EFFECT DISPLAYS FOR MULTINOMIAL AND PROPORTIONAL-ODDS LOGIT MODELS

An "effect display" is a graphical or tabular summary of a statistical model based on high-order terms in the model. Effect displays have previously been defined by Fox (1987, 2003) for generalized linear models (including linear models). Such displays are especially compelling for complicated models—for example, those including interactions or polynomial terms. This paper extends effect displays to models commonly used for polytomous categorical response variables: the multinomial logit model and the proportional-odds logit model. Determining point estimates of effects for these models is a straightforward extension of results for the generalized linear model. Estimating sampling variation for effects on the probability scale in the multinomial and proportional-odds logit models is more challenging, however, and we use the delta method to derive approximate standard errors. Finally, we provide software for effect displays in the R statistical computing environment.     

Overcoming the Reference Category Problem in the Presentation of Statistical Models

Effects of categorical variables in statistical models typically are reported in terms of comparison either with a reference category or with a suitably defined "mean effect," for reasons of parameter identification. A conventional presentation of estimates and standard errors, but without the full variance–covariance matrix, does not allow subsequent readers either to make inference on a comparison of interest that is not presented or to compare or combine results from different studies where the same variables but different reference levels are used. It is shown how an alternative presentation, in terms of "quasi standard errors," overcomes this problem in an economical and intuitive way. A primary application is the reporting of effects of categorical predictors, often called factors, in linear and generalized linear models, hazard models, multinomial–response models, generalized additive models, etc. Other applications include the comparison of coefficients between related regression equations—for example, log–odds ratios in a multinomial logit model—and the presentation of multipliers or "scores" in models with multiplicative interaction structure.     

Marginal Structural Models: An Application to Incarceration and Marriage During Young Adulthood

Advanced methods for panel data analysis are commonly used in research on family life and relationships, but the fundamental issue of simultaneous time‐dependent confounding and mediation has received little attention. In this article the authors introduce inverse‐probability‐weighted estimation of marginal structural models, an approach to causal analysis that (unlike conventional regression modeling) appropriately adjusts for confounding variables on the causal pathway linking the treatment with the outcome. They discuss the need for marginal structural models in social science research and describe their estimation in detail. Substantively, the authors contribute to the ongoing debate on the effects of incarceration on marriage by applying a marginal structural model approach to panel data from the National Longitudinal Survey of Youth 1997 (N = 4,781). In line with the increasing evidence on the collateral consequences of contact with the criminal justice system, the authors find that incarceration is associated with reduced chances of entering marriage.     

Klasseneinflüsse auf das Wahlverhalten und die Wahlbeteiligung

The thesis of a declining impact of social class is widely accepted in the social sciences. A central tenet of this thesis is that in particular the impact of social class on voting has declined. Despite a plethora of empirical studies concerning this issue the mechanisms leading to this postulated decline have been relatively less explored. The current paper investigates the thesis of a substitution between class effects on voting and class effects on turnout. Under study are the United States of America and the Federal Republic of Germany. Using multinomial logit and logistic regression models for both countries a decline in class voting could be observed, but class effects on turnout increased in both countries. More specifically, the propensity to vote relatively to the non-manual classes has declined among the manual classes. In conjunction with the observation that class voting is higher among the manual classes this result supports the theory that the decline of class voting is due to an increasing political frustration within the manual classes. This reasoning suggests a substitution between class effects on voting and turnout.     

Generalized Linear Models in Family Studies

Generalized linear models (GLMs), as defined by J. A. Nelder and R. W. M. Wedderburn (1972) , unify a class of regression models for categorical, discrete, and continuous response variables. As an extension of classical linear models, GLMs provide a common body of theory and methodology for some seemingly unrelated models and procedures, such as the logistic, Poisson, and probit models, that are increasingly used in family studies. This article provides an overview of the principle and the key components of GLMs, such as the exponential family of distributions, the linear predictor, and the link function. To illustrate the application of GLMs, this article uses Canadian national survey data to build an example focusing on the number of close friends among older adults. The article concludes with a discussion of the strengths and weaknesses of GLMs.     

