# Find the likelihood ratio (or Bayes factor) based on the bivariate distribution of fit indices Find the log-likelihood of the observed fit indices on Model 1 and 2 from the real data on the bivariate sampling distribution of fit indices fitting Model 1 and Model 2 by the datasets from the Model 1 and Model 2. Then, the likelihood ratio is computed (which may be interpreted as posterior odd). If the prior odd is 1 (by default), the likelihood ratio is equivalent to Bayes Factor. ```r likRatioFit(outMod1, outMod2, dat1Mod1, dat1Mod2, dat2Mod1, dat2Mod2, usedFit=NULL, prior=1) ``` ## Arguments - `outMod1`: `lavaan` that saves the analysis result of the first model from the target dataset - `outMod2`: `lavaan` 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. - `prior`: The prior odds. The prior probability that Model 1 is correct over the prior probability that Model 2 is correct. ## Returns The likelihood ratio (Bayes Factor) in preference of Model 1 to Model 2. If the value is greater than 1, Model 1 is preferred. If the value is less than 1, Model 2 is preferred. ## Author(s) Sunthud Pornprasertmanit (psunthud@gmail.com ) ## See Also `SimResult` for a detail of simResult `pValueNested` for a nested model comparison by the difference in fit indices `pValueNonNested` for a nonnested model comparison by the difference in fit indices ## Examples ```r ## Not run: # Model A; Factor 1 --> Factor 2; Factor 2 --> Factor 3 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, 1] <- NA path.A[3, 2] <- NA model.A <- estmodel(LY=loading, BE=path.A, modelType="SEM", indLab=c(paste("x", 1:3, sep=""), paste("y", 1:8, sep=""))) out.A <- analyze(model.A, PoliticalDemocracy) # Model A; Factor 1 --> Factor 3; Factor 3 --> Factor 2 path.B <- matrix(0, 3, 3) path.B[3, 1] <- NA path.B[2, 3] <- NA model.B <- estmodel(LY=loading, BE=path.B, modelType="SEM", indLab=c(paste("x", 1:3, sep=""), paste("y", 1:8, sep=""))) out.B <- analyze(model.B, PoliticalDemocracy) loading.mis <- matrix("runif(1, -0.2, 0.2)", 11, 3) loading.mis[is.na(loading)] <- 0 # Create SimSem object for data generation and data analysis template datamodel.A <- model.lavaan(out.A, std=TRUE, LY=loading.mis) datamodel.B <- model.lavaan(out.B, std=TRUE, LY=loading.mis) # Get sample size n <- nrow(PoliticalDemocracy) # The actual number of replications should be greater than 20. output.A.A <- sim(20, n=n, model.A, generate=datamodel.A) output.A.B <- sim(20, n=n, model.B, generate=datamodel.A) output.B.A <- sim(20, n=n, model.A, generate=datamodel.B) output.B.B <- sim(20, n=n, model.B, generate=datamodel.B) # Find the likelihood ratio ;The output may contain some warnings here. # When the number of replications increases (e.g., 1000), the warnings should disappear. likRatioFit(out.A, out.B, output.A.A, output.A.B, output.B.A, output.B.B) ## End(Not run) ```

likRatioFit function