Coefficient Logit Research Articles

COMPARING ALTERNATIVE MODELS OF HETEROGENEITY IN CONSUMER CHOICE BEHAVIOR

SUMMARYWhen modeling demand for differentiated products, it is vital to adequately capture consumer taste heterogeneity, But there is no clearly preferred approach. Here, we compare the performance of six alternative models. Currently, the most popular are mixed logit (MIXL), particularly the version with normal mixing (N‐MIXL), and latent class (LC), which assumes discrete consumer types. Recently, several alternative models have been developed. The 'generalized multinomial logit' (G‐MNL) extends N‐MIXL by allowing for heterogeneity in the logit scale coefficient. Scale heterogeneity logit (S‐MNL) is a special case of G‐MNL with scale heterogeneity only. The 'mixed‐mixed' logit (MM‐MNL) assumes a discrete mixture‐of‐normals heterogeneity distribution. Finally, one can modify N‐MIXL by imposing theoretical sign constraints on vertical attributes. We call this 'T‐MIXL'. We find that none of these models dominates the others, but G‐MNL, MM‐MNL and T‐MIXL typically outperform the popular N‐MIXL and LC models. Copyright © 2012 John Wiley & Sons, Ltd.

Est-il possible et souhaitable traduire sous forme de probabilites un coefficient logit ?- Réponse aux remarques formulées par Marion Selz à propos de mon article paru dans le BMS en 2010

Is It Possible and Desirable to Translate a Logit Coefficient into Probabilities — Reply to Comments by Marion Selz on My BMS 2010 Article: Marion Selz responded to my BMS article on the translation of a logit coefficient into probabilities. I propose here to respond to her objections by showing that the translation is not a problem when one thoroughly understands what takes place. We first show the relationship between linear models and logistic models, and then the relationship between the translation of a logit coefficient and standardization in demography, and finally the sociological interest of such a translation in the general framework of logit modeling.

Patient satisfaction with obstetricians and gynecologists compared with other specialties: analysis of US self-reported survey data

Background:Few studies in the US have evaluated patient satisfaction with physicians across different specialties. We examined patient satisfaction and attitudes toward physicians during outpatient visits in the health care system, including obstetricians and gynecologists and other specialty physicians.Methods:We conducted a cross-sectional and national Web-based survey among anonymous patients who rated their physicians according to satisfaction with treatment on the basis of their experience during their most recent outpatient visits. The survey was user-friendly, validated, and helped patients identify their physicians according to specialty and rate them on a scale of 0 (“not at all satisfied”) to 10 (“extremely satisfied”). The patient satisfaction in obstetricians and gynecologists and other specialists were assessed using logistic regression analysis.Results:A total of 7938 patients who rated physicians belonging to the categories of obstetricians and gynecologists (n = 1903) and other specialties (n = 6035) were included in the study. Other things being equal, the odds of earning a satisfaction rating were almost 55% higher for visits to obstetricians and gynecologists than for other specialties (odds ratio [OR] 1.55 [1.15, 2.09], P < 0.01). Also, other things being equal, compared with other specialists, the odds of patient satisfaction due to the caring and friendly attitude of a physician were three times higher for obstetricians and gynecologists, with a logit coefficient of 1.28 (OR, 3.59 [3.17, 4.07], P < 0.001).Conclusion:Patient satisfaction ratings associated with caring and friendly attitude were higher for obstetricians and gynecologists compared to other specialists. Even though several factors influence patient satisfaction, adoption of factors like reducing waiting times, effective patient–physician communication, and involving patients in the decision-making process might aid physicians in achieving optimal results.

Comparing performances of logistic regression and neural networks for predicting melatonin excretion patterns in the rat exposed to ELF magnetic fields

Various studies have been reported on the bioeffects of magnetic field exposure; however, no consensus or guideline is available for experimental designs relating to exposure conditions as yet. In this study, logistic regression (LR) and artificial neural networks (ANNs) were used in order to analyze and predict the melatonin excretion patterns in the rat exposed to extremely low frequency magnetic fields (ELF-MF). Subsequently, on a database containing 33 experiments, performances of LR and ANNs were compared through resubstitution and jackknife tests. Predictor variables were more effective parameters and included frequency, polarization, exposure duration, and strength of magnetic fields. Also, five performance measures including accuracy, sensitivity, specificity, Matthew's Correlation Coefficient (MCC) and normalized percentage, better than random (S) were used to evaluate the performance of models. The LR as a conventional model obtained poor prediction performance. Nonetheless, LR distinguished the duration of magnetic fields as a statistically significant parameter. Also, horizontal polarization of magnetic fields with the highest logit coefficient (or parameter estimate) with negative sign was found to be the strongest indicator for experimental designs relating to exposure conditions. This means that each experiment with horizontal polarization of magnetic fields has a higher probability to result in "not changed melatonin level" pattern. On the other hand, ANNs, a more powerful model which has not been introduced in predicting melatonin excretion patterns in the rat exposed to ELF-MF, showed high performance measure values and higher reliability, especially obtaining 0.55 value of MCC through jackknife tests. Obtained results showed that such predictor models are promising and may play a useful role in defining guidelines for experimental designs relating to exposure conditions. In conclusion, analysis of the bioelectromagnetic data could result in finding a relationship between electromagnetic fields and different biological processes.

