Age-period-cohort analysis: an illustration of the problems in assessing interaction in one observation per cell data

The age–period–cohort conundrum as two fundamental problems

“…If not the results will not mirror the data generating process. To the extent that the constraint, represented by the vector c times the vector of population effect coefficients is not zero (c β = 0), then the estimates of the effect coefficients are biased (see Kupper et al 1983 for an explication of the bias associated with violating this assumption).…”

“…Specifically, v is the null vector (the vector of coefficients that when multiplied times the columns of the X-matrix results in the zero vector). To the extent that this assumption is not true, the estimates associated with this constraint will be biased (again Kupper et al 1983 explicate the degree of bias associated with violating this assumption). The generalized inverse that is associated with this the constraint used by Yang et al (2008) is the Moore-Penrose generalized inverse (Mazumdar et al 1980).…”

“…The assumption is that c T β = 0, where c is the m × 1 vector for the constraint and β is the m × 1 vector of population effect coefficients. To the extent that c T β = 0 is not true, the estimates will be biased (see Kupper et al 1983 for an explication of the bias associated with violating this assumption).…”

Age, cohort and period effects on hip fracture incidence: analysis and predictions from New Zealand data 1974-2007

“…The methodological challenge in the estimation of the individual effects of age, period, and cohort in APC models is that multiple estimators yield the same fitted values, thus true effects are difficult to estimate simultaneously [27]. Any analysis within the framework of CGLM requires an additional assumption about those effects.…”

Understanding the Effects of Age, Period, and Cohort on Incidence and Mortality Rates

“…Because the interactions saturate the model that only includes main effects due to age and period, you might think of the cohort effect as a particular type of age-period interaction (25). Similarly , you could describe the period effect as a particular type of age-cohort interaction.…”