Minimum Logit Research Articles

On Second Order Admissibilities in Two-Parameter Logistic Regression Model

In two-parameter family of distribution, conditions for a modified maximum likelihood estimator to be second-order admissible are given. Applying these results to two-parameter logistic regression model, it is shown that the maximum likelihood estimator is always second-order inadmissible and the Rao-Blackwellized minimum logit chi-squared estimator is second-order admissible if and only if the number of the doses is greater than or equal to 6.

Civil liability, criminal law, and other policies and alcohol-related motor vehicle fatalities in the United States: 1984–1995

This study examines the associations between alcohol policies and motor vehicle fatality rates from 1984 to 1995 in the United States. State policies and state characteristics variables were merged with motor vehicle fatality rates over an 11 year period and analyzed using minimum logit chi-square method and fixed effects to create a quasi time-series analysis. Laws allowing individuals to sue bars for the drunken behavior of their patrons were the policies most strongly associated with lower minor and adult fatality rates. The mandatory first offense fine was associated with lower minor fatality rates but not adult fatality rates, while minor and adult rates fell after administrative per se license suspension and anti-consumption laws for all vehicle occupants. Many other public policies evaluated were not associated with lower fatality rates.

A Minimum Logit Chi-Squared Estimator for Asymmetric Generalizations of the Logistic Model

A Minimum Logit Chi-Squared Estimator for Asymmetric Generalizations of the Logistic Model

Further investigations of berkson's example

Berkson's bioassay problem is investigated in detail. In addition to maximum likelihood estimators and Berkson's proposed minimum logit χ2 estimators, several modified estimators are considered. Two Rao-Blackwellized estimators - a conditional mean and conditional median, given the sufficient statistics - as well as Amemiya's bias-corrected and partially bias-correct estimators are included. The estimators are compared with respect to bias, variance, mean squared error, and Pitman's measure of closeness. The experiment is examined at four different levels of the parameters, and is re-examined subject to a monotonicity condition imposed on the sample space. The results provide a new insight into the controversy over the comparison of minimum χ2 and maximum likelihood estimators.

Microcomputer BASIC programs for rapid determination of lethal dosages of biocides using logit transformations.

The probit analysis model is generally used for the determination of lethal dosages in bioassay applications. However, the logit models, which use the logistic curve instead of the integrated normal curve, could also be effectively used for the determination of lethal dosages and regression coefficients. In this paper, two types of logit models, namely minimum logit chi square and maximum likelihood, have been described in detail for the estimation of the parameters. The results of these two models are also compared with those of the probit model.

Comparison of minimum logit chi‐square and Bayesian item parameter estimation

Under the minimum logit chi‐square estimation procedures implemented in the MICRO‐IRT computer program, an ancillary outcome of the application of the 1/2n rule was that large‐valued estimates of discrimination can often be prevented. Since the use of prior distributions on the discrimination parameters in Bayesian estimation also prevents such values, a comparison of the two estimation procedures was conducted. The two estimation procedures were applied to 36 simulated data sets involving small numbers of items and groups of examinees to compare their parameter recovery characteristics. Overall, the item and ability parameter estimates yielded by the two estimation procedures were comparable to each other and to the results of previous parameter recovery studies. Both approaches seemed to prevent excessively large item discrimination estimates. However, the minimum logit chi‐square procedure yielded a higher proportion of deviant estimates of item difficulty than did the Bayesian procedures of the BILOG computer program. This appears to be due to the 1/2n rule yielding small‐valued item discrimination estimates. The results suggest that the Bayesian procedures of the BILOG computer program are to be preferred.

An example arising from berkson's conjecture

Berkson (1980) conjectured that minimum x2 was a superior procedure to that of maximum likelihood, especially with regard to mean squared error. To explore his conjecture, we analyze his (1955) bioassay problem related to logistic regression. We consider not only the criterion of mean squared error for the comparison of these estimators, but also include alternative criteria such as concentration functions and Pitman's measure of closeness. The choice of these latter criteria is motivated by Rao's (1981) considerations of the shortcomings of mean squared error. We also include several Rao-Blackwellized versions of the minimum logit x2 the purpose of these comparisons.