Using Heterogeneous Choice Models to Compare Logit and Probit Coefficients Across Groups

Allison (1999) notes that comparisons of logit and probit coefficients across groups can be invalid and misleading, proposes a procedure by which these problems can be corrected, and argues that ``routine use [of this method] seems advisable'' and that ``it is hard to see how [the method] can be improved.'' In this article, the author argues that as originally proposed, Allison's method can have serious problems and should not be applied on a routine basis. However, this study also shows that his model belongs to a larger class of models variously known as heterogeneous choice or location-scale models. Several advantages of this broader and more flexible class of models are illustrated. Dependent variables can be ordinal in addition to binary, sources of heterogeneity can be better modeled and controlled for, and insights can be gained into the effects of group characteristics on outcomes that would be missed by other methods.

Characteristics of Merging Firms in India: An Empirical Examination

The process of corporate restructuring through mergers and acquisitions has occupied much relevance in post-liberalization period. The financial characteristics of a firm play a critical role in the merger decision process. This study analyses the distinctive financial characteristics of the acquirer and the target firms in the period of merger. In addition, the empirical challenge is to determine the measurable factors that make a firm attractive as a takeover target. The fundamental research focus is on the characteristics that make a firm an acquirer and on identifying those characteristics of a firm, which will have a significant impact on the probability that firms will be acquired. The ratios involved in the study were reflective of the financial and product market characteristics. The sample firms consisting of 227 acquirer and 215 target firms represented the mergers during the period 1993—2004. The distinctive characteristics of the acquirer and the target firms were analysed with Mann Whitney U test and Kolgomorov Smirnov test on the assumption of non-normality of the sample distribution. The final step involved using the logit regression to examine the likelihood that a given firm will be the target of an acquisition attempt. The same sample of target firms merged between 1993-2004 period and a random sample of 490 non-acquired firms based on a matched industry sector and similar size (sales) are obtained for the logit model estimation. The comparative study of the acquirer and the target firms in the year of merger and the logit analysis reveals the following: The size of the target firms was much smaller compared to the acquirer firms. The acquirer firms have higher cash flow, higher PE ratios, higher book value, higher liquid assets, and lower debt to total assets ratio, which are statistically significant when compared to the target firms. Some evidence points out higher leverage for the target firms especially for measures of market leverage. The lesser the liquidity position, greater the probability of a firm becoming a target. The larger firms are less likely to become acquisition targets. Logit coefficients are consistent with the size hypothesis and inefficient management hypothesis. The advertising intensity ratio and the cash flow to market value of assets show statistical significance based on logit results. The results of the study indicate that firms generating free cash flows and having low debt levels have a tendency to incur agency costs. Capital structure characteristics provide the acquirers and the target firms a motive for mergers. The acquirer firms with unused debt capacity can use mergers as a strategic business tool for gaining financial synergy.

For Those Who Like Odds: A Direct Interpretation of the Logit Coefficient for Continuous Variables*

Objective. Researchers have suggested a number of different methods for interpreting the coefficients in a logit model. Unfortunately, many of these interpretations suffer from a lack clarity or involve a substantial number of manipulations of the logit coefficient prior to interpretation. In this article, we discuss a straightforward method of interpreting logit coefficients for continuous dependent variables without the need for extensive transformation.Method. Drawing on Stolzenberg's (1979) techniques for interpreting logarithmic regression models, we demonstrate that the logit coefficient multiplied by 100 can be directly interpreted as the percentage change in the odds given a unit change in the independent variable. We also derive an analogous interpretation for ordinal logit models.Results. After these derivations, the ease of this technique is demonstrated using a simple logit model.Conclusion. Given the generality of this interpretation, as well as its ease of computation, it is hoped that researchers from a number of disciplines will adopt this strategy for interpreting logit models.

