bayesian factor analysis for mixed ordinal and continuous ......make everything continuous (standard...

IntuitionModel

Example

Bayesian Factor Analysis for Mixed Ordinal andContinuous Responses

Kevin M. Quinn (2004)

Political Analysis

April 19, 2017

Kevin M. Quinn (2004) Bayesian Factor Analysis

IntuitionModel

Example

Outline

1 Intuition

2 Model

3 ExampleSurveyCode

IntuitionModel

Example

Factor Analysis

Motivation for factor analysis

Explain patterns influence the covariance of observed variablesthrough underlying latent factors

IntuitionModel

Example

Factor Analysis

Motivation for factor analysis

Explain patterns influence the covariance of observed variablesthrough underlying latent factors

IntuitionModel

Example

Factor Analysis

Depression

Insomnia Loss of Appetite

Factor effects

Figure 1: Factor Effect on Observables

IntuitionModel

Example

Factor Analysis

Two methods traditions being integrated:

Normal theory factor analysis (continuous variables)

Item Response Theory (Ordinal/Likert-type variables)

x∗ = φλ′ + E (1)

Problem: posterior density of X would have to come fromdifferent types of distribution

IntuitionModel

Example

Factor Analysis

x∗ = φλ′ + E (1)

IntuitionModel

Example

Factor Analysis

x∗ = φλ′ + E (1)

IntuitionModel

Example

Factor Analysis

x∗ = φλ′ + E (1)

IntuitionModel

Example

Factor Analysis for Mixed Factors

Depression

hours of sleep appetite quality

Factor effects

Figure 2: Mixed Factors

IntuitionModel

Example

Standard Solutions

Make everything continuous (standard normal theory)

Discretize everything (IRT)

Discard one set of the variables

Do something else that isn’t model based

IntuitionModel

Example

Standard Solutions

IntuitionModel

Example

Standard Solutions

IntuitionModel

Example

Standard Solutions

IntuitionModel

Example

Proposed Solution

Generalize the IRT and standard models

Should look familiar:

X∗ = φλ′ + E (2)

IntuitionModel

Example

Proposed Solution

Generalize the IRT and standard models

Should look familiar:

X∗ = φλ′ + E (2)

IntuitionModel

Example

Posterior Density for Mixed FA

IntuitionModel

Example

Posterior Density for Mixed FA

IntuitionModel

Example

SurveyCode

Data and Context

Survey of SOC204 students (n=130)

Mixture of survey questions designed to be easily influencedby political content

Each precept wrote a question, so there’s a mixture of ordinal,continuous, and open ended responses

So we might assume at least one underlying factor: liberalness(conservativeness)

IntuitionModel

Example

SurveyCode

Data and Context

IntuitionModel

Example

SurveyCode

Data and Context

IntuitionModel

Example

SurveyCode

Data and Context

IntuitionModel

Example

SurveyCode

Code Pointers

Variables have to be numeric or ordered factors

All factor levels have to be represented

IntuitionModel

Example

SurveyCode

Code Pointers

Variables have to be numeric or ordered factors

All factor levels have to be represented

IntuitionModel

Example

SurveyCode

mcmc.out = MCMCmixfactanal(variables, factors = 1,data = dataframe, store.scores = TRUE)

IntuitionModel

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SurveyCode

Results

λ1 λ2Trump Approval - -0.09Islam Threat 0.71 0.15Trump Score - -0.83Econ Score - -0.84Foreign Score - -0.80Social Score - -0.89Env Score - -0.80Min Wage 2.73 0.72Crime Issue 0.40 0.05Gun Rights - -0.17Immigration - 0.41Health - 0.55Outsourcing - -0.03Tax Reform - -0.03Dakota Access - -0.02Ed Access - 0.35Military Involvement - 0.03Climate Role 0.12 -0.25Facebook Use 2.92 -0.06Facebook Posts 0.47 0.11Johnson Approval 2.92 -0.16

bayesian factor analysis for mixed ordinal and continuous ......make everything continuous (standard...

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