Monitoring habitat types by the mixed multinomial logit model using panel data

Habitats in the Wadden Sea, a world heritage area, are affected by land subsidence resulting from naturalgas extraction and by sea level rise. Here we describe a method to monitor changes in habitat types byproducing sequential maps based on point information followed by mapping using a multinomial logitregression model with abiotic variables of which maps are available as predictors.In a 70 ha study area a total of 904 vegetation samples has been collected in seven sampling roundswith an interval of 2–3 years. Half of the vegetation plots was permanent, violating the assumptionof independent data in multinomial logistic regression. This paper shows how this dependency can beaccounted for by adding a random effect to the multinomial logit (MLN) model, thus becoming a mixedmultinomial logit (MMNL) model. In principle all regression coefficients can be taken as random, butin this study only the intercepts are treated as location-specific random variables (random interceptsmodel). With six habitat types we have five intercepts, so that the number of extra model parametersbecomes 15, 5 variances and 10 covariances.The likelihood ratio test showed that the MMNL model fitted significantly better than the MNL modelwith the same fixed effects. McFadden-R2for the MMNL model was 0.467, versus 0.395 for the MNL model.The estimated coefficients of the MMNL and MNL model were comparable; those of altitude, the mostimportant predictor, differed most. The MMNL model accounts for pseudo-replication at the permanentplots, which explains the larger standard errors of the MMNL coefficients. The habitat type at a givenlocation-year combination was predicted by the habitat type with the largest predicted probability. Theseries of maps shows local trends in habitat types most likely driven by sea-level rise, soil subsidence,and a restoration project.We conclude that in environmental modeling of categorical variables using panel data, dependencyof repeated observations at permanent plots should be accounted for. This will affect the estimatedprobabilities of the categories, and even stronger the standard errors of the regression coefficients.