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Confirmatory Factor Analysis Using OpenMx & R

Confirmatory Factor Analysis Using OpenMx & R. (CFA ) Practical Session Timothy C. Bates. Confirmatory Factor Analysis to test theory. Are there 5 independent domains of personality? Do domains have facets? Is Locus of control the same as primary control?

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Confirmatory Factor Analysis Using OpenMx & R

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  1. Confirmatory Factor AnalysisUsing OpenMx & R (CFA) Practical SessionTimothy C. Bates

  2. Confirmatory Factor Analysisto test theory • Are there 5 independent domains of personality? • Do domains have facets? • Is Locus of control the same as primary control? • Is prosociality one thing , or three? • Is Grit independent of Conscientiousness?

  3. Prosocial Obligations • Prosociality covers several domains, e.g. • Workplace: voluntary overtime • Civic life: Giving evidence in court • Welfare of others: paying for other’s healthcare • CFA can test the fit of theories • Which hypothesised model fits best? • 3 indicators of one factor? • 3 correlated factors? • 3 independent factors?

  4. Factor structure of Prosociality • Distinct domains? Work Civic Welfare Work1 Work 2 Work 3 Civic 1 Civic 2 Civic 3 Welfare 1 Welfare 2 Welfare 3

  5. Factor structure of Prosociality • One underlying prosociality factor? Prosociality Work1 Work 2 Work 3 Civic 1 Civic 2 Civic 3 Welfare 1 Welfare 2 Welfare 3

  6. Factor structure of Prosociality • Hierarchical structure: Common and distinct factors? Prosociality Work Civic Welfare Work1 Work 2 Work 3 Civic 1 Civic 2 Civic 3 Welfare 1 Welfare 2 Welfare 3

  7. Note: These last two models are equivalent! Work Civic Welfare Work1 Work 2 Work 3 Civic 1 Civic 2 Civic 3 Welfare 1 Welfare 2 Welfare 3

  8. CFA with R & OpenMx • library(OpenMx) • What is OpenMx? • “OpenMx is free and open source software for use with R that allows estimation of a wide variety of advanced multivariate statistical models.” • Homepage: http://openmx.psyc.virginia.edu/ • # library(sem)

  9. Our data • Dataset: Midlife Study of Well-Being in the US (Midus) • Prosocial obligations - c. 1000 individuals • How much obligation do you feel… • to testify in court about an accident you witnessed?’ [civic] • to do more than most people would do on your kind of job?’ [work] • to pay more for your healthcare so that everyone had access to healthcare? [welfare]

  10. Preparatory code First we need to load OpenMx require(OpenMx) Now lets get the data (R can read data off the web) myData= read.csv("http://www.subjectpool.com/prosocial_data.csv") ? What are the names in the data? summary(myData) # We have some NAs myData= na.omit(myData) # imputation is another solution summary(myData)

  11. Core OpenMx functions • mxModel() • this will contain all the objects in our model • mxPath(): each path in our model • mxData(): the data for the model • mxRun() • Generate parameter estimates by sending the model to an optimizer • Returns a fitted model

  12. CFA on our competing models • Three competing models to test today: • One general factor • Three uncorrelated factors • Three correlated factors

  13. Model 1: One general factor Prosociality Work1 Work 2 Work 3 Civic 1 Civic 2 Civic 3 Welfare 1 Welfare 2 Welfare 3

  14. Quite a bit more code than you have used before: • We’ll go through it step-by-step

  15. Model 1 – Step 1 # Get set up latents = "F1” manifests = names(myData) observedCov = cov(myData) numSubjects= nrow(myData) # Create a model using the mxModel function cfa1<- mxModel("Common Factor Model”, type="RAM”,

  16. Model 1 – Step 2 # Here we set the measured and latent variables manifestVars= manifests, latentVars = latents,

  17. Model 1 – Step 3 # Create residual variance for manifest variables using mxPath mxPath( from=manifests, arrows=2, free=T, values=1, labels=paste("error”, 1:9, sep=“”)), # using mxPath, fix the latent factor variance to 1 mxPath( from="F1", arrows=2, free=F, values=1, labels ="varF1”), # Using mxPath, specify the factor loadings mxPath(from="F1”, to=manifests, arrows=1, free=T, values=1, labels =paste(”l”, 1:9, sep=“”)),

