Linear Logit Model Research Articles

Singularity and Autoregressive Disturbances in Linear Logit Models

The implications of including autoregressive disturbances in linear logit models of demand systems are explored. It is argued that the normality assumption of the error terms is more appropriate in the linear logit model than in a share equation model with additive disturbances (commonly found in the literature). Autoregressive disturbances and their implications for model estimation are discussed in that context. Both theoretical arguments and empirical evidence are presented in favor of the logit specification given the presence of serial correlation.

The Use of Linear Logit Models for Dynamic Input Demand Systems

This paper demonstrates that a linear logit model, with appropriate constraints, can be used to specify a system of cost share equations that satisfy neoclassical economic conditions. Unlike many other flexible functional forms, the logistic function is particularly well suited for incorporating dynamic adjustment mechanisms. The empirical results suggest that the use of static models overstates short-run own-price elasticities and understates the corresponding long-run price effects.

The Use of Linear Logit Models in Marketing Research

The author discusses the use of the linear logit model in marketing research. A brief review of the linear logit model focuses on model formulation, estimation, evaluation, and inference procedures. Some of the underlying properties of the linear logit model which have not received due attention in marketing research are examined. Also presented are some recent developments in testing for independence of irrelevant alternatives, discrete choice models free of this assumption, modification to the standard logit model to account more adequately for specification errors, and logit estimation procedures in choice-based sampling. The author concludes by identifying several directions for future research in this area.

Age, period, and cohort effects on maternal mortality: a linear logit model.

This analysis was aimed at disentangling the age, period, and cohort effects on the decline in maternal mortality in the 1917-77 period in New York State. New York maternal mortality rates were consistentley lower than US rates from 191-56, but fell considerably more slowly than national rates since 1957. Cohort analysis can potentially provide separate measures of age, period, and cohort effects by use of linear ligit models. Comparison of various age-period-cohort linear logit models on the logits of maternal mortality rates indicated that period and age effects are the dominant influences on maternal mortality. Cohortship did not make a significant contribution after age and period were already in the model. Age parameter results suggest that the 20-24 year age group faces the lowest maternal mortality risk, and risk increases rapidly with age after age 30 years. The infuctuation in the residuals for the 40-44 year age group is slightly higher due to the stochastic variation in diminishing small numbers of maternal deaths and pregnancies in this group. In addition, adding the period dimension after adjustment for age had a greater impact than adding the cohort dimension after adjustment for age. The implication of these findings is that, as a set, changes in temporal variables that cut across cohorts seem to be more important than those variables that distinguish cohorts.

Use of catchability equations for population estimation of marron, Cherax tenuimanus (Smith) (Decapoda : Parastacidae)

Marron in a 0 .01-ha hatchery pond were sampled after sunset on 14 occasions over 2 years in a standardized manner using baited drop nets. An inventory of the total population was taken after each sampling by draining the pond. Variation in catchability. p, was analysed by linear logit models of p/(1 - p) using the likelihood ratio χ2- statistic G2 as a measure of goodness of fit. A reduction in G2 of 83% was produced by inclusion of water temperature. T� (C); relative position of marron in the size distribution, S (rather than absolute size); and a between-years factor, Y. The following catchability equation was calculated: In[pI/(l-pI)] = -5.40 +0.523S-0.246S2 +0.220T+1.40Y. The catchability equation was then applied to drop-net catch numbers from stocks of marron of 2-2+ years old in 10 0.1-ha farm dams. Estimated cohort numbers were compared with 'true' values obtained by independent removal of the stocks by seining. Agreement was improved by adjusting these estimates for differences in Secchi disk values, D. between dams (because daytime sampling was pursued and illuminance markedly influences catch rates) and in coefficient of size variation, V, The latter was negatively correlated with catchability and appeared to reflect the intensity of size dominance in feeding competition. A catchability equation. including these additional factors, was calculated: In[pI/(l -pI)] = -0.081 +0.664S -0.214S2 +0,284T -0.668ln D - 19.5V. Compared with other methods of estimation in which equal catchability is assumed, this method takes into consideration variation in catchability, requires no marking of individuals, and needs only one sampling occasion to obtain an estimate of crayfish numbers. Because of dependence of catchability on size of marron, sample means over estimated mean individual body weight by 13-48%. The catchability equation was also used to correct for this bias.

A Warning on the Use of Linear Logit Models in Transport Mode Choice Studies

It is argued that linear logit models are inappropriate to use for transport demand studies because they impose many rigid a priori restrictions on the parameters of price responsiveness of demand, such as the elasticities of substitution and cross price elasticities, and the structure of technology (or preference) underlying the linear logit models has severe irregularity and inconsistency. This has a serious implication for the credibility of the findings of several recent studies which attempted to measure the welfare loss of traffic misallocation attributable to the Interstate Commerce Commission's railroad minimum rate regulation.

Use of Binary Attributes in the Multiplicative Competitive Interactive Choice Model

In 1974, Nakanishi, Cooper, and Kassarjian proposed the multiplicative competitive interactive (MCI) choice model for predicting outcome of election results. The authors pointed out the superiority of the multiplicative model over the additive model, which was popular in political science (Muller 1970). The model, which is an extension of the gravitational market share model of consumers' spatial behavior originally suggested by Huff (1963), is extremely popular in marketing. It has been used for site selection (Huff 1963; LaLonde 1962), estimating sales potential (Hlavac and Little 1966; Jain and Mahajan 1978; Stanley and Sewall 1976), identifying trading area (Haines, Simon, and Alexis 1972), and market share estimation (Kotler 1971; Mahajan, Jain, and Bergier 1977). The sophistication of the model is obvious. The MCI model has been shown to be a special case of the multinomial extension of the linear logit model developed by Theil (1969) and applied to market share relations by Buletz and Naert (1975). McGuire, Weiss, and Houston (1977) provide a comprehensive discussion of these similarities. The initial application of the model was limited because of the problem in parameter estimation. However, due to the efforts of Kotler (1971), Teekens (1972), and Nakanishi and Cooper (1974), it is possible to calibrate the model using least squares procedures. Some of the conceptual and operational problems associated with the model are discussed in Huff and Batsell (1975) and Mahajan and Jain (1977). The MCI model postulates the consumer choice from among m alternatives as follows:

Analyzing Multiple Alternative Dependent Variables

In an earlier paper [5] it was noted that the linear logit model discussed there could be extended to provide a means of analysis suitable for situations in which the dependent variable under investigation had a polychotomous form. Such situations’occur frequently in research in human geography, particularly in social investigation where the researcher often wishes to analyze the causes of a set of behavior patterns, or attitudes held, or simply has available data in category form. It is often impossible in such situations to place categories of interest along a continuous scale and to analyze in the normal manner a continuous dependent variable. Chi-squared tests do present a means of statistical analysis. However, they have commonly been employed in the analysis of essentially dichotomous situations. They also involve reducing any explanatory variables with continuous form to category form, with a consequent waste of information. Furthermore it has been unusual for researchers to compute parameter estimates summarizing the effect of the explanatory variables when using chi-squared tests. Direct analysis of polychotomous dependent variables does not appear to have been attempted in geographical research and the lack of a commonly available method of analysis has undoubtedly resulted in a rephrasing of the questions researchers have felt able to ask, to fit commonly available methods of analysis. The aim of this paper is to present two methods of analyzing such situations and to illustrate them with an example taken from the author’s current research.