Most educational research I see (and this is my field) uses a residualized change score model in these situations. The combination of measurement models, in the form of Item Response Theory (IRT) models, and population-structure models, in the form of latent regression models with student group indicators as independent variables, provides an estimated distribution of underlying performance for the population and subgroups of interest. I'm not sure this is needed, unless your theory is specifically about this issue. Your proposed gain score model still fixes the $eta$ at 1, but further allows for gains to be linearly associated with the time 1 value. The residualized change score model empirically estimates the $eta$ for $X$ while the traditional gain score model fixes this $eta$ at 1. Your proposed gain score: $Y_2-Y_1 = a + bY_1 + bX + e$ Residualized change: $Y_2 = a + eta Y_1 + bX + e$ Traditional gain score (no time 1 control): $Y_2-Y_1 = a + bX + e$ Ignoring the multilevel aspect and assuming $X$ is treatment, note the difference between the models (hat tip to David Kenny): It might if those who are higher at time 1 typically change less (or more) from time 1 to time 2, but wouldn't help you if this was not the case. It is unclear to me whether your proposal to additionally control for time 1 score in your gain score model will help you power-wise. Likewise, the second approach can increase power to detect the effect of interest because time 1 is typically strongly correlated with the time 2 outcome. Score for students with the same test score value at time 1 (and anyīoth are valid, but the change score model has an additional assumption baked in (see below). Then yourĮstimate of the intervention effect is its effect on the time 2 The time 1 score plus treatment and any other covariates. In such a model, you are regressing the time 2 score on You can run a 'residualized change score model' instead of a gain I don't view that as 'evidence of growth.' The intercept in this model is the gain score for a student in the control condition and a value of 0 on the time 1 test score.

Treatment variable, you are evaluating whether there isĪ difference in treatment vs. Then add the time 1 variable to your regression model with your You have a couple of options with two time point data.

Hlm statistics student version