The best way to learn multilevel structural equation modeling in xxM is to work through concrete examples. This page will lead you through different examples of linear mixed effects (lme) models, traditional multilevel models (MLM), and multilevel structural equation models (ML-SEM). Each example includes a path-diagram, complete model specification using scalar equations and matrices and complete specification of the model using xxM. Log and output of interactive session of fitting xxM models are also included.

First time users should begin with the “Hello xxM” example which describes everything you need to know about specifying a “two level – bivariate mixed-effects model”. Once you understand how models are ML-SEM models are specified in xxM, you could work through examples similar to your own data.

Name | Source | Data | Levels | Latent variable | Random slope | Structure | Model | LME |

Hello xxM | Mehta | Simulated | 2 | No | No | Nested | Bivariate random-intercepts model | Yes |

Stuff to dye for | Bates | Dyestuff | 2 | No | No | Nested | Random-intercepts model | Yes |

Strong stuff | Bates | Pastes | 3 | No | No | Nested | Random-intercepts model | Yes |

Big bugs | Bates | Penicillin | 3 | No | No | Crossed | Random-intercepts model | Yes |

Reading to learn | Branum-Martin | Reading | 2 | No | Yes | Nested | Random-slope for a continuous covariate | Yes |

Boys & Girls | Goldstein | GCSEMV | 2 | No | No | Nested | Random-slope for a categorical covariate | Yes |

Feeling better – long | Hedeker | Reisby | 2 | No | Yes | Longitudinal | Linear growth curve model | Yes |

Feeling better – wide | Hedeker | Reisby | 1 | Yes | Yes | Longitudinal | Latent growth curve model | No |

Learning to read | Mehta | Reading | 2 | Yes | No | Nested | Two-level Confirmatory Factor Analysis | No |

Pretty faces | Wickham | Faces | 3 | No | No | Crossed | bivariate cross-classified model | Yes |

Quality schools or effective teachers | Mehta | Simulated | 3 | Yes | No | Nested | Across-level latent variable regression | No |

Two-level CFA with random-slope | Mehta | Simulated | 2 | Yes | Yes | Nested | Random slopes with latent dependent variable | No |