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Keywords:

  • continuous time modeling;
  • ALT model;
  • exact discrete model;
  • approximate discrete model;
  • stochastic differential equation;
  • reciprocal relations;
  • structural equation modeling

Over the past decades, several analytic tools have become available for the analysis of reciprocal relations in a non-experimental context using structural equation modeling (SEM). The autoregressive latent trajectory (ALT) model is a recently proposed model [BOLLEN and CURRAN Sociological Methods and Research (2004) Vol. 32, pp. 336–383; CURRAN and BOLLEN New Methods for the Analysis of Change (2001) American Psychological Association, Washington, DC], which captures features of both the autoregressive (AR) cross-lagged model and the latent trajectory (LT) model. The present article discusses strengths and weaknesses and demonstrates how several of the problems can be solved by a continuous-time version: the continuous-time autoregressive latent trajectory (CALT) model. Using SEM to estimate the exact discrete model (EDM), the EDM/SEM continuous-time procedure is applied to a CALT model of reciprocal relations between antisocial behavior and depressive symptoms.