Wage Mobility in Europe. A Comparative Analysis Using restricted Multinomial Logit Regression

In this paper, we investigate cross-country differences in wage mobility in Europe using the European Community Household Panel. The paper is particularly focused on examining the impact of economic conditions, welfare state regimes and employment regulation on wage mobility. We apply a log-linear approach that is very much similar to a restricted multinomial logit model and much more flexible than the standard probit approach. It appears that regime, economic conditions and employment regulation explain a substantial part of the cross-country variation. The findings also confirm the existence of an inverse U-shape pattern of wage mobility, showing a great deal of low and high-wage persistence in all countries.wages; wage mobility; wage dynamics; multinomial logit regression; loglinear models; welfare states

The Lazy Bootstrap. A Fast Resampling Method for Evaluating Latent Class Model Fit

The latent class model is a powerful unsupervised clustering algorithm for categorical data. Many statistics exist to test the fit of the latent class model. However, traditional methods to evaluate those fit statistics are not always useful. Asymptotic distributions are not always known, and empirical reference distributions can be very time consuming to obtain. In this paper we propose a fast resampling scheme with which any type of model fit can be assessed. We illustrate it here on the latent class model, but the methodology can be applied in any situation. The principle behind the lazy bootstrap method is to specify a statistic which captures the characteristics of the data that a model should capture correctly. If those characteristics in the observed data and in model-generated data are very different we can assume that the model could not have produced the observed data. With this method we achieve the flexibility of tests from the Bayesian framework, while only needing maximum likelihood estimates. We provide a step-wise algorithm with which the fit of a model can be assessed based on the characteristics we as researcher find important. In a Monte Carlo study we show that the method has very low type I errors, for all illustrated statistics. Power to reject a model depended largely on the type of statistic that was used and on sample size. We applied the method to an empirical data set on clinical subgroups with risk of Myocardial infarction and compared the results directly to the parametric bootstrap. The results of our method were highly similar to those obtained by the parametric bootstrap, while the required computations differed three orders of magnitude in favour of our method.Comment: This is an adaptation of chapter of a PhD dissertation available at https://pure.uvt.nl/portal/files/19030880/Kollenburg_Computer_13_11_2017.pd

Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables

The Rasch family of models considered in this paper includes models for polytomous items and multiple correlated latent traits, as well as for dichotomous items and a single latent variable. An R package is described that computes estimates of parameters and robust standard errors of a class of log-linear-by-linear association (LLLA) models, which are derived from a Rasch family of models. The LLLA models are special cases of log-linear models with bivariate interactions. Maximum likelihood estimation of LLLA models in this form is limited to relatively small problems; however, pseudo-likelihood estimation overcomes this limitation. Maximizing the pseudo-likelihood function is achieved by maximizing the likelihood of a single conditional multinomial logistic regression model. The parameter estimates are asymptotically normal and consistent. Based on our simulation studies, the pseudo-likelihood and maximum likelihood estimates of the parameters of LLLA models are nearly identical and the loss of efficiency is negligible. Recovery of parameters of Rasch models fit to simulated data is excellent.

Who benefits from a job change: The dwarfs or the giants?

Empirical studies have shown that voluntary job-to-job changes have a positive effect on wage mobility. In this paper, we suggest that the impact of a job change on wage growth depends on the position in the wage distribution. Using panel data from the UK and Germany, we investigate the effect of employer changes and within-firm job changes on year-to-year wage mobility. We show that a change of employer results into a wage increase for the low-paid workers but not for the high-paid workers. Within-firm job changes produce, on average, moderate wage gains for the low-paid workers in the UK, but have no effect in Germany. Results on 3-year wage mobility are shown to be very similar to the results on year-to-year wage growth.low pay ; high pay ; job mobility ; wage mobility

How to perform three-step latent class analysis in the presence of measurement non-invariance or differential item functioning

The practice of latent class (LC) modeling using a bias-adjusted three-step approach has become widely popular. However, the current three-step approach has one important drawback–its key assumption of conditional independence between external variables and latent class indicators is often violated in practice, such as when a (nominal) covariate represents subgroups showing measurement non-invariance (MNI) or differential item functioning (DIF). In this article, we demonstrate how the current three-step approach should be modified to account for MNI; that is, covariates causing DIF should be included in the step-one model and the step-three classification error adjustment should differ across the values of the DIF covariates. We also propose a model-building strategy that makes the new methodology practically applicable also when it is unknown which of the external variables cause DIF. The new approach, implemented in the program Latent GOLD, is illustrated using a synthetic and a real data example