Much ado about nothing: conditional logit vs. random coefficient models for estimating labour supply elasticities

This study compares several specifications of discrete choice labour supply estimations on basis of the German Socio Economic Panel. The results suggest that despite the restrictive assumptions of the error terms the conditional logit model provides an adequate model choice for the analysis of labour supply functions. Significance tests, which are based on bootstrapped confidence intervals, show that labour supply elasticities derived within the conditional logit model do not significantly differ from elasticities derived in flexible random coefficient models.

Avoiding Boundary Estimates in Latent Class Analysis by Bayesian Posterior Mode Estimation

In maximum likelihood estimation of latent class models, it often occurs that one or more of the parameter estimates are on the boundary of the parameter space; that is, that estimated probabilities equal 0 (or 1) or, equivalently, that logit coefficients equal minus (or plus) infinity. This not only causes numerical problems in the computation of the variance-covariance matrix, it also makes the reported confidence intervals and significance tests for the parameters concerned meaningless. Boundary estimates can, however, easily be prevented by the use of prior distributions for the model parameters, yielding a Bayesian procedure called posterior mode or maximum a posteriori estimation. This approach is implemented in, for example, the Latent GOLD software packages for latent class analysis (Vermunt & Magidson, 2005). Little is, however, known about the quality of posterior mode estimates of the parameters of latent class models, nor about their sensitivity for the choice of the prior distribution. In this paper, we compare the quality of various types of posterior mode point and interval estimates for the parameters of latent class models with both the classical maximum likelihood estimates and the bootstrap estimates proposed by De Menezes (1999). Our simulation study shows that parameter estimates and standard errors obtained by the Bayesian approach are more reliable than the corresponding parameter estimates and standard errors obtained by maximum likelihood and parametric bootstrapping.

Confounded Coefficients: Extending Recent Advances in the Accurate Comparison of Logit and Probit Coefficients Across Groups

The logit and probit models are critical parts of the social scientists analytical arsenal. We often want to know if a covariate has the same effect for different groups, e.g., men and women. Unfortunately, many attempts to compare the effect of covariates across groups make the unwarranted assumption that each group has the same residual variation. If this assumption is false, comparisons of coefficients can reveal differences where none exist and conceal differences that do exist. Recent work has emphasized the theoretical potential for this problem and proposed a test of whether the effect of covariates differs across groups that is accurate, if limited, despite differences in residual variation. This paper extends these advances in three ways. First, it uses simulations to show that this theoretical problem is substantively significant under a wide range of common conditions, meaning that traditionally executed comparisons of logit coefficients should be viewed skeptically. Second, it uses simulations to assess the power of the test recently proposed to overcome the problem, finding that they are an improvement over naive comparisons of coefficients, but have significant limitations. Third, it proposes and tests two alternative means of comparing coefficients across groups that avoid the assumption of equal residual variation entirely. The article closes with implications for the practice of research.

High-density lipoprotein subpopulation profile and coronary heart disease prevalence in male participants of the Framingham Offspring Study.

High-density lipoprotein (HDL) is a heterogeneous lipoprotein class and there is no consensus on the value of HDL subspecies in coronary heart disease (CHD) risk assessment. We tested the hypothesis whether specific HDL subpopulations are significantly associated with CHD-prevalence. ApoA-I concentrations (mg/dL) in HDL subpopulations were quantitatively determined by native 2d gel electrophoresis, immunoblotting, and image analysis in male participants in the Framingham Offspring Study (FOS). CHD cases (n=169) had higher prebeta-1 and alpha-3 particle and lower alpha-1, prealpha-3, and prealpha-1 particle levels than either all (n=1277) or HDL cholesterol-matched (n=358) controls. alpha-1 and prealpha-3 levels had an inverse association, whereas alpha-3 and prealpha-1 particle levels had a positive association with CHD prevalence after adjusting the data for established CHD risk factors. Standardized logit coefficients indicated that alpha-1 HDL was most significantly associated with CHD prevalence. Moreover, each mg/dL increase in alpha-1 particle level decreased odds of CHD by 26% (P<0.0001), whereas each mg/dL increase in HDL cholesterol decreased odds of CHD by 2% in a model including all established CHD risk factors. Specific HDL subpopulations were positively correlated, whereas others were inversely correlated with CHD prevalence in male subject in the FOS, indicating that the various HDL particles might have different roles in the cause of CHD.