The 1/kn rules in the minimum logit chi‐square estimation procedure when small samples are used

Under the minimum logit chi‐square item parameter estimation procedure, observed proportions of correct response of zero or unity result in infinite logits and estimates cannot be obtained. The paper examines the application of three rules (l/2n, l/4n and elimination) for dealing with such cases. A simulation study is conducted in which sample size, number of grouping intervals, underlying item discrimination and difficulty are varied. The outcome variables are the square of the difference between the estimates and the underlying parameter values for item discrimination and difficulty. The results indicate that a complex set of interactions exist among the factors employed in the study. Overall, the 1/4n rule is preferred over the other two rules as it generally yields the smallest RMSE for both item discrimination and difficulty. However, as sample size increases the differences among the three rules decreased.

A Monté Carlo Comparison of Estimators for the Multinomial Logit Model

Marketing researchers use the multinomial logit (MNL) model to analyze discrete choice, and estimate parameters either by maximum likelihood (ML) or minimum logit chi square (MLCS). Some controversy persists, however, over which is better. Review articles in marketing recommend ML over MLCS, but the statistics literature suggests that MLCS should be preferred. No studies have directly compared the performance of ML and MLCS in a marketing context. The authors assess the relative performance of ML, MLCS, and three other candidate estimators for MNL marketing applications involving repeated-measures datasets collected by means of multiple-subset designs. In contrast to most previous findings in the statistics literature, the results strongly support the use of ML. ML is found to outperform the other estimators on a variety of point estimation, predictive accuracy, and statistical inference criteria and ML test statistics are found to have asymptotic behavior for datasets involving relatively few replications.

Changing Rates of Return on Rental Property and Condominium Conversions

In the 1970s about 350,000 housing units in multi-family structures in the US were converted to a condominium or co-operative form of ownership. This paper shows how changes in both rents and housing prices influence the expected rate of return on rental property and therefore the probability of conversion. A minimum logit chi-square model was applied to data from 34 metropolitan areas to estimate the effects of these changes. The evidence suggests that changes in housing prices had a greater effect on conversions than changes in the expected net return on rental property.

Modification of the Minimum Logit Chi‐Squared Estimator in Simple Linear Logistic Regression

AbstractA new modification of Berkson's minimum logit chi‐squared estimator in simple linear logistic regression is suggested in order to achieve reduction of first order bias of the estimator as well as in the model. Furthermore, unlike estimators currently available, our procedure is quite simple to apply in practice and is valid even in the presence of zero frequencies in the table.

Item parameter estimation via minimum logit chi‐square

The minimum logit chi‐square procedure was used in the item parameter estimation stage of the Birnbaum joint estimation paradigm. Simulated item response data for 36 data sets were analysed via this approach. Overall, the results yielded by the minimum chi‐square procedure compared very favourably with the results yielded by the LOGIST computer program for these data sets. As would be expected, test length, sample size and match of the test difficulty to the ability of the examinees all had an impact upon the level of agreement of the estimates with the underlying item parameter values. The empirical results suggest that in this context the minimum logit‐square procedure yields acceptable item parameter estimates.

Comparison of Item Responses of English- and Spanish-Speaking Children Using Minimum Logit Chi-Squared Regression

A total of 102 Spanish-speaking preschool pupils and 104 English-speaking pupils were individually administered the Spanish and English versions of the Cooperative Preschool Inventory. Minimum logit chi-squared regression was applied to each of the 33 items of the verbal scale of the inventory. Several differences in the response patterns of the two groups were noted, although the number of potentially biased items was small (12%).

Consistency and Asymptotic Normality of the Minimum Logit Chi-Squared Estimator When the Number of Design Points is Large

When the number of design points goes to infinity, we show that the minimum logit chi-squared estimator of the parameter in a linear logistic regression model for binomial response data is asymptotically normal. We also give conditions under which it is consistent.

