Kristian Bernt Karlson

Comparing Regression Coefficients Between Same-sample Nested Models Using Logit and Probit: A New Method

Logit and probit models are widely used in empirical sociological research. However, the common practice of comparing the coefficients of a given variable across differently specified models fitted to the same sample does not warrant the same interpretation in logits and probits as in linear regression. Unlike linear models, the change in the coefficient of the variable of interest cannot be straightforwardly attributed to the inclusion of confounding variables. The reason for this is that the variance of the underlying latent variable is not identified and will differ between models. We refer to this as the problem of rescaling. We propose a solution that allows researchers to assess the influence of confounding relative to the influence of rescaling, and we develop a test to assess the statistical significance of confounding. A further problem in making comparisons is that, in most cases, the error distribution, and not just its variance, will differ across models. Monte Carlo analyses indicate that other methods that have been proposed for dealing with the rescaling problem can lead to mistaken inferences if the error distributions are very different. In contrast, in all scenarios studied, our approach performs as least as well as, and in some cases better than, others when faced with differences in the error distributions. We present an example of our method using data from the National Education Longitudinal Study.

Total, Direct, and Indirect Effects in Logit and Probit Models

This article presents a method for estimating and interpreting total, direct, and indirect effects in logit or probit models. The method extends the decomposition properties of linear models to these models; it closes the much-discussed gap between results based on the “difference in coefficients” method and the “product of coefficients” method in mediation analysis involving nonlinear probability models models; it reports effects measured on both the logit or probit scale and the probability scale; and it identifies causal mediation effects under the sequential ignorability assumption. We also show that while our method is computationally simpler than other methods, it always performs as well as, or better than, these methods. Further derivations suggest a hitherto unrecognized issue in identifying heterogeneous mediation effects in nonlinear probability models. We conclude the article with an application of our method to data from the National Educational Longitudinal Study of 1988.

Counterfactual Causal Analysis and Nonlinear Probability Models

Nonlinear probability models, such as logits and probits for binary dependent variables, the ordered logit and ordered probit for ordinal dependent variables and the multinomial logit, together with log-linear models for contingency tables, have become widely used by social scientists in the past 30 years. In this chapter, we show that the identification and estimation of causal effects using these models present severe challenges, over and above those usually encountered in identifying causal effects in a linear setting. These challenges are derived from the lack of separate identification of the mean and variance in these models. We show their impact in experimental and observational studies, and we investigate the problems that arise in the use of standard approaches to the causal analysis of nonexperimental data, such as propensity scores, instrumental variables, and control functions. Naive use of these approaches with nonlinear probability models will yield biased estimates of causal effects, though the estimates will be a lower bound of the true causal effect and will have the correct sign. We show that the technique of Y-standardization brings the parameters of nonlinear probability models on a scale that we can meaningfully interpret but cannot measure. Other techniques, such as average partial effects, can yield causal effects on the probability scale, but, in this case, the linear probability model provides a simple and effective alternative.

Using mediation analysis to identify causal mechanisms in disease management interventions

For over two decades, disease management (DM) has been touted as an intervention capable of producing large scale cost savings for health care purchasers. However, the preponderance of scientific evidence suggests that these programs do not save money. This finding is not surprising given that the theorized causal mechanism by which the intervention supposedly influences the outcome has not been systematically assessed. Mediation analysis is a statistical approach to identifying causal pathways by testing the relationships between the treatment, the outcome, and an intermediate variable that is posited to mediate the relationship between the treatment and outcome. This analysis can therefore help identify how to make DM interventions effective by determining the causal mechanisms between intervention components and the desired outcome. DM interventions can then be optimized by eliminating those activities that are ineffective or even counter-productive. In this article we seek to promote the application of mediation analysis to DM program evaluation by describing the two principal frameworks generally followed in causal mediation analysis; structural equation modeling and potential outcomes. After comparing several approaches within these frameworks using real and simulated data, we find that some methods perform better than others under the conditions imposed upon the models. We conclude that mediation analysis can assist DM programs in developing and testing the causal pathways that enable interventions to be effective in achieving desired outcomes.

Correlations and Nonlinear Probability Models

Although the parameters of logit and probit and other nonlinear probability models (NLPMs) are often explained and interpreted in relation to the regression coefficients of an underlying linear latent variable model, we argue that they may also be usefully interpreted in terms of the correlations between the dependent variable of the latent variable model and its predictor variables. We show how this correlation can be derived from the parameters of NLPMs, develop tests for the statistical significance of the derived correlation, and illustrate its usefulness in two applications. Under certain circumstances, which we explain, the derived correlation provides a way of overcoming the problems inherent in cross-sample comparisons of the parameters of NLPMs.

