# Leo A GoodmanUniversity of CA, Berkeley · Dept. of Soc. & Dept. of Stat.

Leo A Goodman

Ph.D. in Mathematics, from Princeton Univ.

## About

145

Publications

15,803

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

21,294

Citations

## Publications

Publications (145)

We craft a historically sensitive model of entrepreneurship linking individual actors to the evolving social structures they must navigate to acquire resources and launch new ventures. Theories of entrepreneurship and industry evolution suggest two opposing hypotheses: as an industry develops, launching a new venture may become more difficult for a...

In this article we present a method for obtaining simultaneous confidence intervals for the parameters of a multinomial distribution, and we compare this method with the one suggested recently by Quesenberry and Hurst (1964). For the usual probability levels, we find, for example, that the confidence intervals introduced here have the desirable pro...

A statistical argument was presented quite recently, as an Op-Ed in The Los Angeles Times, purporting to conclude that the US Ninth Circuit Court of Appeals should be split. A corresponding statistical counterargument and critique are introduced in the present paper, by making use of some combinatorial formulas and by proposing an alternative empir...

This essay describes in simple terms some of the major concepts of categorical data analysis (CDA) that have been and will continue to be useful in the analysis of sociological data, examples of which include data in the area of social stratification and mobility, and in many other areas that make use of survey data and/or panel studies data, and i...

Consider an m-way cross-classification table (for m = 3, 4, …) of m dichotomous variables that describes (1) the 2m possible response patterns to a set of m questions (where the response to each question is binary), and (2) the number of individuals whose responses to the m questions can be described by a particular response pattern, for each of th...

Discussion of ``The William Kruskal Legacy: 1919--2005'' by Stephen E. Fienberg, Stephen M. Stigler and Judith M. Tanur [arXiv:0710.5063]

This article has two main purposes. The first main purpose is to take note of some of Dudley Duncan's major contributions as a quantitative sociologist, as the leader in introducing path analysis and related structural equation models to sociology, as a pioneer in applying loglinear models and related models in many different sociological contexts,...

Many interesting sociological questions pertain to how the association between two variables depends on a third variable. In sociological applications, the third variable often pertains to countries, to subgroups of a population, or to time periods. We propose a regression-type approach that specifies that the log-odds- ratios that describe the two...

This note considers various ways of analyzing survey data pertaining to a central thesis of The Time Bind(Hochschild, 1997), and it comments on the particular analysis presented by Brown and Booth (2002). The following kinds of problems will be discussed here: (1) problems pertaining to the measurement of concepts, (2) problems pertaining to the se...

This paper begins by comparing Henri Caussinus' con- cept of quasi-symmetry with a related but different concept that I shall call Karl Pearson's quasi-symmetry; and we shall find that Caussinus' concept is preferable to and more useful than Pearson's concept. I shall then introduce a set of quasi-symmetric log-bilinear models that are more

We introduce some simple models that can be viewed as special cases of the general model and general approach to analyzing the association in multiway tables that we first presented in 1998. We use two empirical examples to demonstrate the flexibility and utility of the simple models introduced here and of our general approach.

Interesting gender differences are found in this article in the observed patterns of the job characteristics that are considered here characteristics of men's jobs and characteristics of women's jobs. By applying the methods of latent structure analysis to analyze data on job characteristics obtained in a British national survey, the authors find t...

In the usual statistical analysis of the entries (frequencies) in a contingency table having I rows and J columns (I ≥ 2, J ≥ 2), an important role is often played by the usual null hypothesis of independence (i.e., the hypothesis that the row variable and the column variable are statistically independent of each other). In the situation considered...

Singular value decompositions are used to study interactions in two-way layouts. In contrast to traditional treatments, emphasis is on description of the nature of the interactions rather than on tests of whether they do or do not exist. The first model considered assumes that the matrix of interactions has rank 1, so in a singular value decomposit...

