Latent Class Marginal Models for Cross-Classifications of Counts

The standard latent class model is a finite mixture of indirectly observed multinomial distributions, each of which is assumed to exhibit statistical independence. Latent class analysis has been applied in a wide variety of research contexts, including studies of mobility, educational attainment, agreement, and diagnostic accuracy, and as measurement error models in social research. One of the attractive features of the latent class model in these settings is that the parameters defining the individual multinomials are readily interpretable marginal probabilities, conditional on the unobserved latent variable(s), that are often of substantive interest. There are, however, settings where the local-independence axiom is not supported, and hence it is useful to consider some form of local dependence. In this paper we consider a family of models defined in terms of finite mixtures of multinomial models where the multinomials are parameterized in terms of a set of models for the univariate marginal distributions and for marginal associations. Local dependence is introduced through the models for marginal associations, and the standard latent class model obtains as a special case. Three examples are analyzed with the models to illustrate their utility in analyzing complex cross-classifications.     

A PARTIAL INDEPENDENCE ITEM RESPONSE MODEL FOR SURVEYS WITH FILTER QUESTIONS

In many surveys, responses to earlier questions determine whether later questions are asked. The probability of an affirmative response to a given item is therefore nonzero only if the participant responded affirmatively to some set of logically prior items, known as "filter items." In such surveys, the usual conditional independence assumption of standard item response models fails. A weaker "partial independence" assumption may hold, however, if an individual's responses to different items are independent conditional on the item parameters, the individual's latent trait, and the participant's affirmative responses to each of a set of filter items. In this paper, we propose an item response model for such "partially independent" item response data. We model such item response patterns as a function of a person-specific latent trait and a set of item parameters. Our model can be seen as a generalized hybrid of a discrete-time hazard model and a Rasch model. The proposed procedure yields estimates of (1) person-specific, interval-scale measures of a latent trait (or traits), along with person-specific standard errors of measurement; (2) conditional and marginal item severities for each item in a protocol; (3) person-specific conditional and marginal probabilities of an affirmative response to each item in a protocol; and (4) item information and total survey information. In addition, we show here how to investigate and test alternative conceptions of the dimensionality of the latent trait(s) being measured. Finally, we compare our procedure with a simpler alternative approach to summarizing data of this type.     

A law of large numbers for weighted plurality

Consider an election between $k$ candidates in which each voter votes randomly (but not necessarily independently) for a single candidate, and suppose that there is a single candidate that every voter prefers (in the sense that each voter is more likely to vote for this special candidate than any other candidate). Suppose we have a voting rule that takes all of the votes and produces a single outcome and suppose that each individual voter has little effect on the outcome of the voting rule. If the voting rule is a weighted plurality, then we show that with high probability, the preferred candidate will win the election. Conversely, we show that this statement fails for all other reasonable voting rules. This result is an extension of one by Häggström, Kalai and Mossel, who proved the above in the case $k=2$ .     

DURATION MODELS FOR CREDIT RATING MIGRATION: EVIDENCE FROM THE FINANCIAL CRISIS

We introduce a specific duration model to analyze the prediction of the credit rating migration. We consider hazard rate processes based on multi‐state autoregressive conditional duration models. To take account of the economic context, we model the conditional mean of the duration between two ratings by means of a latent process. To this purpose, a dynamic‐ordered probit model is developed to describe the directions taken by the ratings in the presence of multiple states. As an illustration, we study the migration of credit rating during periods before and after the financial crisis. (JEL C14, C41, G24)     

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.     

MEASURING AND ANALYZING CLASS INEQUALITY WITH THE GINI INDEX INFORMED BY MODEL-BASED CLUSTERING

The most widely used measure for studying social, economic, and health inequality is the Gini index/ratio. Whereas other measures of inequality possess certain useful characteristics, such as the straightforward decomposability of the generalized entropy measures, the Gini index has remained the most popular, at least in part due to its ease of interpretation. However, the Gini index has a limitation in measuring inequality. It is less sensitive to how the population is stratified than how individual values differ. The twin purposes of this paper are to explain the limitation and to propose a model-based method—latent class/clustering analysis for understanding and measuring inequality. The latent cluster approach has the major advantage of being able to identify potential "classes" of individuals who share similar levels of income or one or more other attributes and to assess the fit of the model-based classes to the empirical data, based on different cluster distributional assumptions and the number of latent classes. This paper distinguishes class inequality from individual inequality, the type that is better captured by the Gini. Once the classes are estimated, the membership of estimated classes obtained from the best fitting model facilitates the decomposition of the Gini index into individual and class inequality. Class inequality is then measured by two relative stratification indices based on either the relative size of the Gini between-class components or the relative number of stratified individuals. Therefore, the Gini index is extended and assisted by model-based clustering to measure class inequality, thereby realizing its great potential for studying inequality. Income data from France and Hungary are used to illustrate the application of the method.     

