How to test the effect of condition on change scores for a possibly ordinal dependent variable? I have a categorical independent variable (two levels: condition 1; condition 2) and ordinal(?) dependent variables (numerical magnitude shifts (e.g. -3 if there was a decrease in number magnitude from 4 to 1). I now want to assess whether the condition predicts a change in the dependent variable. It is a repeated measurements design.
Now I have got the following questions:


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*Can I conduct a linear regression for DV = ordinal (categorical)?

*Can I conduct a linear regression for repeated measurements design?

 A: Note: If your study design is an intervention trial (that is, the repeated measurements are arising from observations made "before" and "after" some sort of treatment and nothing else) and you're trying to estimate the average effect of treatment, I would just calculate the differences ("after" minus "before", for example) and do analysis on the differences. This sweeps the entire repeated measures business under the rug since the differences can be reasonably viewed as having independent identically distributed errors. Assuming you don't have data from an intervention trial.........
If the repeated measurements are correlated then the errors will not be independent and identically distributed (iid), which violates a key assumption underlying the inference (e.g. confidence intervals, $p$-values) for your regression coefficients in ordinary regression, which might make the ordinary inference misleading. Depending on the type of departure from the "independent, identically distributed errors" assumption, you would do different things. 
If there is heteroskedasticity (non-constant variance) weighted least-squares is frequently used (which is a special case of generalized least-squares). Related to your first question - it doesn't seem like you have a continuous response, so you may want a more general all-purpose method. The only way you can rationalize using your categorical DV and pretending like it's continuous is if it is both an ordinal and an interval scale. That is, is the difference between level 3 and level 2 the same as the difference between level 2 and level 1, etc...? if so, you may be able to make a rational argument that you can view it as continuous. Otherwise, no. 
I'll point you in a direction for further research (either of the following will probably work for you and can be used for either categorical or continuous data but are different in subtle ways): 
(1) Generalized Estimating Equations (GEE): Allows you to estimate regression coefficients from data with non-iid errors even when you've misspecified the within-cluster (repeated measurements on individuals in your case) association structure. The coefficients estimated from a GEE are interpreted as the average effect across the population for a one unit increase in the predictor. (R package: geepack, gee)
(2) Random Effects Models: Within-cluster correlations in the errors are modeled by partitioning the error into parts shared within a cluster (what causes the correlation between repeated measurements) and parts not shared within a cluster ("measurement error"). The coefficients here are interpreted as the effect associated with a one unit increase in the predictor for a particular individual chosen from the population. (R package: lme4)
Note: The interpretation of the GEE and Random Effects Model coefficients will only be the same when you have a linear model (that is, when you have a continuous response). 
