# Vuong Tests for Model Comparison Test pairs of models using Vuong's (1989) theory. This includes a test of model distinguishability and a test of model fit. ```r vuongtest( object1, object2, nested = FALSE, adj = "none", ll1 = llcont, ll2 = llcont, score1 = NULL, score2 = NULL, vc1 = vcov, vc2 = vcov ) ``` ## Arguments - `object1`: a model object - `object2`: a model object - `nested`: if `TRUE`, models are assumed to be nested - `adj`: Should an adjusted test statistic be calculated? Defaults to none , with possible adjustments being aic and bic - `ll1`: an optional function for computing log-likelihood contributions of object1 - `ll2`: an optional function for computing log-likelihood contributions of object2 - `score1`: an optional function for computing scores of object 1 - `score2`: an optional function for computing scores of object 2 - `vc1`: an optional function for computing the asymptotic covariance matrix of the object1 parameters - `vc2`: an optional function for computing the asymptotic covariance matrix of the object2 parameters ## Returns an object of class `vuongtest` containing test results. ## Details For non-nested models, the test of distinguishability indicates whether or not the models can possibly be distinguished on the basis of the observed data. The LRT then indicates whether or not one model fits better than another. For nested models (`nested=TRUE`), both tests serve as robust alternatives to the classical likelihood ratio tests. In this case, the `adj` argument is ignored. Users should take care to ensure that the two models have the same dependent variable (or, for lavaan objects, identical modeled variables), with observations ordered identically within each model object. Assuming the same data matrix is used to fit each model, observation ordering should generally be identical. There are currently no checks for this, however. ## Examples ```r ## Not run: ## Count regression comparisons require(MASS) house1 <- glm(Freq ~ Infl + Type + Cont, family=poisson, data=housing) house2 <- glm(Freq ~ Infl + Sat, family=poisson, data=housing) house3 <- glm(Freq ~ Infl, family=poisson, data=housing) ## house3 is nested within house1 and house2 anova(house3, house1, test="Chisq") anova(house3, house2, test="Chisq") ## house 2 is not nested in house1, so this test is invalid anova(house2, house1, test="Chisq") ## Use vuongtest() instead vuongtest(house2, house1) ## Application to models with different distributional assumptions require(pscl) bio1 <- glm(art ~ fem + mar + phd + ment, family=poisson, data=bioChemists) bio2 <- hurdle(art ~ fem + mar + phd + ment, data=bioChemists) bio3 <- zeroinfl(art ~ fem + mar + phd + ment, data=bioChemists) vuongtest(bio2, bio1) vuongtest(bio3, bio1) vuongtest(bio1, bio2) vuongtest(bio1, bio3) vuongtest(bio3, bio2) ## Application to latent variable models require(lavaan) HS.model <- 'visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit1 <- cfa(HS.model, data=HolzingerSwineford1939) fit2 <- cfa(HS.model, data=HolzingerSwineford1939, group="school") vuongtest(fit1, fit2) ## Supplying custom vcov function require(lme4) require(merDeriv) fm1 <- lmer(Reaction ~ Days + (Days | Subject), sleepstudy, REML=FALSE) fm2 <- lmer(Reaction ~ Days + (Days || Subject), sleepstudy, REML=FALSE) vcl <- function(obj) vcov(obj, full=TRUE) vuongtest(fm1, fm2, vc1=vcl, vc2=vcl, nested=TRUE) ## End(Not run) ``` ## References Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. **Econometrica, 57**, 307-333. Merkle, E. C., You, D., & Preacher, K. (2016). Testing non-nested structural equation models. **Psychological Methods, 21**, 151-163. ## Author(s) Ed Merkle and Dongjun You

vuongtest function