Multinomial Data Research Articles

An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials

Abstract Traditional discussions of goodness-of-fit tests for multinomial data consider asymptotic chi-squared properties under the assumption that all expected cell frequencies become large. This condition is not always satisfied, however, and another asymptotic theory must be considered. For testing a specified simple hypothesis, Morris (1975) and Hoist (1972) gave conditions for the asymptotic normality of the Pearson and likelihood ratio statistics when both the sample size and number of cells become large (even if the expected cell frequencies remain small). Monte Carlo techniques are used to examine the applicability of the normal approximations for moderate sample sizes with moderate numbers of cells.

An Empirical Investigation of Goodness-of-Fit Statistics for Sparse Multinomials

Abstract Traditional discussions of goodness-of-fit tests for multinomial data consider asymptotic chi-squared properties under the assumption that all expected cell frequencies become large. This condition is not always satisfied, however, and another asymptotic theory must be considered. For testing a specified simple hypothesis, Morris (1975) and Hoist (1972) gave conditions for the asymptotic normality of the Pearson and likelihood ratio statistics when both the sample size and number of cells become large (even if the expected cell frequencies remain small). Monte Carlo techniques are used to examine the applicability of the normal approximations for moderate sample sizes with moderate numbers of cells.

Catanova for multidimensional contingency tables: Nominal-scale response

This paper extends an analysis of variance for categorical data (CATANOVA) procedure to multidimensional contingency tables involving several factors and a response variable measured on a nominal scale. Using an appropriate measure of total variation for multinomial data, partial and multiple association measures are developed as R2 quantities which parallel the analogous statistics in multiple linear regression for quantitative data. In addition, test statistics are derived in terms of these R2 criteria. Finally, this CATANOVA approach is illustrated within the context of 2 three-way contingency table from a multicenter clinicaltrial.

GUHA-style processing of mixed data

In the present paper some suggestions concerning the GUHA-style processing of mixed data are presented. Mixed data are data obtained by simultaneous observation of dichotomous, multinomial and real-valued quantities. In the first part of the paper, attention is focused on mixed dichotomous and multinomial data, and in the second part on mixed dichotomous and real-valued data. In both cases reasonable sets of relevant questions (hypotheses) are defined and, in the first case, algorithms for evaluating these sets in data are given. More complex questions are investigated in the following two papers.

Upper and Lower Probability Inferences from Ordered Multinomial Data

Abstract Dempster's method of upper and lower probabilities represents an attempt to obtain posterior probability statements about parameters without the necessity to incorporate prior information. We apply Dempster's method to the case of multinomial data for which there is some natural ordering of the categories. Inferences are derived for the sum of an arbitrary set of categories, the ratio of two such sums, and linear combinations of the category probabilities. Numerical examples are given, and some effort is made to interprete Dempster's approach and relate it to the standard approaches to statistical inference.

Upper and Lower Probability Inferences from Ordered Multinomial Data

Upper and Lower Probability Inferences from Ordered Multinomial Data

A Double Sampling Scheme for Estimating from Misclassified Multinomial Data with Applications to Sampling Inspection

In some situations, it is desired to estimate multinomial proportions from data which have been misclassified. One such area is the sampling inspection area of quality control. In this paper, it is assumed that two measuring devices are available to classify units into one of r mutually exclusive categories. The first device is an expensive procedure which classifies units correctly; the second device is a cheaper procedure which tends to misclassify units. In order to estimate the proportions pi (i = 1,2, …, r) a double sampling scheme is presented. At the first stage, a sample of N units is taken and the fallible classifications are obtained; at the second stage a subsample of n units is drawn from the main sample and the true classifications are obtained. The maximum likelihood estimates of the pi are derived along with their asymptotic variances. Optimum values of n and N which minimize the measurement costs for a fixed precision of estimation and which minimize the precision for fixed cost are derived. The procedures of estimation and allocation of sample size are illustrated by an example in quality control.

A Double Sampling Scheme for Estimating from Misclassified Multinomial Data with Applications to Sampling Inspection

In some situations, it is desired to estimate multinomial proportions from data which have been misclassified. One such area is the sampling inspection area of quality control. In this paper, it is assumed that two measuring devices are available to classify units into one of r mutually exclusive categories. The first device is an expensive procedure which classifies units correctly; the second device is a cheaper procedure which tends to misclassify units. In order to estimate the proportions pi (i = 1,2, …, r) a double sampling scheme is presented. At the first stage, a sample of N units is taken and the fallible classifications are obtained; at the second stage a subsample of n units is drawn from the main sample and the true classifications are obtained. The maximum likelihood estimates of the pi are derived along with their asymptotic variances. Optimum values of n and N which minimize the measurement costs for a fixed precision of estimation and which minimize the precision for fixed cost are derive...

318. Note: A Comparison of Some Distance Measures Applicable to Multinomial Data, Using a Rotational Fit Technique

318. Note: A Comparison of Some Distance Measures Applicable to Multinomial Data, Using a Rotational Fit Technique

THE MARKOV CHAIN AS NULL HYPOTHESIS IN A DEVELOPMENT SURVEY1

Development criteria observed as time series on nominal variables pose a problem for research design. Markov chains are attractive in the first instance because they can handle such multivariate multinomial data sets, with results that are described and demonstrated on Career Development Study data. The power of the formal probability model is purchased at the expense of assumptions that may be unrealistic. It is argued and demonstrated that where the Markov chain theory for the data breaks down is precisely where the most interesting part of the message contained in the data resides. The Markov chain is shown to be a better null hypothesis against which to array the psychometric or other prediction model than is the usually employed random walk. A new prediction system that combines information from the Markov chain with the psychometric predictors is described and operated.