A Goodness-Of-Fit Test for the Latent Class Model When Expected Frequencies Are Small

In this paper, a goodness-of-fit test for the latent class model is presented. The test uses only the limited information in the second-order marginal distributions from a set of k dichotomous variables, and it is intended for use when k is large and the sample size, n, is moderate or small. In that situation, a 2^k contingency table formed by the full cross-classification of k variables will be sparse in the sense that a high proportion of cell frequencies will be equal to zero or 1, and the chi-square approximation for traditional goodness-of-fit statistics such as the likelihood ratio will not be valid. The second-order marginal frequencies, which correspond to the bivariate distributions, are rarely sparse even when the joint frequencies have a high proportion of zero cells. Results from Monte Carlo experiments are presented that compare the rates of Type I and Type II errors for the proposed test to the rates for traditional goodness-of-fit tests. Results show that under commonly encountered conditions, a test of fit based on the limited information in the second-order marginals has a Type II error rate that is no higher than the error rate found for full-information test statistics, and that the test statistic given in this paper does not suffer from ill effects of sparseness in the joint frequencies.     

Loss of Control as a Discriminating Factor Between Different Latent Classes of Disordered Gambling Severity

Analyses of disordered gambling assessment data have indicated that commonly used screens appear to measure latent categories. This stands in contrast to the oft-held assumption that problem gambling is at the extreme of a continuum. To explore this further, we report a series of latent class analyses of a number of prevalent problem gambling assessments (PGSI, SOGS, DSM-IV Pathological Gambling based assessments) in nationally representative British surveys between 1999 and 2012, analysing data from nearly fifty thousand individuals. The analyses converged on a three class model in which the classes differed by problem gambling severity. This identified an initial class of gamblers showing minimal problems, a additional class predominantly endorsing indicators of preoccupation and loss chasing, and a third endorsing a range of disordered gambling criteria. However, there was considerable evidence to suggest that classes of intermediate and high severity disordered gamblers differed systematically in their responses to items related to loss of control, and not simply on the most ‘difficult’ items. It appeared that these differences were similar between assessments. An important exception to this was one set of DSM-IV criteria based analyses using a specific cutoff, which was also used in an analysis that identified an increase in UK problem gambling prevalence between 2007 and 2010. The results suggest that disordered gambling has a mixed latent structure, and that present assessments of problem gambling appear to converge on a broadly similar construct.     

Contesting Stigma: On Goffman's Assumptions of Normative Order

Goffman's classic analysis of stigma tacitly suggests that it has a conditional nature. An important shortcoming, however, is that his analysis proceeds from the existence of a normatively shared understanding of the criteria for and the distribution of stigma assignment. I use data from Somali immigrants to Canada to further that argument by showing that stigma as a social object cannot be created when its cultural and structural contexts are disjunctive. Through reverse stigmatization, counter devaluation, and rejection of discrimination, Somalis reveal the problematics of stigma establishment and therein raise the question of who is stigmatizing whom.     

Modelling financial satisfaction across life stages: A latent class approach

We explore the determinants of financial satisfaction using a modelling framework which allows the drivers of financial satisfaction to vary across life stages. Given that financial satisfaction is measured as an ordered variable, our modelling approach is based on a latent class ordered probit model with an ordered probit class assignment function. Our analysis of household survey data indicates that four life stages are supported by the data. Our results suggest that such flexibility is important in understanding the drivers of financial satisfaction over the life cycle since there is a substantial amount of parameter heterogeneity across the four classes.     

Britain's Colonial Emergencies and the Invisible Nationalists

Abstract From the perspective of imperial propaganda Britain's colonial emergencies of the forties and fifties have straightforward, even self-evident explanations. In the case of Malaya the state of emergency declared in June 1948 was a response to an international communist plot designed to seize power. In Kenya, an underground conspiracy of tribal extremists necessitated the implementation of emergency powers in October 1952 and the intervention of the British military. In British Guiana, the October 1953 state of emergency was essential to prevent a communist-inspired reign of terror and sabotage.¹
More objective researchers and journalists have questioned the familiar justification for Britain's colonial emergencies.² However, controversy persists, not simply about the interpretation of these events but about the basic facts.³ This is not surprising, because a study of the available files in the Public Records Office shows that the relationship between the colonial emergencies and their purported causes is far from straightforward. While imperial propaganda projected a sense of single-minded clarity, behind the scenes the leading experts of the Colonial Office were uncertain and deeply disturbed by events that they did not entirely comprehend. Nevertheless, despite their lack of a clear understanding of the situation in the affected colonies, the Colonial administration fully supported a military response. Indeed a study of the emergencies in Malaya, Kenya and British Guiana reveals a common pattern in the response of the British government and helps to place each of these conflicts in a wider perspective.     

