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.

Work stress, smoking status and smoking intensity: an observational study of 46 190 employees

Study objective: To examine the relationship between work stress, as indicated by the job strain model and the effort-reward imbalance model, and smoking. Setting: Ten municipalities and 21 hospitals in Finland. Design and Participants: Binary logistic regression models for the prevalence of smoking were related to survey responses of 37 309 female and 8881 male Finnish public sector employees aged 17-65. Separate multinomial logistic regression models were calculated for smoking intensity for 8130 smokers. In addition, binary logistic regression models for ex-smoking were fitted among 16 277 former and current smokers. In all analyses, adjustments were made for age, basic education, occupational status, type of employment and marital status. Main results: Respondents with high effort-reward imbalance or lower rewards were more likely to be smokers. Among smokers, an increased likelihood of higher intensity of smoking was associated with higher job strain and higher effort-reward imbalance and their components such as low job control and low rewards. Smoking intensity was also higher in active jobs in women, in passive jobs and among employees with low effort expenditure. Among former and current smokers, high job strain, high effort-reward imbalance and high job demands were associated with a higher likelihood of being a current smoker. Lower effort was associated with a higher likelihood of ex-smoking. Conclusions: This evidence suggests an association between work stress and smoking and implies that smoking cessation programs may benefit from the taking into account the modification of stressful features of work environment. Key words: effort-reward imbalance; job strain; smoking. Abbreviations: OR, odds ratio; CI, confidence interval; SES, socioeconomic status

Effort-reward imbalance at work and the co-occurrence of lifestyle risk factors: cross-sectional survey in a sample of 36,127 public sector employees

Background In occupational life, a mismatch between high expenditure of effort and receiving few rewards may promote the co-occurrence of lifestyle risk factors, however, there is insufficient evidence to support or refute this hypothesis. The aim of this study is to examine the extent to which the dimensions of the Effort-Reward Imbalance (ERI) model – effort, rewards and ERI – are associated with the co-occurrence of lifestyle risk factors. Methods Based on data from the Finnish Public Sector Study, cross-sectional analyses were performed for 28,894 women and 7233 men. ERI was conceptualized as a ratio of effort and rewards. To control for individual differences in response styles, such as a personal disposition to answer negatively to questionnaires, occupational and organizational -level ecological ERI scores were constructed in addition to individual-level ERI scores. Risk factors included current smoking, heavy drinking, body mass index ≥25 kg/m2, and physical inactivity. Multinomial logistic regression models were used to estimate the likelihood of having one risk factor, two risk factors, and three or four risk factors. The associations between ERI and single risk factors were explored using binary logistic regression models. Results After adjustment for age, socioeconomic position, marital status, and type of job contract, women and men with high ecological ERI were 40% more likely to have simultaneously ≥3 lifestyle risk factors (vs. 0 risk factors) compared with their counterparts with low ERI. When examined separately, both low ecological effort and low ecological rewards were also associated with an elevated prevalence of risk factor co-occurrence. The results obtained with the individual-level scores were in the same direction. The associations of ecological ERI with single risk factors were generally less marked than the associations with the co-occurrence of risk factors. Conclusion This study suggests that a high ratio of occupational efforts relative to rewards may be associated with an elevated risk of having multiple lifestyle risk factors. However, an unexpected association between low effort and a higher likelihood of risk factor co-occurrence as well as the absence of data on overcommitment (and thereby a lack of full test of the ERI model) warrant caution in regard to the extent to which the entire ERI model is supported by our evidence.