This paper describes new methods for analyzing the intrinsic character of qualitative variables (variables pertaining to nominal attributes and/or to ordinal categorical classifications), using the observed cross-classification table pertaining to these variables. The new methods can be applied to determine whether the particular variables of inter...

This paper is an expanded version of an invited paper presented by the author at the 45th Session of the International Statistical Institute in Amsterdam, Netherlands. It describes how correspondence analysis models can serve as an extension of the usual correspondence analysis approach, and how log-bilinear models can serve as an extension of the...

Statistical methods are presented to facilitate a more complete analysis of results obtained when a scaling model is applied to data from two or more groups. These methods can be used to (a) compare the corresponding estimated latent distributions obtained using the scaling model applied to the different groups, (b) compare the corresponding estima...

Statistical methods are introduced for latent structure analysis of a set of two or more multidimensional contingency tables. Three basic classes of models are considered: (a) models that assume complete homogeneity across tables, (b) models that allow partial homogeneity across tables, and (c) models that allow complete heterogeneity. Methods are...

To analyse the dependence of a qualitative (dichotomous or polytomous) response variable upon one or more qualitative explanatory variables, log-linear models for frequencies are compared with log-linear models for odds, when the categories of the response variable are ordered and the categories of each explanatory variable may be either ordered or...

Association models considered by Goodman (1979) for contingency tables with ordered categories are presented here in a somewhat different form to facilitate comparison with the bivariate normal. Association models can be applied when an underlying bivariate normal is assumed and also under more general conditions, and they provide alternatives to t...

The association models considered in Goodman (1979a) for the analysis of cross-classifications having ordered categories are presented in a somewhat different form in the present article to facilitate comparison of the results obtained using these models with those obtained using the earlier canonical correlation approach. Both the association mode...

For the analysis of square contingency tables having ordered categories, this paper introduces the diagonals-parameter symmetry model and other related multiplicative models. When these models are applied to the 4 × 4 table on unaided vision first analysed by Stuart (1953, 1955), a possible explanation is obtained for (i) the `strange residual patt...

A class of models is proposed for the analysis of association in a contingency table with ordered rows and ordered columns. Association is measured in terms of the odds-ratios in 2 × 2 subtables formed from adjacent rows and adjacent columns. This class includes the null association model, the uniform association model, and models that describe the...

This brief note on quasi-independent triangular contingency tables uses the simple partitioning method, and corresponding explicit formulae for the estimated parameters, presented by Goodman (1968) for such tables, in order to obtain a simple explanation and further understanding of (a) the formulae for estimated parameters and their standard error...

Appropriate methods for the causal analysis of certain kinds of systems of quantitative variables have been available for some time now, and they provide useful tools for the research worker in sociology, and in other fields as well, who may be concerned with the study of quantitative variables. Appropriate methods for the causal analysis of corres...

The latent structure model considered here postulates that a population of individuals can be divided intom classes such that each class is homogeneous in the sense that for the individuals in the class the responses toN dichotomous items or questions are statistically independent. A method is given for deducing the proportions of the population in...

The abstract for this document is available on CSA Illumina.To view the Abstract, click the Abstract button above the document title.

To analyze the "scalability" of the observed response patterns for a set of m dichotomous items, we introduce a model in which a given individual in the population is either "intrinsically scalable" or "intrinsically unscalable" (with respect to the m items), and there are d different types of "intrinsically scalable" individuals. With this model,...

This note solves a problem posed by Berkson and Nagnur at the end of their recent article [2]. The problem pertains to the relationship between two particular statistics that can be used in the three-way contingency table to test the null hypothesis H<sub>0</sub> of zero three-factor interaction; viz., the usual chi-square goodness-of-fit statistic...

This paper considers a wide class of latent structure models. These models can serve as possible explanations of the observed
relationships among a set of m manifest polytomous variables. The class of models considered here includes both models in which the parameters are identifiable
and also models in which the parameters are not. For each of the...

A set of age-specific rates of birth and death implies expected numbers of kin. An individual girl or woman chosen at random out of a population whose birth and death rates are specified can be expected to have a certain number of older sisters, younger sisters, nieces, cousins; expressions for these values are provided for both total kin and kin w...

