I am analyzing data from a birth cohort, where maternal depression data were collected at 6 different time points.

However, 3 different questionnaires were used to measure maternal depression at different time points: CESD was used at the 1st time point, EPDS was used at the 2nd time point, and POMS was used in the remaining time points. All these questionnaires are well-established measures of maternal depression. I am considering using the z-value of these test scores to generate different maternal depression trajectories.

My question is: what test can I use to determine whether these different questionnaires measure the same thing across different time points?

Time invariance test tests whether the same instrument measures the same thing across different time points, but doesn't seem to apply to different instruments.