Hi everyone! I am investigating the link between language and mathematics. I have two language components and hence two assessments of language that were tested at two time points (X_t1, X_t2, Y_t1, Y_t2). These are my predictors. My outcome variables (i.e., three different mathematical abilities) were also tested twice, namely: Z_t1, Z_t2, K_T1, K_t2, M_t1, M_t2. I am looking at the longitudinal associations between language and mathematics by taking into account autoregressive effects (i.e., from X and Y to Z, K and M). Additionally, I am also examining bidirectionality, namely from mathematics to language. My sample size includes 134 participants, however I keep getting very poor fit in my models even when I try different combinations of the measures (e.g., combining the language components and having one single language predictor). Can there be any other explanation than insufficient sample size? Are there any analyses you would suggest instead of CLPA? Thanks :)
It is difficult to say without seeing the specifics of your model. Typically, a poor fit is not due to a small sample (and yours isn't that small). Rather, misfit is typically due to omitted paths (i.e., implicit or explicit restrictions) in the model. For example, there may be statistically significant direct effects (paths from one variable to another) that you are missing or correlations between residual variables at the same time point that are perhaps currently not included in the model. You can look at standardized covariance residuals to examine which covariances between variables are currently not well reproduced by the model.
The sample size is an important consideration when using a cross-lagged panel model (CLPM) or any statistical modeling approach. If the sample size is too small, the statistical power of the analysis may be insufficient to detect true effects or to distinguish them from measurement errors.
In the context of a CLPM, small sample size may result in poor model fit, which can be indicated by low statistical power, low model chi-square values, and poor model fit indices such as the root mean square error of approximation (RMSEA), comparative fit index (CFI), and Tucker-Lewis Index (TLI). Poor model fit may also be indicated by high standard errors or low parameter estimates.
If you have a small sample size, you may want to consider alternative modeling approaches, such as simpler cross-sectional analyses, or using Bayesian methods which can provide better parameter estimation with smaller sample sizes. Another option is to collect additional data to increase the sample size, although this may not always be feasible.
In summary, small sample size can be a challenge for CLPMs and may result in poor model fit, but there are alternative approaches that can be used to address this issue.
Christian Geiser thank you very much for your answer! Indeed, the sample might not be too small and maybe I did a mistake with the model specification. I will have a closer look at this :)
And also thank you Ma'Mon Abu Hammad for this explanation!
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