Hi Amanda, 

I am assuming that this is a hierarchical/multilevel model so you can use the log-likelihood as a measure of fit. On its own it doesn't mean much but you can compare it to a null model. ie a model without predictors and a random intercept for the participants (assuming that the repeated measures are from participants). Then you can calculate the difference in log-likelihood between the two models  multiplied by -2. This will give you a score that is chi-square distributed. The degrees of freedom for the chi-square score is the difference in degrees of freedom between the full model and the null model. 

If you also a have a random slope for the effect of time, then you can first provide model comparisons between the random intercept and the random slope model, and then provide model comparisons between that and the full model.

Note that when you compare models that differ in their random effects you need to fit the model using restricted maximum likelihood (REML) but when you compare models that differ in their fixed effects you need to use Maximum likelihood (ML).  

Regarding the R2 - it is usually considered problematic and there are different suggestions in the literature. The easiest is to use the residual variance of the null and the full model:

R2 = 1 - residual_variance_of_full_model/residual_variance_of_null_model

(again, if you have a random effect for the slope you can do the comparison between that model and your full model - but that would give you the additional variance explained by you predictors above the variance explained by the growth curve). 

Thanks George! You're awesome! 

Your growth curve modelling is on the basis of a specific hypothesized model. Therefore it is proper to be asked to find the degree of goodness-of-fit of the hypothesized model to actual data. It can be R2 or chi-square.