New Light on the 16-Fold Table

Duncan, Otis Dudley

doi:10.1086/228246

Cited by 20 publications

(8 citation statements)

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“…The statistical methods that were developed earlier to be able to apply appropriate multiplicative models in the analysis of survey data then led me to be able to see how to develop the corresponding statistical methods to be able to apply, in turn, the corresponding models appropriate for the analysis of panel data. For additional models for the analysis of panel data, the interested reader is referred to Goodman (1962;1973a,b;1979e) and Duncan (1985).…”

Section: Consider Now Tablesmentioning

confidence: 99%

“…In Duncan's description of my work on statistical methods for latent structure analysis, which was quoted above in this section, he was referring implicitly to Goodman (1974a,b). Readers interested in this general topic are also referred to, e.g., Clogg & Goodman 1984, 1985Goodman 1979d;1987a,b;2002b;2004;2005;2007. In concluding this section, let me again note that the three-way table latent-class analysis presented above in this section is used here for the sake of simplicity. Latent-class analysis can be applied, more generally, in the analysis of an m-way table (for m = 2,3,4, .…”

Section: Concepts Useful In Latent-structure Analysis: Latent-class Mmentioning

confidence: 99%

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Statistical Magic and/or Statistical Serendipity: An Age of Progress in the Analysis of Categorical Data

Goodman

2007

Annu. Rev. Sociol.

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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 in empirical studies of latent types, latent variables, and latent structures. The exposition does not make use of any mathematical formulas, and the only arithmetic used is very simple multiplication, division, and addition. Simple numerical examples, constructed for expository purposes, are used as an aid in describing the concepts of categorical data analysis that are considered in the essay. These concepts include quasi-independence, quasi-symmetry, symmetric association, uniform association, and other related concepts useful in the analysis of mobility tables, and also other concepts that are useful in other areas of study.

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Section: Consider Now Tablesmentioning

confidence: 99%

Section: Concepts Useful In Latent-structure Analysis: Latent-class Mmentioning

confidence: 99%

Statistical Magic and/or Statistical Serendipity: An Age of Progress in the Analysis of Categorical Data

Goodman

2007

Annu. Rev. Sociol.

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“…The analysis of 16-fold tables, first investigated by Lazarsfeld (1948), has attracted the attention of some of the most distinguished sociological methodologists for more than thirty years (Coleman, 1964a(Coleman, , b, 1981Duncan, 1980Duncan, , 1985Goodman, 1973aGoodman, , b, 1974Lazarsfeld, 1948Lazarsfeld, , 1978. Mathematically, the models described here for the analysis of interdependence between two processes are related to Goodman's causal analysis of 16-fold tables without assuming the effect of latent-class variables (1973a, b).…”

Section: Introductionmentioning

confidence: 99%

Logit and multinomial logit models for discrete-time event-history analysis: a causal analysis of interdependent discretestate processes

Yamaguchi

1990

Qual Quant

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This paper introduces a new direction of methodological elaborations in event-history analysis based on discrete-time logit and multinomial logit models. The methodological elaborations address (1) simultaneous analysis of two-way transitions between two states, and (2) its extension for a causal analysis of two interdependent two-state processes. The former elaboration permits a more parsimonious and unambiguous expression for the effects of covariates on the dependent process than can be obtained by separate analyses of each direction of transition. The latter elaboration provides an extension for a log-linear causal analysis of 16-fold tables presenting two-wave-two-variable panel data, and relates the log-linear analysis to event-history analysis. An illustrative application, focusing on the dynamic relationship between premarital cohabitation and marijuana use, demonstrates the usefulness of the new models and methods.

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“…One of these models, the &dquo;linear logistic model with relaxed assumptions&dquo; (LLRA;Fischer, 1972Fischer, , 1976; for similar models see Breslow, 1976;Duncan, 1985aDuncan, , 1985bKoch, Landis, Freeman, Freeman, & Lehnen, 1977;Marascuilo & Serlin, 1979;Plewis, 1981), is based on Rasch's (1960/1980) concept of specific objectivity which is realized in his well-known one-parameter logistic model for item analysis. In contrast to the latter model, the LLRA does not require homogeneous categorical items, that is, items which measure one and the same latent trait.…”

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confidence: 99%

Measuring Change By Means of a Hybrid Variant of the Linear Logistic Model With Relaxed Assumptions

Formann

Spiel

1989

Applied Psychological Measurement

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The linear logistic model with relaxed assumptions (LLRA) was developed for measuring changes in qualitative data. It assumes item-specific person parameters and thus does not require homogeneous items to be presented to the persons at two points in time. The hybrid variant of this model maintains the multidimensionality of the person parameters, but it allows for different sets of items each of which is presented only once. In the model, a Rasch homogeneous item at t 2 with possibly differing difficulty corresponds to each item at t 1 . A short description of both models is followed by a first application of the hybrid LLRA to empirical data from a study on text comprehension. This example not only serves to demonstrate possible results when applying the LLRA, but is also used to outline the principle of hypothesis testing and model controls.Index terms: dichotomous data, linear logistic model, measuring change, Rasch model, text comprehension.The quantification of change has become a topic of great interest in many fields. Traditionally, change is defined in terms of differences of values measured at different points in time. Applying this concept to the social sciences (see Harris, 1963) would require a natural metric of those persons' scores which are used to infer the changes. However, most of the observations collected in the social sciences are qualitative, and thus lack a natural metric. On the other hand, quantitative statements about change are desired which, by the traditional method, cannot be obtained other than by an artificial quantification of the observations.To overcome these problems, special models can be formulated for measuring change in qualitative data. One of these models, the &dquo;linear logistic model with relaxed assumptions&dquo; (LLRA;Fischer, 1972Fischer, , 1976; for similar models see Breslow, 1976;Duncan, 1985aDuncan, , 1985bKoch, Landis, Freeman, Freeman, & Lehnen, 1977;Marascuilo & Serlin, 1979;Plewis, 1981), is based on Rasch's (1960/1980) concept of specific objectivity which is realized in his well-known one-parameter logistic model for item analysis. In contrast to the latter model, the LLRA does not require homogeneous categorical items, that is, items which measure one and the same latent trait. The LLRAIn the simplest case, there are two groups of persons-the experimental group and the control group. The reactions of all persons to the same k dichotomous items (e.g., presence vs. absence of a certain APPLIED PSYCHOLOGICAL MEASUREMENT

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New Light on the 16-Fold Table

Cited by 20 publications

References 6 publications

Statistical Magic and/or Statistical Serendipity: An Age of Progress in the Analysis of Categorical Data

Statistical Magic and/or Statistical Serendipity: An Age of Progress in the Analysis of Categorical Data

Logit and multinomial logit models for discrete-time event-history analysis: a causal analysis of interdependent discretestate processes

Measuring Change By Means of a Hybrid Variant of the Linear Logistic Model With Relaxed Assumptions

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