A simplified approach for establishing estimable functions in fixed effect age-period-cohort multiple classification models.

Estimable functions play an important role in learning about certain aspects of the impact of ages, periods, and cohorts in age-period-cohort multiple classification (APCMC) models. The advantage of these estimates is that they are unbiased estimates of, for example, the deviations of age, period, and cohort effects from their linear trends, or changes in the linear trends of cohort effects within cohorts, or the residuals of fixed effect APCMC models. If the fixed effect APCMC model contains the relevant variables (is well specified), these estimable functions are unbiased estimates of functions of the parameters that generated the dependent variable data, even though the parameters that generated that data are not identified.

A consistent and general modified Venn diagram approach that provides insights into regression analysis.

Venn diagrams are used to provide an intuitive understanding of multiple regression analysis and these diagrams work well with two variables. The area of overlap of the two variables has a one-to-one relationship to the squared correlation between them. This approach breaks down, however, with three-variables.

Mixed models, linear dependency, and identification in age-period-cohort models.

This paper examines the identification problem in age-period-cohort models that use either linear or categorically coded ages, periods, and cohorts or combinations of these parameterizations. These models are not identified using the traditional fixed effect regression model approach because of a linear dependency between the ages, periods, and cohorts. However, these models can be identified if the researcher introduces a single just identifying constraint on the model coefficients.

Visualizing rank deficient models: a row equation geometry of rank deficient matrices and constrained-regression.

Situations often arise in which the matrix of independent variables is not of full column rank. That is, there are one or more linear dependencies among the independent variables. This paper covers in detail the situation in which the rank is one less than full column rank and extends this coverage to include cases of even greater rank deficiency.

Variations in age-specific homicide death rates: a cohort explanation for charges in the age distribution of homicide deaths.

An age-period-cohort characteristic model previously used to explain age-period-specific rates of homicide arrests for those 15 to 49 from 1960 to 1995 is applied to measures of age-period-specific homicide deaths. The extension of this model to the examination of homicide victimization is significant because we are able to test the utility of the model across a longer time span (1930 to 1995) and a wider range of ages (10 to 79) and disaggregated by sex and race (Whites and non-Whites). Although the results indicate that past and recent shifts in age-period-specific rates of homicide deaths are associated with specific characteristics of cohorts, there are some important differences across race and sex groupings in the effects of these characteristics.