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

This paper discusses the specific problems of age-period-cohort (A-P-C) analysis within the general framework of interaction assessment for two-way cross-classified data with one observation per cell. The A-P-C multiple classification model containing the effects of age groups (rows), periods of observation (columns), and birth cohorts (diagonals of the two-way table) is characterized as one of a special class of models involving interaction terms assumed to have very specific forms. The so-called A-P-C identification problem, which results from the use of a particular interaction structure for detecting cohort effects, is shown to manifest itself in the form of an exact linear dependency among the columns of the design matrix. The precise relationship holding among these columns is derived, as is an explicit formula for the bias in the parameter estimates resulting from an incorrect specification of an assumed restriction on the parameters required to solve the normal equations. Current methods for modeling A-P-C data are critically reviewed, an illustrative numerical example is presented, and one potentially promising analysis strategy is discussed. However, gien the large number of possible sources for error in A-P-C analyses, it is strongly recommended that the results of such analyses be interpreted with a great deal of caution.     

Time series analysis of stratospheric ozone

Time series analyses of monthly average total ozone measured at 37 stations throughout the world were used to estimate the extent to which the average ozone trend correlates with the depletion curve hypothesized as due to chlorofluorocarbons (CFCs). Statistical characteristics of stations in the ensemble were used to help define appropriate model and station selection criteria. The maximum likelihood procedure developed herein estimates the weighted average trend, its. variance, and the intra- and inter-station variance components of the trend. Correlations among trends at different stations are also taken into account. The models were subjected to much checking and criticism. Variations in statistical methodology are used to show that the results are insensitive to details of the model selection criteria. The method does not discriminate well between the hypothesized CFC trend and a linear trend. The trend estimates represent the sum of all long-term global effects. The variance includes all effects that differ from station-to-station. The estimated trend and 2α limits for 14 stations with 20-year records (1958-79) is an ozone increase through 1979 of (1.5+1.0) percent. At the 23 stations with shorter records, the trend is (1.0=1.7) percent. It is concluded that no significant depletion in stratospheric ozone has occurred from any cause through the end of 1979.     

Comparison of tests for bivariate symmetry versus location and/or scale alternatives

This paper studies the performance of tests which use a null hypothesis of bivariate symmetry and detect the broad class of location and/or scale alternatives . The conditionally distribution-free tests of Sen (1967) and Hollander (1971) and parametric tests related to those of Bell and Haller (1969) are compared in a Monte Carlo study which also includes a new conditionally distribution-free test.     

Bayesian prediction bounds for the pareto lifetime model

Suppose that the length of time in years for which a business operates until failure has a Pareto distribution. Let x₁ ≤ x₂ x₃ ≤…≤z_k denote the survival lifetimes of the first k of a random sample of n businesses. Bayesian predictions are to be made on the ordered failure times of t h e remaining (n-k) businesses, using the conditional probability density function. Examples are given to illustrate our results.     

A simple method for constructing confounded designs for mixed factorial experiments

This paper presents the sinplesr procedure that uses wodular aryithmetic for constructing confounded designs for mixed factorial experiments. The present procedure and the classical one for confounding in symmetrical factorial experiments are both at the same mathema.tical level. The present procedure is written for

practitioners and is lllustrared with several examples.     

The relationship between two parameterizations of linear patterned mean and covariance models

Andrade and Helms (1984) study problems involving estimation and testing of linearly patterned mean and covariance matrices. They parameterize their models under the null hypothesis by using linear constraints on the alternative hypothesis parameterization. In this paper, we show that the nested models that Andrade and Helms consider can be transformed into the nested models considered by Anderson (1969, 1970, 1973) and Szatrowski (1979, 1980, 1981, 1983, 1985).     

Moment properties of estimators for a type 1 extreme-value regression model

A regression model is considered in which the response variable has a type 1 extreme-value distribution for smallest values. Bias approximations for the maximum likelihood estimators are pivm and a bias reduction estimator for the scale parameter is proposed. The small sample moment properties of the maximum likelihood estimators are compared with the properties of the ordinary least squares estimators and the best linear unbiased estimators based on order statistics for grouped data.     

An extension of the median test to analysis of variance

In a k-way analysis of variance model, the major concern is testing for main effects and for the presence of interaction between the factors. When the assumptions of normality and equal variances are satisfied, the appropriate test to use is the usual F-test for ANOVA. However, when the normality assumption is not satisfied then a robust or nonparametric test is needed to conduct the analysis. In this paper a nonparametric method based on cell counts is proposed. Each cell is divided into L subcells based on predetermined outpoints and the resulting frequencies are laid out in a contingency table. Then the Pearson x² and tne likelihood ratio tests are performed. A comparison with the classical ANOVA F-test indicates that the proposed method is preferable when the data comes from a thick-tailed highly skewed distribution.