Meta-analysis: an introduction using regression models

Research synthesis of evaluation findings is a multistep process. An investigator identifies a research question, acquires the relevant literature, codes findings from that literature, and analyzes the coded data to estimate the average treatment effect and its distribution in a population of interest. The process of estimating the average treatment effect is meta-analysis. Meta-analysis is gaining popularity across the social sciences, but introductions and even advanced treatments of the subject are often formula-driven. Researchers, who apply formulas without understanding, risk both misapplication and misinterpretation. This article derives formulas used in meta-analysis using standard regression models so this article seeks to introduce readers with an understanding of regression analysis to meta-analysis, intending thereby to motivate and facilitate a deeper reading of the meta-analysis literature.     

AVERAGE PREDICTIVE COMPARISONS FOR MODELS WITH NONLINEARITY, INTERACTIONS, AND VARIANCE COMPONENTS

In a predictive model, what is the expected difference in the outcome associated with a unit difference in one of the inputs? In a linear regression model without interactions, this average predictive comparison is simply a regression coefficient (with associated uncertainty). In a model with nonlinearity or interactions, however, the average predictive comparison in general depends on the values of the predictors. We consider various definitions based on averages over a population distribution of the predictors, and we compute standard errors based on uncertainty in model parameters. We illustrate with a study of criminal justice data for urban counties in the United States. The outcome of interest measures whether a convicted felon received a prison sentence rather than a jail or non-custodial sentence, with predictors available at both individual and county levels. We fit three models: (1) a hierarchical logistic regression with varying coefficients for the within-county intercepts as well as for each individual predictor; (2) a hierarchical model with varying intercepts only; and (3) a nonhierarchical model that ignores the multilevel nature of the data. The regression coefficients have different interpretations for the different models; in contrast, the models can be compared directly using predictive comparisons. Furthermore, predictive comparisons clarify the interplay between the individual and county predictors for the hierarchical models and also illustrate the relative size of varying county effects.     

MULTILEVEL COVARIANCE STRUCTURE ANALYSIS BY FITTING MULTIPLE SINGLE-LEVEL MODELS

Data in social and behavioral sciences are often hierarchically organized. Multilevel statistical procedures have been developed to analyze such data while taking into account the dependence of observations. When simultaneously evaluating models at all levels, a significant statistic provides no information on the level at which the model is misspecified. Model misspecification can exist at one or several levels simultaneously. When one level is misspecified, the other levels may be affected even when they are correctly specified. Motivated by these observations, we propose to separate a multilevel covariance structure into multiple single-level covariance structure models and to fit these single-level models as in conventional covariance structure analysis. A procedure for segregating the multilevel model into single-level models is developed. Five test statistics for evaluating a model at each level are provided. Standard error formulas for the separate estimators are also provided, and their efficiency is compared to simultaneous estimators. Empirical and Monte Carlo results demonstrate the advantages of the segregated procedure over the simultaneous procedure. Computer programs that will allow the developed procedure to be used in practice are also presented.     

A CROSS-SECTION ANALYSIS OF THE DEMAND FOR NEW AND USED AUTOMOBILES IN THE UNITED STATES

This paper investigates the effects of income and other family characteristics on the demand for new and used automobiles. The multinomial logit probability model is employed to explain a family's choice of age and number of automobiles. Two cross-section surveys are analyzed to ascertain how well these components of demand can be explained by socio-economic variables.     

Welfare, freedom of choice and composite utility in the logit model

Discrete choice models characterize the alternatives in the choice set by utilities/attributes. The decision making is described by a probability distribution over the choice set. In this paper we introduce a welfare measure based on expected payoff and expected freedom of choice for the simple one parameter logit model. In this case the welfare measure turns out to be the so called composite utility. This means that the composite utility can be interpreted as the combined benefit of expected payoff and expected freedom of choice. The proposed welfare measure can be extended to the linear-in-parameters logit model and nested logit models and others. The proposed welfare measure is formulated in terms of the choice probability distribution. It depends on the form of the probabilities, but not on any particular derivation of the distribution.     

THE PREDICTABILITY OF COLLEGE FINANCIAL AID OFFERS: EVIDENCE FROM THE CLASS OF 1972

Two aid predictor models (binomial logit/regression and Tobit) were fitted to the subset of aid applicants from the National Longitudinal Survey of the High School Class of 1972 who had been accepted for admission by at least one college. Although undergraduate financial aid programs are designed to compensate for financial need, variables related to financial need were found to be relatively poor predictors of college aid offers and the inclusion of "non-need" variables did not measurably improve the predictive power of the model. These results suggest that disbursement of financial aid funds through college aid offices in 1972 was both inefficient and inequitable.     

