On the Robustness of LISREL (Maximum Likelihood Estimation) Against Small Sample Size and Non-normality.

Abstract

This book is a comprehensive and readable guide to the large body of literature on unequal probability sampling. It may be recommended strongly to students and practitioners of sampling theory. After a brief introduction, the authors list in their order of appearance in the literature (1949-79) 50 procedures for probability proportional to sampling without replacement. They classify these by manner of selection, joint inclusion probabilities, and the appropriate type of estimator. In Chapter 2 the procedures are described in detail and given more refined classifications. Their strengths and limitations are compared in Chapters 3 and 4, with useful summary tables rounding out the discussion. Chapter 5 gives a brief look at the algebra of unequal probability multistage sampling. In Chapter 6 (to this reviewer the most interesting) the authors discuss recent work on robust sampling estimation, particularly Brewer (1979). The approach taken is conventional in that the performance criteria for design-estimator strategies include ease of implementation, designunbiasedness or asymptotic design-unbiasedness of the estimator, and availability of a design-unbiased variance estimator. Although a regression model with size as the independent variable is used to compare expected mean-squared errors of the strategies, the influence of the model on the inference itself is downplayed. Nevertheless, the authors often invoke for estimators what they called the ratio estimator property.' They do not define it in full generality, but it seems mathematically equivalent to unbiasedness under the regression model. Also, the large-sample variance estimator that they suggest when the design-based one is difficult to compute is one that estimates expected variance under the model. The authors have attempted to argue that the conventional approach is appropriate for enumerative as opposed to analytic inference. Some effort has been made at a theoretical justification of the performance criteria they consider. However, the authors are most convincing when they argue for unequal probability sampling, on practical grounds, as an alternative to fine stratification. There are infrequent misprints in the text, and Chapter 5 could have referred to Stuart (1963) and Durbin (1953). All in all, however, the book may be hailed as a fitting summary of 30 years of sampling research.