This article presents methods for analyzing the relationships among a set of qualitative variables when some of these variables are specified manifest (i.e., observed) variables and others are latent (i.e., unobserved or unobservable) variables. We shall show how to estimate the magnitude of the various effects represented in pathdiagram models tha...

Models and methods for analyzing the relations among a set of polytomous variables, when some of the variables are posterior to others, are presented. The techniques proposed here yield 'path diagrams' that are somewhat analogous to those used in path analysis. Earlier path analysis models are not suited to the case where the variables are polytomo...

The combined use of direct estimation (in saturated models) and indirect testing (of unsaturated models), proposed in [7, 8] for the analysis of a given multidimensional contingency table, is extended here to the analysis of a set of T multidimensional tables (T ≥ 2). For this set of tables, a three-fold classification of models is introduced: (1)...

The asymptotic sampling theory discussed in our 1963 article [3] for measures of association presented in earlier articles [1, 2] turns on the derivation of asymptotic variances that may be complex and tedious in specific cases. In the present article, we simplify and unify these derivations by exploiting the expression of measures of association a...

The abstract for this document is available on CSA Illumina.To view the Abstract, click the Abstract button above the document title.

To illustrate the models and methods of the present article, we shall reanalyze those data in the famous study of The American Soldier by Stouffer et al. (1949), subsequently analyzed by Coleman (1964), Zeisel (1968), and Theil (1970). The methods we present reveal how the odds pertaining to a given dichotomized variable (e.g., the odds that a sold...

In this article, we first present a brief elementary exposition of the discrete model of population growth, and some of the results that can be derived from that model. We then use these results to study the sensitivity of the intrinsic growth rate to (a) certain kinds of over-all multiplicative changes in the age-specific birth and death rates, (b...

A step-by-step method is presented herein for partitioning a certain kind of hypothesis H about the m-way contingency table into (a) a series of hypotheses about marginal tables formed from the m-way table by ignoring one or more of table's m dimensions; and (b) a hypothesis about independence, conditional independence, or conditional equiprobabili...

For the m-way contingency table, we consider models that describe the possible multiplicative interactions among the m variables of the table, and we show how to select models that fit the data in the table, using methods that are, in part, somewhat analogous to the usual stepwise procedures in regression analysis. (The m variables here are dichoto...

For the m-way contingency table, we discuss both the direct estimation of the multiplicative interactions among the m variables, and the indirect testing of hypotheses pertaining to these interactions. We consider, among other things, hierarchical hypotheses pertaining to the interactions among the m variables, including hypotheses that can be expr...

We trace the social positions of the men and women who found new enterprises from the earliest years of one industryâ€™s history to a time when the industry was well established. Sociological theory suggests two opposing hypotheses. First, pioneering entrepreneurs are socially prominent individuals from fields adjacent to the new industry and later...

How has access to the public sphere been affected by the rise of mass media? We address this question by studying magazines in America from the eighteenth century, when all periodicals had small circulations, to the mid-nineteenth century, when many reached mass audiences. Specifically, we investigate how the social positions of those who founded n...

Typewritten ms., dated 1950. Thesis (Ph.D.)--Princeton University, 1951. Includes bibliographical references leaf 70. Abstract: 2 leaves at beginning. (Copy 2) Carbon copy of typewritten ms.

Considering a cross-classification table that describes an aspect of social mobility (the relation between origin status and destination status) for a population of individuals, this paper shows that the usual indices of mobility (or immobility), which are based upon a comparison of the observed frequencies in the mobility table with the correspond...

This paper presents a method of partitioning a χ2 statistic for the I x J x K contingency table (viz. the χ2 statistic that is based upon the likelihood‐ratio criterion for testing the null hypothesis that the three variables pertaining to the three‐way table are mutually independent) into additive components that can be used to test (1) the null h...