MULTIPLE IMPUTATION OF INCOMPLETE CATEGORICAL DATA USING LATENT CLASS ANALYSIS

We propose using latent class analysis as an alternative to log-linear analysis for the multiple imputation of incomplete categorical data. Similar to log-linear models, latent class models can be used to describe complex association structures between the variables used in the imputation model. However, unlike log-linear models, latent class models can be used to build large imputation models containing more than a few categorical variables. To obtain imputations reflecting uncertainty about the unknown model parameters, we use a nonparametric bootstrap procedure as an alternative to the more common full Bayesian approach. The proposed multiple imputation method, which is implemented in Latent GOLD software for latent class analysis, is illustrated with two examples. In a simulated data example, we compare the new method to well-established methods such as maximum likelihood estimation with incomplete data and multiple imputation using a saturated log-linear model. This example shows that the proposed method yields unbiased parameter estimates and standard errors. The second example concerns an application using a typical social sciences data set. It contains 79 variables that are all included in the imputation model. The proposed method is especially useful for such large data sets because standard methods for dealing with missing data in categorical variables break down when the number of variables is so large.     

Social scientists as technicians,advisors and meaning producers

In this paper, we are addressing three issues that are at the core of scholarly reflections about the societal role of social science knowledge: (1) Social scientists tend to follow – although this is not always a deliberate choice – one of three models that describe their role as the producers of practical knowledge. For the sake of simplicity we have called the three models the “model of the technician”, the “model of the advisor” and the “model of the meaning producer”. (2) Due to the need for social inquiry to adopt a particular, restrictive perspective of its domain, useful knowledge is a complicated matter. Hence the need to put into question a widely supported notion at least among social scientists: When asked about the reasons for the limited “power” of social science knowledge the response frequently is that the adequacy and practical usefulness of social science knowledge is a function of its capturing the full complexity of what indeed are complex social phenomena. (3) Social scientists often tend to lament the marginal impact their intellectual efforts have on society, and they look with great envy across the divide of the so-called two cultures, wondering how and when they will be able to achieve the same kind of success and prestige the natural sciences and technology appear to enjoy in most societies. However, this unhappy view systematically understates the actual power of social science knowledge, in particular its role as a mind maker or meaning producer.     

FOUR USEFUL FINITE MIXTURE MODELS FOR REGRESSION ANALYSES OF PANEL DATA WITH A CATEGORICAL DEPENDENT VARIABLE

This paper describes and contrasts two useful ways to employ a latent class variable as a mixture variable in regression analyses of panel data with a categorical dependent variable. One way is to model unobserved heterogeneity in the trajectory, or change in the distribution, of the dependent variable. Two models that accomplish this are the latent trajectory model and latent growth curve model for a categorical dependent variable having ordered categories. Each latent class here represents a distinct trajectory of the dependent variable. The latent trajectory model introduces covariate effects on the composition of latent classes, while the latent growth curve model introduces covariate effects on both the "intercept" and the "slope" of growth in logit, which may vary among latent classes.
The other useful way is to model unobserved heterogeneity in the state dependence of the dependent variable. Two models that accomplish this are introduced for a simultaneous analysis of response probability and response stability, and the latent class variable is employed to distinguish two latent populations that differ in the stability of responses over time. One of them is the switching multinomial logit model with a time-lagged dependent variable as its separation indicator, and the other is the mover-stayer regression model.
By applying these four models to empirical data, this paper demonstrates the usefulness of these models for panel-data analyses. Example programs for specifying these models based on the LEM program are also provided.     

IMPLICATION ANALYSIS: A PRAGMATIC PROPOSAL FOR LINKING THEORY AND DATA IN THE SOCIAL SCIENCES

Sociology and other social sciences struggle to emulate a model of scientific evidence that is often inappropriate. Not only do social researchers encounter special limits, but they are also handicapped by a distorted and idealized picture of practices in the "hard sciences." Ironically, while often obliged to use data of lower quality, sociology employs standards for evaluating a theory that are not attained in the hard sciences. After a brief review of these obstacles, we describe a set of procedures for using empirical data to rigorously evaluate theories and hypotheses without resorting to the mimicking of hard science. The interaction between theory and evidence normally involves deriving implications from the theory (usually referred to as hypotheses) and then ascertaining how closely the empirical evidence meets these implications. The appropriateness of the implications is a key factor in the entire operation, linking as they do the data and the theory. The evaluation of a theory is no better than the theory's implications (as generated by the investigator) coupled with the quality and appropriateness of the evidence. It is our impression, however, that because this step is insufficiently addressed, there are unnecessary problems in the evaluation of theories. We use the term "Implication Analysis" to describe our efforts to review and improve current procedures.     