Comparing Social Groups: Wald Statistics for Testing Equality Among Multiple Logit Models

Social scientists often study the differential effects of explanatory variables among multiple social groups such as race, ethnic group, and nation.This paper examines the Wald test for testing equality of logit coefficients from models of multiple social groups. I propose a Wald statistic that can perform some joint tests of group comparisons that the usual likelihood ratio test cannot. Two examples apply the Wald statistic for testing various hypotheses, and show that the Wald test is flexible and straightforward for making comparisons across social groups, and that the proposed Wald test may find wide applications in the social sciences.

Using General Population Data to Project Idiopathic Physical Symptoms in the U.S. Army

Many personnel deployed to the 1991 Persian Gulf War complained of symptoms that sometimes remained unexplained after comprehensive clinical examinations. We used existing population-based data from the Epidemiologic Catchment Area survey to estimate the expected incidence, prevalence, resolution, and mortality for multiple idiopathic physical symptoms (MIPS) among Army active duty personnel. Multinomial logistic regression was used to model the relationship between sociodemographic characteristics and the distribution of MIPS in U.S. workers. We used logit coefficients and known sociodemographic characteristics of U.S. Army active duty personnel to predict MIPS status in the Army. High, medium, and low estimates of MIPS incidence, prevalence, resolution, and MIPS-related mortality were obtained by altering logit intercepts. Among workers, the estimated MIPS prevalence and annual incidence, resolution, and mortality were 4.62%, 2.11%, 63.85%, and 0.26%, respectively. In contrast, the same predicted rates among Army active duty personnel were 3.89%, 1.64%, 71.33%, and 0.15%.

Unobserved Product Differentiation in Discrete Choice Models: Estimating Price Elasticities and Welfare Effects

Standard discrete choice models such as logit, nested logit, and random coefficients models place very strong restrictions on how unobservable product space increases with the number of products. We argue (and show with Monte Carlo experiments) that these restrictions can lead to biased conclusions regarding price elasticities and welfare consequences from additional products. In addition, these restrictions can identify parameters which are not intuitively identified given the data at hand. We suggest two alternative models that relax these restrictions, both motivated by structural interpretations. Monte-Carlo experiments and an application to data show that these alternative models perform well in practice.

Racial Differences in the Hurdling of Prenatal Care Barriers

The success of black or white mothers in obtaining adequate prenatal care is examined. Two departures from public health convention are employed. The independent variables’ marginal effects are calculated from their logit coefficients. The odds ratio of care adequacy between races is derived from race-specific regressions. It yields a smaller variance and type II decision error likelihood compared to the race dummy method. A working-class life outlook and apathetic fathers are the highest barriers to adequate care. Wantedness, in the form of desired timing, is a very strong motivator. Improving upward socioeconomic mobility and paternal attitudes are important aspects of increasing prenatal care adequacy rates.

College relations and fund-raising expenditures: Influencing the probability of alumni giving to higher education

Costs of fund raising and college relations data for each of three years from 17 colleges and universities have been combined with the schools' institutional characteristics to predict ratios of alumni donors to total alumni for each school. With factor analysis, expenditure and institutional variables were classified into three descriptor influences on giving: fund-raising effort, donor wealth, and school resources. The expected ratio of donors to number of available alumni for each school was then projected with the use of logit coefficients derived from the limited factor model.

When Will They Ever Learn That First Derivatives Identify the Effects of Continuous Independent Variables or "Officer, You Can't Give Me a Ticket, I Wasn't Speeding for an Entire Hour"

The reasons for using the first derivative to identify the effect of continuous independent variables in a logit function are explained with simple examples and more mathematics than in my original article (Roncek 1991). I show how a common practice of examining the difference in a dependent variable for values of X and X+1 to find the effect of a continuous independent variable in an ordinary, linear, additive regression cannot and should not be applied to nonlinear models including logit. I show that the definitional formula for the ratio of exponentiated logit coefficients contains an inherent indeterminacy due to the ratio involving a single equation with two unknowns. Any numerical value of this ratio is consistent with a wide range of probabilities for the groups being contrasted with the ratio. Thus, having only this ratio reported does not permit a precise understanding of the difference between the groups. Using the value of the first derivative for continuous variables and the differences between probabilities for dummy variables representing groups avoids the problems of these other strategies.

Odds versus Probabilities in Logit Equations: A Reply to Roncek

Odds versus Probabilities in Logit Equations: A Reply to Roncek

Using Logit Coefficients to Obtain the Effects of Independent Variables on Changes in Probabilities

Using Logit Coefficients to Obtain the Effects of Independent Variables on Changes in Probabilities

Using Logit Coefficients to Obtain the Effects of Independent Variables on Changes in Probabilities

Using Logit Coefficients to Obtain the Effects of Independent Variables on Changes in Probabilities