First of all, it would be useful to know what the sample size was, what time intervals you had between your measurements, what type of longitudinal SEM you estimated, and what the fit statistics looked like for the model in question.

If your model didn't fit well, this could lead to bias in some or all of the estimated parameters. Also, do you have evidence from the observed variable correlations that stability increased dramatically after the second time point? Could this indicate an artifact or error in the data? Did you check for outliers and extreme values? It definitely seems like an unusual and unexpected finding that stability would increase from basically zero to almost perfect.

Christian Geiser, thanks for responding.

Sample size 277.

Intervals were 6 weeks.

Fit stats were χ2/df = 2.48, CFI = 0.953, RMSEA = .073.

This was a cross-lagged panel model with mediating variables.

The correlation of the variables between the first two time points was significant at .55. The correlation of the variables between the second two time points was significant at .73. I did check for errors, outliers, and extreme values.

The variable in question was related to self-efficacy (belief in ability) on a described, novel assessment (quiz), which the participants had not yet experienced at the first time point. At the second time point, they had taken 14 quizzes. At the third point that had had done around 30 quizzes. So my thoughts were that many students misjudged their ability at the first time point*, but due to the frequency of experiences, their evaluation of their abilities stabilised between the latter two time points.

If this is the case, my understanding is the model fails to capture the interindividual differences that explain the lack of prediction between the first and second time point (i.e., some students overestimated their abilities and some underestimated based on the described experience, but we can't explain who).

It might be helpful to note that the second time point quiz self-efficacy was predicted by their self-efficacy on exams (.64) at the first time point (i.e., beliefs about previously experienced assessments).

I am trying to understand what type of bias could be indicated by these results, and how I should go about testing for it. Thanks!

*I did test for measurement invariance over time.

That makes sense. Are you comparing the cross-lagged panel (auto)regression (path) coefficients to zero-order correlations? This could be part of the issue (explain the "discrepancy"/low autoregressive stability coefficient). Regression coefficients are not equal to zero-order (bivariate) correlations. The regression coefficients take the correlation with other independent variables into account. This may explain why the autoregressive "stability" coefficients in your model look very different from the zero-order correlations. It is impossible to know without looking at your data and model in more detail.

The model fit does not look completely horrible at first sight but the chi-square test is significant and the RMSEA value is a bit high. I would take a look at model residuals and/or modification indices to find out where the model may be misspecified.