Researchers have frequently attempted to decompose temporal trends in social, demographic, economic, and health outcomes into three aspects of time processes: age, period, and cohort. The analytical problem that has faced analysts for decades is that these three distinct processes are linearly related to each other (cohort = period - age), so disaggregation of temporal trends has to rely on statistical assumptions that are difficult to verify. In this dissertation, I critically evaluate the validity and application scope of two commonly used age-period-cohort (APC) methods: the Intrinsic Estimator and the Cross-Classified Fixed/Random Effects Model. I identify the methodological and theoretical limitations of these methods and conclude that these methods should not be used for estimating the underlying age, period, and cohort patterns without explicit theoretical justification. What should researchers do? Drawing on the literature of demography, sociology, and statistics, I develop a new method, called the age-period-cohort-interaction (APC-I) model, for analyzing age, period, and cohort variations. Unlike other APC methods, the APC-I model is fully identified and does not rely on problematic statistical assumptions. It also relaxes this assumption in other methods about within-cohort dynamics. I use the new APC-I model to analyze the 1962 to 2014 data from the Current Population Survey March Supplement to investigate age and period patterns and deviations between cohorts and dynamics within a cohort’s life course in labor force participation (LFP) for white and black men and women. I found that while men’s LFP was sensitive to social and economic events such as economic recessions and wars, the effects of these events may not carry on to their later ages. However, there are substantial variations in women’s LFP associated with cohort membership that cannot be explained by pure age and period main effects. I also found that while white women’s LFP rates caught up with and exceed those of black women by 1980, after adjusting for educational attainment, the racial differences in participation rates among women were substantially reduced after the late 1980s. In addition, the results suggested that a great deal of the period trend and cohort deviations in black women’s LFP can be explained by changes in their educational attainment. This is less true for white women; the cohort deviations in participation rates remained after adjusting for education. Surprisingly, there was little evidence supporting an association between changes in marital status and the temporal trends in LFP; the shape of the age, period, and cohort patterns in LFP did not seem to change qualitatively after controlling for current marital status. This finding suggests that the temporal variation in LFP may stem from changes in the behaviors of subgroups of the population other than changes in the marriage composition of the population.