Analyses
We conducted analyses in 3 stages. First, we explored the possible endogeneity of regular smoking in regression models predicting new onset of mood and anxiety disorders through a series of instrumental variable probit analyses.42 Instrumental variable methods allowed us to assess endogeneity (i.e., an association between smoking and the error terms in the regression models for each outcome as a result of omitted common causes of both smoking and new-onset mental disorders) and to adjust for such endogeneity if present. Each instrumental variable probit regression jointly modeled smoking (as a continuous variable of average number of cigarettes smoked) and the target mental health condition. We used the variables of state-level cigarette taxes and public attitudes toward smoking as instruments in these models.
We assessed endogeneity of smoking in 2 ways: testing the ρ coefficient obtained from the maximum likelihood estimation and the Wald statistics from the 2-step estimation. The ρ coefficient represented the correlation between the error terms of the 2 jointly modeled regressions: the regression of average number of cigarettes smoked on the instrumental variables and the probit regression of new-onset mental disorders on the predicted smoking variable from the first model. A large and statistically significant ρ coefficient and a statistically significant Wald statistic suggest that the estimator for the relationship of exposure and outcome obtained from the naive regression models would not be consistent because of endogeneity of the exposure variable.31 In this case, estimators from instrumental variable probit analyses are more likely to be consistent. A nonsignificant ρ coefficient and Wald statistic would suggest that exposure is not endogenous in the model predicting the outcome and that the results of the naive regression model without instrumental variables are consistent and can be interpreted.
The models adjusted for such potential confounding variables as gender, age, race/ethnicity, household income, education (