Fixed versus Random effects models: An application in building imputation models for missing data in remote camera surveys

Document Type

Conference Proceeding

Publication Date


Conference Title

34th International Workshop on Statistical Modelling in Guimaraes, Portugal

Place of Publication



: imputation of count data, generalized linear mixed models, Bayesian sequential regression, Cholesky transformation


Statistics and Probability


The decision to specify model predictors as fixed or random effects is not always clear cut and at times different interpretations regarding their nature might be possible. This study investigated the imputation of missing counts of powerboat retrievals from camera data using climatic and temporal variables as predictors. The temporal variables could be treated as fixed or random effects. To evaluate the impact of the treatment of the temporal model predictors, patterns of observed outages were applied to a set of complete 12-month hourly camera data. The proportion of missing data ranged from 0.06 to 0.31. A variety of generalized linear and mixed models built on the Bayesian sequential regression multiple imputation framework were formulated to impute the missing values. The models were assessed using the percentage bias, root-mean-square error and skill score. Results from ten replicated multiple imputation schemes showed that the mixed effect models obtained plausible mean estimates of the total number of powerboat retrievals with less variability than those from fixed effect models. A comparison with predictive mean matching was also performed which showed that the popular predictive mean matching performed worse.