An overview of cross-sectional studies of mortality and air pollution and related statistical issues

Abstract A heuristic framework is developed for assessing statistical studies of air pollution and mortality which use the General Linear Model as a principal tool for analysis. Arrays that systematically compare the information of each study are introduced. In addition, a number of studies are contrasted against several statistical criteria to assess the reliability of the study results. Reliability is considered in terms of statistical estimation theory and practice. Finally, there is a discussion of several points of statistical contention which can affect the results of these studies. The conclusion is that statistical studies that use the General Linear Model have made limited use of available methods and tests. Several issues are raised which will require additional research.

[1]  P. Whittle,et al.  Latent Variables in Socio‐Economic Models , 1978 .

[2]  John M. Campbell,et al.  Aggregation Bias and the Demand for Housing , 1978 .

[3]  H. Vinod A Survey of Ridge Regression and Related Techniques for Improvements over Ordinary Least Squares , 1978 .

[4]  D. F. Andrews,et al.  A Robust Method for Multiple Linear Regression , 1974 .

[5]  V. Smith,et al.  Multivariate analysis: Theory and practice , 1974 .

[6]  Zvi Griliches,et al.  A Note on Serial Correlation Bias in Estimates of Distributed Lags , 1961 .

[7]  Robert Mendelsohn,et al.  An empirical analysis of air pollution dose-response curves , 1979 .

[8]  P. Frost Proxy Variables and Specification Bias , 1979 .

[9]  L B Lave,et al.  Air pollution and human health. , 1977, Science.

[10]  R. Bellman,et al.  DISTRIBUTED LAGS: A SURVEY , 1967 .

[11]  G. C. McDonald,et al.  Measures of association of some air pollutants, natural ionizing radiation and cigarette smoking with mortality rates. , 1976, The Science of the total environment.

[12]  Norman R. Draper,et al.  Applied Regression Analysis , 1968 .

[13]  H. Glejser A New Test for Heteroskedasticity , 1969 .

[14]  H. Theil Principles of econometrics , 1971 .

[15]  L. D. Hamilton,et al.  Mortality, migration, income and air pollution: a comparative study. , 1978, Social science & medicine. Medical geography.

[16]  R. W. Farebrother,et al.  The statistical implications of pre-test and Stein-rule estimators in econometrics , 1978 .

[17]  Phoebus J. Dhrymes,et al.  Distributed Lags: Problems of Estimation and Formulation , 1972 .

[18]  James B. Ramsey,et al.  A Monte Carlo Study of Some Small Sample Properties of Tests for Specification Error , 1972 .

[19]  Arnold Zellner,et al.  Statistical Analysis of Econometric Models , 1979 .

[20]  Toshihisa Toyoda,et al.  Pre-testing on part of the data , 1979 .

[21]  G. Maddala,et al.  THE USE OF VARIANCE COMPONENTS MODELS IN POOLING CROSS SECTION AND TIME SERIES DATA , 1971 .

[22]  P. Loeb Specificaton Error Tests and Investment Functions , 1976 .

[23]  Z. Griliches ERRORS IN VARIABLES AND OTHER UNOBSERVABLES , 1974 .

[24]  H. Theil,et al.  Three-Stage Least Squares: Simultaneous Estimation of Simultaneous Equations , 1962 .

[25]  Melvin J. Hinich Estimating the Lag Structure of a Nonlinear Time Series Model , 1979 .

[26]  G. C. McDonald,et al.  Instabilities of Regression Estimates Relating Air Pollution to Mortality , 1973 .

[27]  Jan Kmenta,et al.  Elements of econometrics , 1988 .

[28]  Tsoung-Chao Lee,et al.  The Theory and Practice of Econometrics , 1981 .

[29]  P. J. Huber The 1972 Wald Lecture Robust Statistics: A Review , 1972 .

[30]  N. Davies,et al.  Error Mis-Specification and Spurious Regressions , 1978 .

[31]  S. Shapiro,et al.  A Comparative Study of Various Tests for Normality , 1968 .

[32]  D. F. Morrison,et al.  Multivariate Statistical Methods , 1968 .

[33]  R. Farebrother Estimation with aggregated data , 1979 .

[34]  J. B. Ramsey,et al.  Tests for Specification Errors in Classical Linear Least‐Squares Regression Analysis , 1969 .

[35]  R. Hogg Statistical Robustness: One View of its use in Applications Today , 1979 .

[36]  Kenneth A. Fegley,et al.  Path Analysis in Systems Science , 1974, IEEE Trans. Syst. Man Cybern..

[37]  Allan J. Taub Prediction in the context of the variance-components model , 1979 .

[38]  Norman R. Draper,et al.  Ridge Regression and James-Stein Estimation: Review and Comments , 1979 .

[39]  S. Gerking,et al.  What Do We Know about Benefits of Reduced Mortality from Air Pollution Control , 1981 .

[40]  Raymond J. Carroll,et al.  On Estimating Variances of Robust Estimators When the Errors are Asymmetric , 1979 .

[41]  D. Rubinfeld,et al.  Econometric models and economic forecasts , 2002 .

[42]  A. Goldberger,et al.  On Pure and Mixed Statistical Estimation in Economics , 1961 .

[43]  ENVIRONMENTS AND URBAN MORTALITY. AN ECONOMETRIC APPROACH , 1973 .

[44]  Estimating and Testing a Linear Model When an Extraneous Information Exists , 1978 .

[45]  G. Box,et al.  Robustness to non-normality of regression tests , 1962 .

[46]  T. Hassard,et al.  Applied Linear Regression , 2005 .

[47]  R. Koshal,et al.  Air pollution and the respiratory disease mortality in the United States—a quantitative study , 1974 .

[48]  Regression Analysis Based on the Signs of the Residuals , 1979 .

[49]  J. F. Lawless,et al.  Mean Squared Error Properties of Generalized Ridge Estimators , 1981 .

[50]  L. Lave,et al.  The health effects of air pollution: a reanalysis. , 1982, Journal of urban economics.