Theil [12] proposed three instruments to be applied in regression analysis with prior stochastic information. Two of them are: a quadratic form (known as compatibility test) and a measure of the share of sample information on posterior variance. Duly modified, they are proposed in the paper to investigate if data come from a linear regression model or from a linear latent growth model. We compare a covariance matrix due to sample information and a total variance due to both sample and prior information following the two approaches:  (i) by the difference of two quadratic forms based on the structure of the Theil’s compatibility test and (ii) by the product of two covariance matrices based on a measure of an estimated share of sample information in total variability. The first approach depends on the approximations to chi-square distributions which are discussed in the Appendix. The second one is based on a comparison of empirical cumulative distribution functions. A simple algorithm based on the bootstrap is proposed for this comparison.

linear latent growth model, linear regression model, empirical cumulative distribution function, chi-square approximation, quadratic form.