I divide the sample into different periods, on the basis of year (sorted). And I want to test that a firm enter at period 1 have different performance from another firm enter at period 2. I have been working on latent growth curve models and thinking about studying firm's performance/growth trajectories. But when I use latent growth curve models for different periods, for each period, I only get the average (of all firms in that period) intercept at starting year and average slope of growth trajectories as well as variances and covariance of the intercept and the slope. I could see there are differences in results between period 1 and period 2 for example. However, running latent growth curve models for different periods separately does not directly test my idea above.
I have recently bought Mplus software and have been wondering whether Mplus provides some related estimation techniques/methods to directly test my idea above. (It doesn't have to be related with latent growth curve modeling.)
I would appreciate it if you could give me names of related techniques/methods/Mplus commands that come to your mind. I am not asking for detailed instructions (but they are welcomed for sure), of which I will take care.