The Expected Parameter Change (EPC) for local dependence assessment in binary data latent class models

Binary data latent class models crucially assume local independence, violations of which can seriously bias the results. We present two tools for monitoring local dependence in binary data latent class models: the "Expected Parameter Change" (EPC) and a generalized EPC, estimating the substantive size and direction of possible local dependencies. The asymptotic and finite sample behavior of the measures is studied, and two applications to the U.S. Census estimation of Hispanic ethnicity and medical experts' ratings of x-rays demonstrate its value in arriving at a model that balances realism and parsimony.Comment: R code implementing our proposal and including both example datasets is available online as supplementary materia

On the exploratory road to unraveling factor loading non-invariance:A new multigroup rotation approach

Multigroup exploratory factor analysis (EFA) has gained popularity to address measurement invariance for two reasons. Firstly, repeatedly respecifying confirmatory factor analysis (CFA) models strongly capitalizes on chance and using EFA as a precursor works better. Secondly, the fixed zero loadings of CFA are often too restrictive. In multigroup EFA, factor loading invariance is rejected if the fit decreases significantly when fixing the loadings to be equal across groups. To locate the precise factor loading non-invariances by means of hypothesis testing, the factors’ rotational freedom needs to be resolved per group. In the literature, a solution exists for identifying optimal rotations for one group or invariant loadings across groups. Building on this, we present multigroup factor rotation (MGFR) for identifying loading non-invariances. Specifically, MGFR rotates group-specific loadings both to simple structure and between-group agreement, while disentangling loading differences from differences in the structural model (i.e., factor (co)variances).</p

Building latent class growth trees

Researchers use latent class growth (LCG) analysis to detect meaningful subpopulations that display different growth curves. However, especially when the number of classes required to obtain a good fit is large, interpretation of the encountered class-specific curves might not be straightforward. To overcome this problem, we propose an alternative way of performing LCG analysis, which we call LCG tree (LCGT) modeling. For this purpose, a recursive partitioning procedure similar to divisive hierarchical cluster analysis is used: Classes are split until a certain criterion indicates that the fit does not improve. The advantage of the LCGT approach compared to the standard LCG approach is that it gives a clear insight into how the latent classes are formed and how solutions with different numbers of classes relate. The practical use of the approach is illustrated using applications on drug use during adolescence and mood regulation during the day

Estimating the number of serious road injuries per vehicle type in the Netherlands by using multiple imputation of latent classes

Statistics that are published by official agencies are often generated by using population registries, which are likely to contain classification errors and missing values. A method that simultaneously handles classification errors and missing values is multiple imputation of latent classes (MILC). We apply the MILC method to estimate the number of serious road injuries per vehicle type in the Netherlands and to stratify the number of serious road injuries per vehicle type into relevant subgroups by using data from two registries. For this specific application, the MILC method is extended to handle the large number of missing values in the stratification variable ‘region of accident’ and to include more stratification covariates. After applying the extended MILC method, a multiply imputed data set is generated that can be used to create statistical figures in a straightforward manner, and that incorporates uncertainty due to classification errors and missing values in the estimate of the total variance

Latent class trees with the three-step approach

Latent class (LC) analysis is widely used in the social and behavioral sciences to find meaningful clusters based on a set of categorical variables. To deal with the common problem that a standard LC analysis may yield a large number classes and thus a solution that is difficult to interpret, recently an alternative approach has been proposed, called Latent Class Tree (LCT) analysis. It involves starting with a solution with a small number of "basic" classes, which may subsequently be split into subclasses at the next stages of an analysis. However, in most LC analysis applications, we not only wish to identify the relevant classes, but also want to see how they relate to external variables (covariates or distal outcomes). For this purpose, researchers nowadays prefer using the bias-adjusted three-step method. Here, we show how this bias-adjusted three-step procedure can be applied in the context of LCT modeling. More specifically, an R-package is presented that performs a three-step LCT analysis: it builds a LCT and allows checking how splits are related to the relevant external variables. The new tool is illustrated using a cross-sectional application with multiple indicators on social capital and demographics as external variables and with a longitudinal application with a mood variable measured multiple times during the day and personality traits as external variables