I am struggling with deciding between two path models, both of which have a binary outcome variable. The first has an R-square of .151, chi-square=163.6, CFI=.479, RMSEA=.032, WRMR=3.082. When I remove one of the predictor variables, I get an R-square=.079, chi-square=45.086, CFI=.762, RMSEA=.026, WRMR=2.123.
Why would the R-square improve, but the fit indicies be worse? Which should be used in deciding the best model?
R-square is not a test of model fit. It says how much variance in a dependent variable is explained by a set of independent variables. A well-fitting model can have low R-square values and a poorly-fitting model can have high R-square values.