to determine what is the smallest number of elements that would explain the observed spectrum, if any.

## 입력

The first line contains the number K of data sets. This is followed by K data sets, each of the following form:

The first line contains two integers n,m, the number of frequencies and the number of elements.

This is followed by m + 1 lines. Line i for 1 ≤ i ≤ m describes the ith element, and is a string of n ones and zeros. Line m + 1 is a string of n ones and zeros describing the sample.

## 출력

For each data set, output “Data Set x:” on a line by itself, where x is its number. Then output the minimum number of elements which together would produce the observed spectrum. If there is no such combination of elements, then output “Impossible” instead.

## 예제 입력

2
12 5
000111000000
001100000001
101000000010
111111111111
000000011000
101100000011
4 3
1111
0101
1000
1001

## 예제 출력

Data Set 1:
2

Data Set 2:
Impossible


text:
# Derivative notation

1. Sep 22, 2011

### intervoxel

What is the meaning of

$\frac{\partial F(x)}{\partial(\partial f(x)/\partial x)}$

in which a derivative appears in place of the variable x in the denominator?

2. Sep 23, 2011

### mathman

Let u = ∂f(x)/∂x. Then the expression is ∂F(x)/∂u. In order to make sense out of it you need to know F(x) and f(x).

3. Sep 24, 2011

Thank you.


text:
# Fixing the potential for a quantum particle

I have started studying quantum mechanics and have realised that we can solve the Schrodinger equation for a particle's wave function if we know it's potential energy function. But the potential field in which a particle is, is determined by the presence of other particles, but their positions themselves are not definite (they have probability to be here as well as there). Then how can we fix the potential in which the particle under study is present?

## 1 Answer

A fixed potential is often just an approximation to make things simple and solvable.

In hydrogen, the proton is so much more massive than the electron (1936 times!) that to a first approximation you can consider it stationary and thus consider its electrostatic potential to be fixed in space.

If you don’t like that approximation, then you formulate the Schrodinger equation in a way that takes the motion of the proton into account. In this analysis, the potential then depends only on the separation distance between the proton and the electron, so the Schrodinger equation simplifies again.

In multi-electron atoms, people sometimes make approximations where they consider the inner orbitals to provide an averaged potential that affects the outer electrons. But for more accuracy, you would have to numerically solve a multi-particle Schrodinger equation where the potential energy terms include all the inter-electron repulsions.

So in many realistic situations, fixed potentials don’t exist. They’re just something you learn about in an introductory quantum mechanics course.


text:
# Last season, Everett scored forty-eight points, This is six less than twice the number of points that Max scored. How many points did Max score?

Oct 31, 2016

Max scored 27 points.

#### Explanation:

Let $x$ equal the points that Max scored.

Twice the number of points is $2 x$.

Six less is $- 6$

$48$ is the number of points Everett scored.

The equation is as follows:

$2 x - 6 = 48$

Add $6$ to both sides.

$2 x = 54$

Divide both sides by $2$.

$x = \frac{54}{2}$

$x = 27$

$2 \left(27\right) - 6 = 48$
$54 - 6 = 48$
$48 = 48$