The tests in Chapter 2 were also conducted using various different model specifications to account for possible model-driven results. Tests using traditional ordinary least squares (OLS) models indicate similar substantive results. OLS models 1 through 5 all demonstrate that the percentage Latino in state remains strongly significant across the board. All other variables exhibit similar coefficients, despite the higher standard errors due to autocorrelation. Because OLS assumes independence of the dependent variable, it is an inappropriate method for these data.

Random effects models with both the state and year as the group variables, however, differ in minor ways as explained later. These types of models are appropriate for time-series data but do not account for serial autocorrelation like the feasible generalized least squares (FGLS) procedure (Bertrand et al. 2004). Model 1 is robust across both state and year models. Model 2 with the states as the random effects control indicates the same substantive results with the exception of the implementation of term limits variable, which is not statistically significant, although in the negative direction. This suggests that there are considerable state-to-state differences on the impact of term limits on Latino representation. Model 4 yields the same results for both time and state specifications. Because all other specifications show a strong and significantly negative effect of more professional legislatures on Latino representation, this seems more like a statistical artifact.