Incomplete equalization: The effect of tracking in secondary education on educational inequality

This paper tests whether the existence of vocationally oriented tracks within a traditionally academically oriented upper education system reduces socioeconomic inequalities in educational attainment. Based on a statistical model of educational transitions and data on two entire cohorts of Danish youth, we find that (1) the vocationally oriented tracks are less socially selective than the traditional academic track; (2) attending the vocationally oriented tracks has a negative effect on the likelihood of enrolling in higher education; and (3) in the aggregate the vocationally oriented tracks improve access to lower-tier higher education for low-SES students. These findings point to an interesting paradox in that tracking has adverse effects at the micro-level but equalizes educational opportunities at the macro-level. We also discuss whether similar mechanisms might exist in other educational systems.

Another Look at the Method of Y-Standardization in Logit and Probit Models

This article takes another look at the derivation of the method of Y-standardization used in sociological analyses involving comparisons of coefficients across nested logit or probit models. It shows that the method can be derived under less restrictive assumptions than hitherto suggested. Rather than assuming that the logit or probit fixes the variance of the latent error at a known constant, it suffices to assume that the variance of the error is unknown. A further result suggests that using Y-standardization for cross-model comparisons is likely to be biased by model differences in the fit of the latent error to the assumed logistic or normal distribution. Under correct specification Y-standardization recovers an effect size metric similar to Cohens d.

Præferencer for reproduktion? En analyse af den sociale stratificering af danske unges uddannelsesforventninger i henholdsvis 1968 og 2011

Nyere forskning i social ulighed i uddannelse viser, at den sociale baggrund saetter sig igennem unges uddannelsesvalg ud over de faglige meritter, som man i demokratiske samfund typisk ser som noglen til at bryde den sociale arv. Artiklen belyser arsagerne bag denne regularitet ved at undersoge klasseforskelle i unges forventninger til deres uddannelsesmaessige fremtid for to kohorter af danske unge, der star foran deres forste uddannelsesvalg, i henholdsvis 1968 og 2011. Artiklen tester en hypotese om, at sociale skaevheder i unges uddannelsesforventninger drives af en i familien rodfaestet praeference for fastholdelse af sociale privilegier over generationer. Den empiriske analyse stotter hypotesen og viser samtidig, at de sociale skaevheder i unges uddannelsesforventninger stort set er uforandrede over de godt 40 ar, der adskiller de to kohorter. Yderligere analyser, der inddrager foraeldres forventninger til den unge samt bedsteforaeldrenes uddannelsesniveau, stotter endvidere hypotesen. Analysens resultater peger i retning af, at forskningen med fordel kan rette blikket mod forventningsdannelsesprocesser i familien, hvis den vil forsta, hvorfor den sociale arv kan vaere svaer at bryde. ENGELSK ABSTRACT: Kristian Bernt Karlson: A Taste for Reproduction? Social Class Differences in Danish Adolescents’ Educational Expectations in 1968 and in 2011 Recent research in educational stratification shows that social class background affects schooling decisions among equally talented students. Class inequalities in educational attainment therefore appear to have causes other than the unequal distribution of academic merits, merits that usually are taken to be the main vehicle of social mobility in Western democracies. This article investigates the potential mechanisms behind this unequal distribution by examining class differences in educational expectations among Danish adolescents in 1968 and 2011. The paper tests the hypothesis that class differences in educational expectations are caused by a preference for maintaining social privileges over generations, a preference rooted in bosom of the family. The empirical analysis supports the hypotheses. It shows that class differences in expectations among equally talented students have been remarkably stable over the four decades separating the two cohorts. Further analyses that include information on parents’ expectation for the adolescent and on the educational attainment of grandparents provide additional support for the hypothesis. The paper argues that future research in educational stratification would benefit from focusing on expectation processes located in the family, if it is to fully grasp why class differences in educational attainment appears so persistent even today. Keywords: inequality of opportunity, education, social class, expectations, aspirations.

The Risky Business of Educational Choice in the Meritocratic Society

Education is widely regarded as key to promoting social mobility in postindustrial societies. Most Western countries have invested massively in their educational systems over the course of the twentieth century, leading to significant expansions of the educational system’s secondary and tertiary sectors. Despite these historical developments, stratification scholars have demonstrated that, whereas lower-class students’ absolute chances of educational attainment have increased, their chances relative to higher-class students’ chances have improved only moderately in most Western countries (Breen et al., 2009). For example, among those born between 1954 and 1964 in such diverse countries as France, Germany, and Sweden, the educational prospects of those originating in the unskilled class are respectively roughly ten, nine, and six times worse than the prospects of those originating in the service class (Breen et al., 2009, p. 1510). These figures clearly show that, although variation between countries is substantial, educational inequalities persist in postindustrial society.