Modern quantitative evidence synthesis methods often combine patient-level data from different sources, known as individual participants data (IPD) sets. A specific challenge in meta-analysis of IPD sets is the presence of systematically missing data, when certain variables are not measured in some studies, and sporadically missing data, when measurements of certain variables are incomplete across different studies. Multiple imputation (MI) is among the better approaches to deal with missing data. However, MI of hierarchical data, such as IPD meta-analysis, requires advanced imputation routines that preserve the hierarchical data structure and accommodate the presence of both systematically and sporadically missing data. We have recently developed a new class of hierarchical imputation methods within the MICE framework tailored for continuous variables. This article discusses the extensions of this methodology to categorical variables, accommodating the simultaneous presence of systematically and sporadically missing data in nested designs with arbitrary missing data patterns. To address the challenge of the categorical nature of the data, we propose an accept–reject algorithm during the imputation process. Following theoretical discussions, we evaluate the performance of the new methodology through simulation studies and demonstrate its application using an IPD set from patients with kidney disease.

The inverse probability of treatment weighted (IPTW) estimator can be used to make causal inferences under two assumptions: (1) no unobserved confounders (ignorability) and (2) positive probability of treatment and of control at every level of the confounders (positivity), but is vulnerable to bias if by chance, the proportion of the sample assigned to treatment, or proportion of control, is zero at certain levels of the confounders. We propose to deal with this sampling zero problem, also known as practical violation of the positivity assumption, in a setting where the observed confounder is cluster identity, i.e., treatment assignment is ignorable within clusters. Specifically, based on a random coefficient model assumed for the potential outcome, we augment the IPTW estimating function with the estimated potential outcomes of treatment (or of control) for clusters that have no observation of treatment (or control). If the cluster-specific potential outcomes are estimated correctly, the augmented estimating function can be shown to converge in expectation to zero and therefore yield consistent causal estimates. The proposed method can be implemented in the existing software, and it performs well in simulated data as well as with real-world data from a teacher preparation evaluation study.

Behavioral and psychological researchers have shown strong interests in investigating contextual effects (i.e., the influences of combinations of individual- and group-level predictors on individual-level outcomes). The present research provides generalized formulas for determining the sample size needed in investigating contextual effects according to the desired level of statistical power as well as width of confidence interval. These formulas are derived within a three-level random intercept model that includes one predictor/contextual variable at each level to simultaneously cover various kinds of contextual effects that researchers can show interest. The relative influences of indices included in the formulas on the standard errors of contextual effects estimates are investigated with the aim of further simplifying sample size determination procedures. In addition, simulation studies are performed to investigate finite sample behavior of calculated statistical power, showing that estimated sample sizes based on derived formulas can be both positively and negatively biased due to complex effects of unreliability of contextual variables, multicollinearity, and violation of assumption regarding the known variances. Thus, it is advisable to compare estimated sample sizes under various specifications of indices and to evaluate its potential bias, as illustrated in the example.

It is shown that measurement error in predictor variables can be modeled using item response theory (IRT). The predictor variables, that may be defined at any level of an hierarchical regression model, are treated as latent variables. The normal ogive model is used to describe the relation between the latent variables and dichotomous observed variables, which may be responses to tests or questionnaires. It will be shown that the multilevel model with measurement error in the observed predictor variables can be estimated in a Bayesian framework using Gibbs sampling. In this article, handling measurement error via the normal ogive model is compared with alternative approaches using the classical true score model. Examples using real data are given.

Group-level variance estimates of zero often arise when fitting multilevel or hierarchical linear models, especially when the number of groups is small. For situations where zero variances are implausible a priori, we propose a maximum penalized likelihood approach to avoid such boundary estimates. This approach is equivalent to estimating variance parameters by their posterior mode, given a weakly informative prior distribution. By choosing the penalty from the log-gamma family with shape parameter greater than 1, we ensure that the estimated variance will be positive. We suggest a default log-gamma(2,λ) penalty with λ→0, which ensures that the maximum penalized likelihood estimate is approximately one standard error from zero when the maximum likelihood estimate is zero, thus remaining consistent with the data while being nondegenerate. We also show that the maximum penalized likelihood estimator with this default penalty is a good approximation to the posterior median obtained under a noninformative prior.

Our default method provides better estimates of model parameters and standard errors than the maximum likelihood or the restricted maximum likelihood estimators. The log-gamma family can also be used to convey substantive prior information. In either case—pure penalization or prior information—our recommended procedure gives nondegenerate estimates and in the limit coincides with maximum likelihood as the number of groups increases.