Markovian assignment rules

We analyze dynamic assignment problems where agents successively receive different objects (positions, offices, etc.). A finite set of n vertically differentiated indivisible objects are assigned to n agents who live n periods. At each period, a new agent enters society, and the oldest agent retires, leaving his object to be reassigned. We define independent assignment rules (where the assignment of an object to an agent is independent of the way other objects are allocated to other agents), efficient assignment rules (where there does not exist another assignment rule with larger expected surplus), and fair assignment rules (where agents experiencing the same circumstances have identical histories in the long run). When agents are homogenous, we characterize efficient, independent and fair rules as generalizations of the seniority rule. When agents draw their types at random, we prove that independence and efficiency are incompatible, and that efficient and fair rules only exist when there are two types of agents. We characterize two simple rules (type-rank and type-seniority) which satisfy both efficiency and fairness criteria in dichotomous settings.     

Relationships between landscape pattern metrics,vertical structure and surface urban Heat Island formation in a Colorado suburb

Change in land surface temperature (LST) due to urbanization is a critical influence on the ecohydrological function and human health in cities. Past research has emphasized land cover composition and planimetric landscape pattern as drivers of LST patterns, but there have been few empirical studies examining the effects of vertical structure on thermal variation in cities. We used agglomerative cluster analysis to group 5 ha grid cells with similar land cover composition from high-resolution land cover data for our Aurora, Colorado, USA study area. We then compared the importance of different planimetric landscape pattern metrics and lidar-derived vertical structure variables as predictors of LST estimated from Landsat 5 thermal band data for each group. Variation in LST between cluster groups was analyzed with landscape and vertical structure data using random forest regression models and conditional variable importance metrics. Cluster analysis produced 7 distinct groups differing in land cover composition, planimetric landscape pattern, and vertical structure. Clusters with greater tree cover and higher mean tree height were generally cooler, while the height difference between buildings and trees had high conditional variable importance in random forest regression models. We found that the specific planimetric landscape pattern and vertical structure metrics most important for individual clusters differed, suggesting that the relative importance of variables depends on land-use and land cover. Our results highlight the importance of including vertical structure in empirical analyses of urban LST.     

Individual differences and electronic monitoring at work

Individual differences such as personality and demographic factors have effects on how people react to Electronic Performance Monitoring (EPM), yet the literature on this aspect of electronic monitoring has been scattered. The present paper summarizes this body of empirical research and presents a framework for organizing current research findings based on two dimensions: the probability of successful work under the monitoring and the probability of accepting that the monitoring is of value. The framework also allows researchers to make predictions regarding additional individual difference variables. Managers may use this information to select employees who are likely to respond well to monitoring conditions and to structure monitoring procedures so that they are likely to be accepted by their employees with particular individual difference characteristics.     

Social desire paths: a new theoretical concept to increase the usability of social science research in society

Social scientists are well-trained to observe and chart social trends, but less experienced at presenting scientific findings in formats that can inform social change work. In this article, I propose a new theoretical concept that provides a mechanism by which social science research can be more effectively applied for proactive policy, organizational, and program development. The approach is to use the metaphor of “desire paths” from landscape architecture to show how social scientists can identify and analyze social desire paths that appear on the social structural landscape. Social desire paths usually emerge because existing formal structures do not meet individual or group needs. Such paths are generally started at the individual level, followed by others through individual actions, and ultimately leave an (usually informal) imprint on the social structure, even though the motivations behind those actions are not usually social change. Using what we know about the sociology of interests and what we have learned from trying to apply social science findings to policy, I propose seven criteria for phenomena to be defined as social desire paths. I then apply the criteria to two case studies related to housing, and discuss social desire paths usefulness to social scientists involved in any research that captures interests, deviance, or innovation; and that also has the potential to inform formal structures such as policy, organizations, program development, and participatory democracy.     

Using Experiential Learning to Help Students Understand the Impact of Food Insecurity

Experiential learning theory suggests that students increase their understanding when given the opportunity to experience a particular situation in addition to learning about it intellectually. This theory was used to construct an assignment to assist social work master’s students in better understanding food insecurity and the Supplemental Nutrition Assistance Program (SNAP). Through coding previously collected reactions to the assignment, the researchers discovered multiple reoccurring themes: increased understanding of SNAP, feelings about the program, realizations regarding individual privilege, client stigma, the social experience of eating, and empathy for those who experience food insecurity. Through this exercise, students increased their knowledge of the program and also gained a better understanding of how food insecurity personally affects individuals and families.     

Covariance Models For Latent Structure In Longitudinal Data

We present several approaches to modeling latent structure in longitudinal studies when the covariance itself is the primary focus of the analysis. This is a departure from much of the work on longitudinal data analysis, in which attention is focused solely on the cross-sectional mean and the influence of covariates on the mean. Such analyses are particularly important in policy-related studies, in which the heterogeneity of the population is of interest. We describe several traditional approaches to this modeling and introduce a flexible, parsimonious class of covariance models appropriate to such analyses. This class, while rooted in the tradition of mixed effects and random coefficient models, merges several disparate modeling philosophies into what we view as a hybrid approach to longitudinal data modeling. We discuss the implications of this approach and its alternatives especially on model interpretation. We compare several implementations of this class to more commonly employed mixed effects models to describe the strengths and limitations of each. These alternatives are compared in an application to long-term trends in wage inequality for young workers. The findings provide additional guidance for the model formulation process in both statistical and substantive senses.