Use of posterior predictive assessments to evaluate model fit in multilevel logistic regression

Assessing the fit of a model is an important final step in any statistical analysis, but this is not straightforward when complex discrete response models are used. Cross validation and posterior predictions have been suggested as methods to aid model criticism. In this paper a comparison is made between four methods of model predictive assessment in the context of a three level logistic regression model for clinical mastitis in dairy cattle; cross validation, a prediction using the full posterior predictive distribution and two “mixed” predictive methods that incorporate higher level random effects simulated from the underlying model distribution. Cross validation is considered a gold standard method but is computationally intensive and thus a comparison is made between posterior predictive assessments and cross validation. The analyses revealed that mixed prediction methods produced results close to cross validation whilst the full posterior predictive assessment gave predictions that were over-optimistic (closer to the observed disease rates) compared with cross validation. A mixed prediction method that simulated random effects from both higher levels was best at identifying the outlying level two (farm-year) units of interest. It is concluded that this mixed prediction method, simulating random effects from both higher levels, is straightforward and may be of value in model criticism of multilevel logistic regression, a technique commonly used for animal health data with a hierarchical structure.

Effort-reward imbalance and sedentary lifestyle: an observational study in a large occupational cohort

Objectives: To investigate the association between effort-reward imbalance (ERI) at work and sedentary lifestyle. Methods: Cross-sectional data from the ongoing Finnish Public Sector Study related to 30 433 women and 7718 men aged 17-64 were used (n = 35 918 after exclusion of participants with missing values in covariates). From the responses to a questionnaire, an aggregated mean score for ERI in a work unit was assigned to each participant. The outcome was sedentary lifestyle defined as <2.00 metabolic equivalent task (MET) hours/day. Logistic regression with generalized estimating equations was used as an analysis method to include both individual and work unit level predictors in the models. Adjustments were made for age, marital status, occupational status, job contract, smoking, and heavy drinking. Results: Twenty five percent of women and 27% of men had a sedentary lifestyle. High individual level ERI was associated with a higher likelihood of sedentary lifestyle both among women (odds ratio (OR) = 1.08, 95% CI 1.01 to 1.16) and men (OR = 1.17, 95% CI 1.02 to 1.33). These associations were not explained by relevant confounders and they were also independent of work unit level job strain measured as a ratio of job demands and control. Conclusions: A mismatch between high occupational effort spent and low reward received in turn seems to be associated with an elevated risk of sedentary lifestyle, although this association is relatively weak.