An additive multilevel item structure (AMIS) model with random residuals is proposed. The model includes multilevel latent regressions of item discrimination and item difficulty parameters on covariates at both item and item category levels with random residuals at both levels. The AMIS model is useful for explanation purposes and also for prediction purposes as in an item generation context. The parameters can be estimated with an alternating imputation posterior algorithm that makes use of adaptive quadrature, and the performance of this algorithm is evaluated in a simulation study.

Composite links and exploded likelihoods are powerful yet simple tools for specifying a wide range of latent variable models. Applications considered include survival or duration models, models for rankings, small area estimation with census information, models for ordinal responses, item response models with guessing, randomized response models, unfolding models, latent class models with random effects, multilevel latent class models, models with log-normal latent variables, and zero-inflated Poisson models with random effects. Some of the ideas are illustrated by estimating an unfolding model for attitudes to female work participation.

When using linear models for cluster-correlated or longitudinal data, a common modeling practice is to begin by fitting a relatively simple model and then to increase the model complexity in steps. New predictors might be added to the model, or a more complex covariance structure might be specified for the observations. When fitting models for binary or ordered-categorical outcomes, however, comparisons between such models are impeded by the implicit rescaling of the model estimates that takes place with the inclusion of new predictors and/or random effects. This paper presents an approach for putting the estimates on a common scale to facilitate relative comparisons between models fit to binary or ordinal outcomes. The approach is developed for both population-average and unit-specific models.

In this article, a two-level regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error. Another advantage is that, contrary to observed scores, latent scores are test-independent, which offers the possibility of using results from different tests in one analysis where the parameters of the IRT model and the multilevel model can be concurrently estimated. The two-parameter normal ogive model is used for the IRT measurement model. It will be shown that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. Examples using simulated and real data are given.

We investigated the temporal associations between the severity of foot lesions caused by footrot (FR) and the severity of lameness in sheep. Sixty sheep from one farm were monitored for five weeks. The locomotion of each sheep was scored once each week using a validated numerical rating scale of 0-6. All feet were then examined, FR was the only foot lesion observed; the severity of FR lesions was recorded on a scale from 0 to 4. Sheep had a locomotion score > 0 on 144/298 observations. FR lesions were present on at least one foot on 83% of observations of lame sheep but also present on 27% of observations where sheep were not lame; 95% of these sheep with a lesion but not lame had FR score 1. The results from a linear mixed model with locomotion score as the outcome were that the mean (95% CI) locomotion score of 0.28 (0.02, 0.53) in sheep with no lesions increased by 0.35 (0.05, 0.65) in sheep with FR score 1 or 2 and by 1.55 (1.13, 1.96) in sheep with FR score > 2 at the time of the observation; indicating that as the severity of the lesion increased, the severity of lameness increased. One week before an FR score > 2 was clinically apparent, sheep had a locomotion score 0.81 (0.37, 1.24) higher than sheep that did not have an FR score > 2 in the subsequent week. One week after treatment with intramuscular antibacterials the locomotion score of lame sheep reduced by 1.00 (0.50, 1.49). Our results indicate a positive association between severity of FR lesions and locomotion score and indicate that some non-lame and mildly lame sheep have footrot lesions. Treatment of even those mildly lame will facilitate healing and probably reduce the spread of infection to other sheep in the same group.

The impact of trust on economic performance has been widely explored, but the reasons for its variability across countries are not well understood. We analyse the effect of the quality of government at the regional level on individual generalized trust in a multi-country context across regions in Europe. Social phenomena are often subnational and a number of public services are provided at a subnational level; the trust of individuals living in the same country may, therefore, differ by region depending also on the quality of the local government. As a proxy of the quality of institutions, we use the European Quality of Government Index, calculated at the regional level over 27 European Union (EU) countries. The analysis conducted on data extracted from the European Social Survey 2012 refers to 142 regions from 15 EU member states. Considering the clustered nature of the data, a multilevel approach is used. The findings show that living in a region with high-quality local government positively influences individual trust. This positive association survives the inclusion of several contextual regional variables.