The abstract for this document is available on CSA Illumina.To view the Abstract, click the Abstract button above the document title.

In this paper we present stochastic models to describe the changes that take place with time in the numbers of females and males in the various age-intervals in the population. We first consider the case where females, or males, are marriage dominant, i.e. where the joint distribution of the numbers of boys and girls born at time t depends upon the...

This article presents an elementary approach to the study of the population projection-matrix, the reverse (or inverse) projection-matrix, the process of population growth generated by the projection-matrix, the “prior” process of population growth associated with the reverse projection-matrix, the stable age-distribution that pertains to the proje...

In this paper we determine, for an individual of age x existing at some specified point in time, the probability p(x) that his line of descendants will eventually become extinct, for the age-dependent birth-and-death process studied by D. G. Kendall (1949) and Bartlett (1955) in which the time-scale and age-scale are continuous, and also for the an...

Resumen
Este artículo presenta nuevasfórmulas para calcular la proporción eventual de sexos y la composición eventual de sexos por edad de la población que resultaría de determinadas condiciones de fecundi dad y mortalidad. Estas fórmulas proveen métodos más seguros y son de aplicación más amplia que los primeros méiodos que aparecieron en la liter...

Taking Yule's coefficient, Q, as a measure of the intensity of association in a 2 X 2 contigency table, Costner and Wager recommend in a recent article in this Journal that the statistical significance of the difference between the values of Q calculated for two different 2 X 2 tables can be tested using the usual x test for the second-order intera...

This paper presents new methods for (i) estimating the magnitude of the persistence of events in a chain of multiple events, and (ii) testing hypotheses about this persistence, when the observed chain is of long duration and is of the kind considered earlier by Barton, David & Fix (1962). It also compares these methods with those suggested in the e...

The earlier literature on three-factor interactions in a three-way contingency table was concerned mainly with the null hypothesis H0 that these interactions are all nil. In the present article, we present methods for testing H0 which are easier to apply than those suggested by earlier writers on this subject, and in addition we develop methods for...

In the present article, we shall propose a definition of the $r$th order interactions in a $m$-dimensional $d_1 \times d_2 \times \cdots \times d_m$ contingency table ($r = 0, 1, 2, \cdots, m - 1)$, and we shall present methods for testing the hypothesis that any specified subset of these interactions is equal to zero. In addition, we shall present...

In the present article, we shall present two different methods for obtaining simultaneous confidence intervals for judging contrasts among multinomial populations, and we shall compare the intervals obtained by these methods with the simultaneous confidence intervals obtained earlier by Gold [5] for all linear functions of multinomial probabilities...

Fisher (1962) has proposed a method for obtaining confidence limits for the cross‐product ratio in a 2 × 2 table which requires that the user solve a quartic equation. Based on a different mathematical derivation, Cornfield (1956) had proposed a similar method. In the present article, we shall present simpler methods for obtaining confidence limits...

Selective limitation of family size will reduce the relative incidence R of a disorder if for different values of i there are differences in the probability pi that a child born to the ith set of parents is affected, and if the size si of the ith sibship (in the absence of affected offspring) is independent of pi. When si=s for all i, R will be red...

The population measures of association for cross classifications, discussed in the authors' prior publications, have sample analogues that are approximately normally distributed for large samples. (Some qualifications and restrictions are necessary.) These large sample normal distributions with their associated standard errors, are derived for vari...

Based on a transformation matrix the rows of which are orthogonal to each other, a matrix that comes naturally to analysis of variance users, Plackett (1962) has proposed a test for zero second‐order interaction in an r × s × t contingency table which requires that the user invert t +1 matrices, each having (r — 1) (s — 1) rows and (r —1) (s —1) co...

In this paper we show that the standard error formulae given by Lewis (1962) and others for the Stouffer method of comparison of sets of 2 × 2 tables do not lead, in general, to consistent estimators of the appropriate standard deviations. Simple modifications of these formulae, which do lead to consistent estimators, are presented here. Since the...

## Projects

Project (1)