Alternative moment approximations for berkson's minimum logit chi-squared estimator

Expressions are derived for the bias to order J-1 , the variance to order J-2 and the mean squared error to order J-2 of Berkson's minimum logit chi-squared estimator where J is the number of distinct design points. These moment approximations are numerically compared to Monte Carlo estimates of the true moments and the moment approximations of Amemiya (1980) which are appropriate when the “average” number of observations per design point is large. They are used to compare the mean squared error of the minimum logit chi-squared estimator to that of the maximum likelihood estimator and to investigate the effect of bias on confidence intenrals constructed using the minimum logit chi-squared estimator.

Modification of the empirical logit to reduce bias in simple linear logistic regression

The effect on the bias of Berkson's minimum logit chi-squared estimator of adding a constant to each observed count before forming the empirical logit is examined as a function of the number of design points. It is shown that the ‘best’ constant for reducing bias is essentially a linear function of the reciprocal of the number of design points.

Comments on a Paper by T. Amemiya on Estimation in a Dichotomous Logit Regression Model

Amemiya (1980) derived expressions for the $n^{-2}$-order mean squared errors of the maximum likelihood and the minimum logit chi-squared estimators in the dichotomous logit regression model. He numerically evaluated these expressions for a number of specific examples and in all examples found that the minimum chi-squared estimator has smaller $n^{-2}$-order mean squared error. In this paper, we demonstrate examples in which the maximum likelihood estimator has smaller $n^{-2}$-order mean squared error.

Modeling Migration: Analyzing Migration Histories from a San Blas Cuna Community

This paper discusses the cultural context of migration in a community in eastern San Blas, Panama, describes recent changes in absence rates for male and female age groups, and develops a simple stochastic model for residential change during 1970-71 and 1975-76. Rates of absence have risen markedly among males: in 1968, about 10% of the male labor froce resided outside the community; in 1977, absentees accounted for over 40% of the male labor force. Rates of female absence have remained extremely low. The rate of out-migration for the community as a whole, however, has fluctuated between 4.3% and 4.7% between 1965 and 1976, while the rate of return migration has increased. On the average, the number of years spent in wage work away from the reservation was greater for average households than for wealthy ones. This difference may be linked to the relatively limited amounts of land for staple crops available to average households. Classical Markov chain models assume transition probabilities are uniform for a whole population, but recent studies have used multiple regression to estimate the effects of individual characteristics on transition probabilities. Observed frequencies are outside the range where ordinary least squares techniques are appropriate, so this paper uses minimum logit chi-square regression to estimate the effects of age, sex, education, and position within the household on the log-odds on remaining within the community or remaining outside it. The results agree with what we know of community control over women and over men working in the households of their fathers-in-law.

Small-Sample Quantal Response Methods for Estimating the Location Parameter for a Location-Scale Family of Dose-Response Curves

Abstract When one uses a small number of quantal responses to estimate a location parameter in the presence of an unknown scale parameter for a logistic or normal dose-response curve, it is often possible to substantially improve upon the method of maximum likelihood. Some generalized method-of-moments estimators are proposed for an arbitrary dose-response curve known up to location and scale and a theorem is given that establishes existence and uniqueness properties. In a computer study of the exact distributions of these estimators, they proved to be far superior to maximum likelihood and minimum logit chi-squared estimators of location in the logistic case.

Genetic Evaluation of Animals for Traits with Categorical Responses

A method of genetic evaluation of polychotomies based on the logistic distribution is presented. Logarithmic transformations of counts are expressed as linear combinations of fixed effects and random variables. Realized values of random elements in the model are predicted by the solution of equations similar to Henderson's multi-trait best linear unbiased prediction, but with a variance-covariance matrix of the residuals estimated from the data. It is proved that the method yields consistent estimators and predictors of response probabilities for any desired linear function of the model, provided that the linear combination involving the fixed effects is estimable. The method appears to have properties similar to those of minimum logit chi-square estimators. An example is presented.