pValueNonNested: Find p-values (1 - percentile) for a non-nested model comparison

Description

This function will provide p value from comparing the results of fitting real data into two models against the simulation from fitting the simulated data from both models into both models. The p values from both sampling distribution under the datasets from the first and the second models are reported.

Usage

pValueNonNested(outMod1, outMod2, dat1Mod1, dat1Mod2, dat2Mod1, dat2Mod2, 
usedFit = NULL, nVal = NULL, pmMCARval = NULL, pmMARval = NULL, df = 0, 
onetailed=FALSE)

Arguments

outMod1

SimModelOut that saves the analysis result of the first model from the target dataset

outMod2

SimModelOut that saves the analysis result of the second model from the target dataset

dat1Mod1

SimResult that saves the simulation of analyzing Model 1 by datasets created from Model 1

dat1Mod2

SimResult that saves the simulation of analyzing Model 2 by datasets created from Model 1

dat2Mod1

SimResult that saves the simulation of analyzing Model 1 by datasets created from Model 2

dat2Mod2

SimResult that saves the simulation of analyzing Model 2 by datasets created from Model 2

usedFit

Vector of names of fit indices that researchers wish to getCutoffs from. The default is to getCutoffs of all fit indices.

nVal

The sample size value that researchers wish to find the p value from.

pmMCARval

The percent missing completely at random value that researchers wish to find the p value from.

pmMARval

The percent missing at random value that researchers wish to find the the p value from.

The degree of freedom used in spline method in predicting the fit indices by the predictors. If df is 0, the spline method will not be applied.

onetailed

If TRUE, the function will convert the p value based on two-tailed test.

Value

This function provides a vector of p values based on the comparison of the difference in fit indices from the real data with the simulation results. The p values of fit indices are provided, as well as two additional values: andRule and orRule. The andRule is based on the principle that the model is retained only when all fit indices provide good fit. The proportion is calculated from the number of replications that have all fit indices indicating a better model than the observed data. The proportion from the andRule is the most stringent rule in retaining a hypothesized model. The orRule is based on the principle that the model is retained only when at least one fit index provides good fit. The proportion is calculated from the number of replications that have at least one fit index indicating a better model than the observed data. The proportion from the orRule is the most lenient rule in retaining a hypothesized model.

Details

In comparing fit indices, the p value is the proportion of the number of replications that provide less preference for either model 1 or model 2 than the analysis result from the observed data. In two-tailed test, the function will report the proportion of values under the sampling distribution that are more extreme that one obtained from real data. If the resulting p value is high (> .05) on one model and low (< .05) in the other model, the model with high p value is preferred. If the p values are both high or both low, the decision is undetermined.

Examples

Run this code

library(lavaan)
loading <- matrix(0, 11, 3)
loading[1:3, 1] <- NA
loading[4:7, 2] <- NA
loading[8:11, 3] <- NA
path.A <- matrix(0, 3, 3)
path.A[2:3, 1] <- NA
path.A[3, 2] <- NA
param.A <- simParamSEM(LY=loading, BE=path.A)

model.A <- simModel(param.A, indLab=c(paste("x", 1:3, sep=""), paste("y", 1:8, sep="")))
out.A <- run(model.A, PoliticalDemocracy)

path.B <- matrix(0, 3, 3)
path.B[1:2, 3] <- NA
path.B[1, 2] <- NA
param.B <- simParamSEM(LY=loading, BE=path.B)

model.B <- simModel(param.B, indLab=c(paste("x", 1:3, sep=""), paste("y", 1:8, sep="")))
out.B <- run(model.B, PoliticalDemocracy)

u2 <- simUnif(-0.2, 0.2)
loading.mis <- matrix(NA, 11, 3)
loading.mis[is.na(loading)] <- 0
LY.mis <- simMatrix(loading.mis, "u2")
misspec <- simMisspecSEM(LY=LY.mis)

output.A.A <- runFit(model.A, PoliticalDemocracy, 5, misspec=misspec)
output.A.B <- runFit(model.A, PoliticalDemocracy, 5, misspec=misspec, analyzeModel=model.B)
output.B.A <- runFit(model.B, PoliticalDemocracy, 5, misspec=misspec, analyzeModel=model.A)
output.B.B <- runFit(model.B, PoliticalDemocracy, 5, misspec=misspec)

# The output may contain some warnings here. When the number of replications increases (e.g., 1000), the warnings should disappear.
pValueNonNested(out.A, out.B, output.A.A, output.A.B, output.B.A, output.B.B)