Tests of Non-Nested Models

Testing non-nested models via theory supplied by Vuong (1989) . Includes tests of model distinguishability and of model fit that can be applied to both nested and non-nested models. Also includes functionality to obtain confidence intervals associated with AIC and BIC. This material is partially based on work supported by the National Science Foundation under Grant Number SES-1061334.

nonnest2

nonnest2 provides functionality for comparing non-nested models' fit and distinguishability, relying on theory from Vuong (1989). The authors acknowledge support from NSF grant SES-1061334. The contents of this package are those of the authors and do not reflect the views of the National Science Foundation.

The package is intended to work automatically for models of many classes, including lavaan, mirt, and glm. It can also be applied to models of new, unseen classes, so long as the user provides functions to compute the model's casewise log-likelihoods and casewise first derivatives. A notable example is the merDeriv package, which provides those functions for many models estimated via lme4.

Example

Consider the two factor analysis models below, estimated in lavaan. The models are not nested due to x4 and x7.

library("lavaan")

m1 <- ' visual  =~ x1 + x2 + x3 + x4
        textual =~ x4 + x5 + x6
        speed   =~ x7 + x8 + x9 '
fit1 <- cfa(m1, data=HolzingerSwineford1939)

m2 <- ' visual  =~ x1 + x2 + x3
        textual =~ x4 + x5 + x6 + x7
        speed   =~ x7 + x8 + x9 '
fit2 <- cfa(m2, data=HolzingerSwineford1939)

We can use nonnest2 to compare the models via Vuong tests and to obtain interval estimates of differences in the models' AIC and BIC values.

vuongtest(fit1, fit2)
icci(fit1, fit2)