We tested item-level measurement invariance for birth cohort by using multiple-indicator, multiple-cause (MIMIC) models with a weighted least squares parameter estimates with standard errors and a mean- and variance-adjusted chi-square test statistic that used a full weight matrix (an estimator appropriate for use with categorical data) (Johnson et al., 2008; Kline, 2010). MIMIC models are structural equation models that can examine group-specific effects on item responses relative to a reference group, without mediation through a latent variable (i.e., nicotine dependence). Figure 1 provides an example of a MIMIC model testing an item-level difference in FTND item 5 (smoke more frequently during the first hours after waking than during the rest of the day) by birth cohort, with those born <1945 as the reference. Each FTND item was tested this way. Modeling the direct paths from each birth cohort, adjusting for nicotine dependence level, results in estimates of response differences attributable to measurement non-invariance. Models including direct paths from each birth cohort to each FTND item were compared to nested models, where direct paths were fixed to zero using Mplus difftest
