in their current paper, Wu, West and Taylor (2009) point out the following: "However, as noted by Enders (2001), when FIML is used for Type II longitudinal data, the chi-square test statistic cannot be calculated using the general form, (N - 1)F(FIML), because there is no single N that is applicable to the entire sample. Researchers can calculate the fit indices by following a two-step procedure: (a) estimate the saturated model and the hypothesized model using FIML, and (b) calculate the chi-square test statistics using the formula –2(InL(FIML(hypothesized)) - InLFIM(L(saturated))). Then, the fit indices based on the chi-square test statistics can be calculated by hand using standard formulas (see Table 3)."
I'm using Mplus 5.21. I have missing data and include five auxiliary variables in my model.
Does the chi-square test statistic I get use the above formula? If not, does the output contain information on both log-likelihoods so that I can do the calculations myself?
I have two additional questions: 1. Are fit indices (e.g. CFI, TLI, RMSEA, SRMR) calculated according to the above formula?
2. In addition, Davey, Savla and Luo (2005) point out the following: "Comparison of model fit indexes generated by EM and FIML may thus be informative about the extent to which one's evaluation of a model is likely to be affected by missing data." I use the following commands in Mplus:
" MISSING ARE BLANK;
AUXILIARY = (m) z1 z2 z3 z4 z5;
TYPE = MISSING; ESTIMATOR = ML;"
Does Mplus use an EM-algorithm for estimating the model?
I've got an additional question after having read a paper by Bodner (2008). He recommends reporting the parameter lambda which "represents the fraction of missing information for a given parameter in a particular data set". It is defined as
lambda = 1 - [(v(m)-1)*U(m)/[(v(m)+3)*T(m)]
Is it possible to estimate this value with TYPE = MISSING? If so, what do I have to add to the syntax?
I have a question concerning the amount of missing data.
On our predictor side, we have data for nearly 1200 subjects (8 variables + five auxiliary variables). However, on the criterion side we only have data for 80 subjects (11 variables). We assume missing at random - subjects were admitted (and thus have criterion data) due to their test results (predictors).
We are using the auxiliary option and ML in Mplus to model our data.
How much can I trust the results I get - parameter estimates, model fit? For multiple imputation, there are "rules of thumb" on how many imputations one needs in order to get reliable estimates. Are there any rules of thumb for using FIML?
It sounds like you regress 1 DV on 8 predictors and to that you add 5 auxiliary(m) variables as missing data correlates. If that's right, the Mplus aux(m) ML approach under MAR ("FIML") for the 1200 subjects would work well since you have only 10 regression parameters (8 slopes, 1 intercept, and 1 residual variance) to estimate based on the 80 subjects who got selected. I think it would be difficult to have reliable general rules of thumb for either MI or FIML since it depends so much on the specific setting.