Corruption is a global problem. Despite the importance of this theme, a shortage of theoretical models in both psychology and related areas that favor its understanding and investigation is noted. Due to this scarcity of theoretical models, in addition to the need to systematize studies on the topic, this theoretical article aims to describe the Analytical Model of Corruption (AMC) as an interdisciplinary and multilevel proposal aimed at corruption analysis. To achieve this goal, the concept of corruption was analyzed using related phenomena as reference. Similarities and differences in corruption have been identified with dishonest behavior and unethical behavior. Subsequently, theoretical models on corruption identified in the literature were presented, and their main characteristics and limitations were pointed out. After describing the models, the AMC was presented and its advantages over the previous models were discussed. Finally, it was concluded that the AMC could be configured as a theoretical model that guides interdisciplinary studies on corruption, allowing for a more complete analysis compared to previous theoretical models identified in the literature.

The interval between successive pregnancies (birth interval) is one of the main indexes used to evaluate the health of a mother and her child. This study evaluated birth intervals in Iran using data from the Iranian Multiple Indicators Demographic and Health Survey (IrMIDHS) conducted in 2010–2011. A total of 20,093 married Iranian women aged 15–54 years from the whole country constituted the study sample. Based on the nature of sampling and the unobserved population heterogeneity for birth intervals in each city and province, a multilevel survival frailty model was applied. Data were analysed for women’s first three birth intervals. The median first and second birth intervals were 30.3 and 39.7 months respectively. Higher education, Caesarean delivery, contraceptive use and exposure to public mass media were found to decrease the hazard rate ratio (HRR) of giving birth. Meanwhile, higher monthly income increased the hazard of giving birth. The results suggest that public mass media can play an effective role in encouraging women to have the recommended birth interval. Furthermore, increasing family income could encourage Iranian couples to decrease the time to their next birth.

This paper presents a unilevel and multilevel approach for the analysis and meta-analysis of single-case experiments (SCEs). We propose a definition of SCEs and derive the specific features of SCEs’ data that have to be taken into account when analysing and meta-analysing SCEs. We discuss multilevel models of increasing complexity and propose alternative and complementary techniques based on probability combining and randomisation test wrapping. The proposed techniques are demonstrated with real-life data and corresponding R code.

Research examining racial/ethnic disparities in pollution exposure often relies on cross-sectional data. These analyses are largely insensitive to exposure trends and rarely account for broader contextual dynamics. To provide a more comprehensive assessment of racial-environmental inequality over time, we combine the 1990 to 2009 waves of the Panel Study of Income Dynamics (PSID) with spatially- and temporally-resolved measures of nitrogen dioxide (NO2) and particulate matter (PM2.5 and PM10) in respondents’ neighborhoods, as well as census data on the characteristics of respondents’ metropolitan areas. Results based on multilevel repeated measures models indicate that Blacks and Latinos are, on average, more likely to be exposed to higher levels of NO2, PM2.5, and PM10 than Whites. Despite nationwide declines in levels of pollution over time, racial and ethnic disparities persist and cannot be fully explained by individual-, household-, or metropolitan-level factors.

Typically most studies of individual employees perceptions of the work place adopt multiple regression models (ordinary least squares [OLS]) which ignore inherent clustering in their data. However, such an approach does not supply unbiased and accurate answers to research questions. This study intends to simulate three data alternatives – weighted, disaggregated (individual level), and aggregated (organizational level) using the OLS and multilevel models to compare the results of different research designs. To answer the research questions, the current study investigates the impact of individual and organizational factors on job satisfaction, using a 2000 USA National Partnership for Reinventing Government survey. This study presents the methodological misuse and measurement errors of the previous research and presents guidelines for future research.

It is common for professional associations and regulators to combine the claims experience of several insurers into a database known as an “intercompany” experience data set. In this paper, we analyze data on claim counts provided by the General Insurance Association of Singapore, an organization consisting of most of the general insurers in Singapore. Our data comes from the financial records of automobile insurance policies followed over a period of nine years. Because the source contains a pooled experience of several insurers, we are able to study company effects on claim behavior, an area that has not been systematically addressed in either the insurance or the actuarial literatures.

We analyze this intercompany experience using multilevel models. The multilevel nature of the data is due to: a vehicle is observed over a period of years and is insured by an insurance company under a “fleet” policy. Fleet policies are umbrella-type policies issued to customers whose insurance covers more than a single vehicle. We investigate vehicle, fleet and company effects using various count distribution models (Poisson, negative binomial, zero-inflated and hurdle Poisson). The performance of these various models is compared; we demonstrate how our model can be used to update a priori premiums to a posteriori premiums, a common practice of experience-rated premium calculations. Through this formal model structure, we provide insights into effects that company-specific practice has on claims experience, even after controlling for vehicle and fleet effects.