# Information Criteria Confidence Intervals Calculate confidence intervals of AIC and BIC for non-nested models. ```r icci(object1, object2, conf.level = 0.95, ll1 = llcont, ll2 = llcont) ``` ## Arguments - `object1`: a model object - `object2`: a model object - `conf.level`: confidence level of the interval - `ll1`: an optional function for computing log-likelihood contributions of object1 - `ll2`: an optional function for computing log-likelihood contributions of object2 ## Returns an object of class `icci` containing test results. ## Details Functionality is currently available for models of classes `lm`, `glm`, `glm.nb`, `clm`, `hurdle`, `zeroinfl`, `mlogit`, `nls`, `polr`, `rlm`, and `lavaan`. 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. Note: if models are nested or if the "variance test" from `vuongtest()` indicates models are indistinguishable, then the intervals returned from `icci()` will be incorrect. ## 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) ## CI for BIC icci(house2, house1) ## Further comparisons to hurdle, zero-inflated models 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) icci(bio2, bio1) icci(bio3, bio1) icci(bio3, bio2) ## Latent variable model comparisons require(lavaan) HS.model <- 'visual =~ x1 + x2 + x3 textual =~ x4 + x5 + x6 speed =~ x7 + x8 + x9 ' fit1 <- cfa(HS.model, data=HolzingerSwineford1939, meanstructure=TRUE) fit2 <- cfa(HS.model, data=HolzingerSwineford1939, group="school") icci(fit1, fit2) ## 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

icci function