  18. Model 1 – Step 4 # Give mxData the covariance matrix of ‘data2’ for analysis mxData(observed=observedCov , type="cov", numObs=numSubjects) # make sure your last statement DOESN’T have a comma after it )# Close model

  19. Model 1 – Run the model # The mxRun function fits the model cfa1<- mxRun(cfa1) # Lets see the summary output summary(cfa1) # What is in a model? slotNames(cfa1@output) names(cfa1@output)

  20. Summary Output # Ideally, chi-square should be non-significant chi-square: 564.41; p: < .001 # Lower is better for AIC and BIC AIC (Mx): 510.41 BIC (Mx): 191.47 # < .06 is good fit: This model is a bad fit RMSEA: 0.15

  21. Story so far… • Model 1 (one common factor) is a poor fit to the data)

  22. Model 2 Work Civic Welfare Work1 Work 2 Work 3 Civic 1 Civic 2 Civic 3 Welfare 1 Welfare 2 Welfare 3

  23. Model 2 – Step 1 # Create a model using the mxModel function cfa3<-mxModel("Three Distinct Factors Model Path Specification", type="RAM",

  24. Model 2 – Step 2 # Here we name the measured variables manifestVars=manifests, # Here we name the latent variable latentVars=c("F1","F2", "F3"),

  25. Model 2 – Step 3 # Create residual variance for manifest variables mxPath(from=manifests,arrows=2, free=T,values=1,labels=c("error”, 1:9, sep=“”)),

  26. Model 2 – Step 4 # Specify latent factor variances mxPath(from=c("F1","F2", "F3"), arrows=2,free=F, values=1, labels=c("varF1","varF2", "varF3") ),

  27. Model 2 – Step 5 # Fix the covariance between latent factors to zero (i.e. specify the factors as uncorrelated) mxPath( from="F1", to="F2", arrows=2, free=FALSE, values=0, labels="cov1” ),

  28. Model 2 – Step 6 mxPath(from="F1”,to="F3", arrows=2, free=F, values=0, labels="cov2"), mxPath(from="F2",to="F3", arrows=2, free=F, values=0, labels="cov3"),

  29. Model 2 – Step 7 # Specify the factor loading i.e. here we specify that F1 loads on work1, 2, and 3 mxPath( from="F1", to=c("work1","work2","work3"), arrows=1, free=T, values=1, labels=c("l1","l2","l3") ), mxPath( from="F2", to=c("civic1","civic2", "civic3"), arrows=1, free=T, values=1, labels=c("l4","l5", "l6") ),

  30. Model 2 – Step 8 mxPath( from="F3", to=c("welfare1", "welfare2", "welfare3"), arrows=1, free=T,values=1, labels=c("l7", "l8", "l9") ), # Use the covariance matrix of ‘myData’ for analysis mxData(observed=cov(myData), type="cov", numObs=nrow(myData)) ) # Close the model

  31. Model 2 – Run the model # The mxRun function fits the model threeDistinctFactorFit <- mxRun(threeDistinctfactorModel) # The following line will deliver a lot of output twoFactorFit@output # Lets see the summary output summary(threeDistinctFactorFit)

  32. Summary Output # Ideally, chi-square should be non-significant chi-square: 576.50; p: <.0001 # Lower is better for AIC and BIC AIC (Mx): 522.50 BIC (Mx): 197.51 # <.08 is a reasonable fit: This model is a poor fit RMSEA: 0.16

  33. Now your turn… Install OpenMx repos <- c('http://openmx.psyc.virginia.edu/testing/') If you have your laptop: install.packages('OpenMx', repos=repos) lib <- 'C:/workspace’ install.packages('OpenMx', repos=repos, lib=lib) library(OpenMx, lib=lib)

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