Hello Wenxia Zhou. Did you by any chance GLM > Repeated Measures in SPSS to estimate your model? If so, I suggest that you mean-center the covariate (the T1 score) and then estimate your model again using the mean-centered covariate. See this letter to the editor for more info:

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/2BBC95DC4B17719654CEFD000F9477E0/S1355617707071147a.pdf/use_of_covariates_in_randomized_controlled_trials.pdf

HTH.

Rather than adjusting for baseline, have you considered including it as your outcome with the other 2 time points? There are several articles and modeling texts that recommend not adjusting for the baseline measure in observational studies. Adjusting for baseline in observational studies can inflate the regression coefficients – a bias known as “Lord’s Paradox”. If only univariable analyses are required (and only 2 time ponts), either a paired t-test or the sign-rank test can be used. If adjustment for other covariables is necessary, change scores as the dependent variable in a linear regression or a multilevel model for repeated measures, without baseline adjustment, is my recommendation. (Consider a statistical reason: if the variables on right side of a regression are “fixed”, e.g., assumed to be measured without error, why should the outcome assessed at baseline be assumed to be measured without error, but at a later time, be assumed to be measured with error?)

n observational studies there is usually no expectation that the baseline outcome means for the study groups should be equal. (This can only be assumed in RCTs. Moreover, only in RCTs is there an expectation that the group means equal the grand mean – i.e., baseline outcome scores are balanced across study groups.) Regarding the concern about regression to the mean in observational studies, individuals with extreme values will regress to their group means, not to a grand mean.

See these articles:

Glymour, M Maria, Jennifer Weuve, Lisa F Berkman, Ichiro Kawachi, and James M Robins. 2005. “When is baseline adjustment useful in analyses of change? An example with education and cognitive change.” Am J Epidemiol 162: 267–78

Allison, Paul. 1990. “Change scores as dependent variables in regression analysis.” Sociological Methodology 20: 93–114.)

Paul Visintainer, Wenxia Zhou described the design as a "2 (Time: T2 vs. T3)x 2 (control vs. treatment) design, with the baseline T1 as a [covariate]". (Note I changed covariance to covariate and added the boldface in that quote.) That control vs. treatment wording makes me think this is an experimental study, not an observational study. What makes you think it's observational? Thanks for clarifying.

I don't know if the design is observational or randomized. Controlling for baseline is a particular issue for observational designs, though; hence the caveat. If the design is randomized, then control for baseline is less an issue (it may even improve precision).

Wenxia Zhou, is your study experimental or observational? If it was experimental, how were people allocated to the groups? Thank you for clarifying.