The association between experiential and material expenditures and subjective well-being: New evidence from Hungarian survey data

In the last decade, a number of studies using experimental designs have stated that spending money on experiences rather than on material goods tends to make people happier. In this research we used a novel survey approach to examine the relationships between experiential and material expenditures and life satisfaction. In two studies based on cross-sectional survey data from nationally representative samples in Hungary, we estimated linear and non-linear models. We found no significant evidence supporting the greater return received when buying experiences. Even in the non-linear models the difference between the marginal utilities was not statistically significant at any expenditure rate, although the marginal utility of experiential purchases appeared to be linear, whereas the marginal utility of material purchases was rather decreasing. Nevertheless, our results suggest that a reallocation of an average person’s expenditures (spending more on experiences and less on material goods) might be associated with a slightly higher well-being.     

Dynamic Discrete-time Duration Models: Estimation via Markov Chain Monte Carlo

Discrete-time or grouped duration data, with one or multiple types of terminating events, are often observed in social sciences or economics. In this paper we suggest and discuss dynamic models for flexible Bayesian nonparametric analysis of such data. These models allow simultaneous incorporation and estimation of baseline hazards and time-varying covariate effects, without imposing particular parametric forms. Methods for exploring the possibility of time-varying effects, as for example the impact of nationality or unemployment insurance benefits on the probability of reemployment, have recently gained increasing interest. Our modeling and estimation approach is fully Bayesian and makes use of Markov Chain Monte Carlo (MCMC) simulation techniques. A detailed analysis of unemployment duration data, with full-time job, part-time job and other causes as terminating events, illustrates our methods and shows how they can be used to obtain refined results and interpretations.     

Mediennutzung und Politische Partizipation

A central topic of empirical social research is the problem of unobserved heterogeneity. To solve this problem at least partially, a new statistical model is presented, the finite mixture of conditional mean and covariance structures. The model and the estimation procedures are then applied covering use of media and political participation to identify heterogeneous types of behavior. Since different LISREL models may be used for each type, it is not only possible to identify different degrees of political participation and use of media, but also different types of relationships between the use of media and political participation.     

The Natsal-SF Measure of Sexual Function: Comparison of Three Scoring Methods

The Natsal-SF is a psychometrically validated measure of sexual function for use in community health surveys, derived from 17 questions reflecting three components of sexual function. Scoring requires knowledge of complex statistical modeling and, given the methodological complexities, we assessed the validity of two simplified scoring methods calculated using the factor loadings produced when originally modeling the Natsal-SF items. Method 1 uses these factor loadings to three decimal places, while method 2 assigns whole numbers to each item based on the factor loadings. Scores from these simplified methods are compared to the original score using correlation coefficients, by comparing the distributions and the scores of each method in a linear regression model with key variables. We found scores from the simplified methods both correlate highly with the original score, and the distributions of scores closely match. The simplified methods result in different regression coefficients for gender and relationship context but estimate the coefficients of all other variables similarly to the original method. While the Natsal-SF should ideally be scored using latent variable modeling, the simplified methods perform well so can be used in similar contexts, increasing the utility of the Natsal-SF and enabling future studies to measure sexual function more comprehensively.     

Does Revenue Diversification Predict Financial Vulnerability Among Non-governmental Organizations in sub-Saharan Africa?

Non-governmental organizations (NGOs) in sub-Saharan Africa (SSA) experience financial challenges that hinder efforts to promote social change and development. Revenue diversification is one adaptive response to these challenges, yet there is a lack of evidence concerning the relationship between revenue diversification and financial vulnerability among NGOs in SSA. Using data from an online survey of NGOs (N = 170), we hypothesized that a greater number of revenue sources is associated with lower probability of financial vulnerability, while a greater level of dependence on international funding is associated with higher probability of financial vulnerability. Results from probit regression models controlling for organizational characteristics indicated partial support for hypotheses. Having four or more types of revenue was associated with 87% lower probability of financial vulnerability compared to having one type of revenue (p < 0.001). Also, NGOs with up to half of their budgets covered by international sources had 17% lower probability of financial vulnerability compared to NGOs with no international funding (p < 0.05). Implications for future research to further explore these relationships are discussed.