# change scores as predictor variables in a repeated measures multilevel model

I am using SPSS mixed to create a longitudinal multilevel model. Level 1 is observations and Level 2 is participants, so observations are nested within participants. I have multiple continuous and dichotomous predictors relating to health measures and social support etc. Predictors were grand mean centered. I have a single continuous dependent variable of loneliness measured at three waves. Some predictors were measured at T1 only and some were measured at all three waves. N is about 3000 and there are missing data, data were measured at the same time for each participant at each wave.

My research question relates to changes in loneliness over time and relationship to predictors. I am assuming a simple linear growth trajectory. I have modeled an unconditional means model and unconditional growth model. X axis = time in years 0,2,4 and these are the same as the data collection waves T1,T2,T3. I have used T1 predictors including Time to explain changes in loneliness with good results. These were simple random intercept models with no other random components so slopes are parallel for various predictor groups. I used autocorrelated heterogeneous covariance structure as it had the best fit and used maximum likelihood estimation.

I have used T1 predictors (including time) * Time interactions to examine how the T1 predictors affect loneliness over time with good results. These were also random intercept models and my understanding is that the interactions with time result in differing slopes as time = rate of change / slope in this context.

I now want to see how changes in the predictors over time affect loneliness. These predictors are time varying covariates, some are continuous and some are binary. I have used changes in predictors between waves to create change scores and use these change scores as predictors. The idea is to examine how each instance of change in the predictor affects loneliness. I have computed changes two change scores per participant T2-T1 and T3-T2. I ensured sign was correct by adding 100 to the score before doing this. So, +3 change score = increase of 3 points in predictor and -2 = decrease of two points. For binary predictors (eg. employment) +1 = appearance of the predictor and -1 = disappearance, 0 = no change.

The literature on change scores confuses me and raises many issues. Regarding the last analysis involving change scores, what are the main problems with change scores in this context? I am keen to work with change scores and explain their limitations in my work. I understand there are some manipulations that can be made to the change scores to improve their validity? or perhaps including error terms. I only have access to SPSS and possibly AMOS. I have heard of latent growth curve mixture modeling but know little about it and SPSS cannot use this.