Unbalanced Random Effects Research Articles

Building reliable and generalizable clerkship competency assessments: Impact of ‘hawk-dove’ correction

Purpose Systematic differences among raters’ approaches to student assessment may result in leniency or stringency of assessment scores. This study examines the generalizability of medical student workplace-based competency assessments including the impact of rater-adjusted scores for leniency and stringency. Methods Data were collected from summative clerkship assessments completed for 204 students during 2017–2018 the clerkship at a single institution. Generalizability theory was used to explore variance attributed to different facets (rater, learner, item, and competency domain) through three unbalanced random-effects models by clerkship including applying assessor stringency-leniency adjustments. Results In the original assessments, only 4–8% of the variance was attributed to the student with the remainder being rater variance and error. Aggregating items to create a composite score increased variability attributable to the student (5–13% of variance). Applying a stringency-leniency (‘hawk-dove’) correction substantially increased the variance attributed to the student (14.8–17.8%) and reliability. Controlling for assessor leniency/stringency reduced measurement error, decreasing the number of assessments required for generalizability from 16–50 to 11–14. Conclusions Similar to prior research, most of the variance in competency assessment scores was attributable to raters, with only a small proportion attributed to the student. Making stringency-leniency corrections using rater-adjusted scores improved the psychometric characteristics of assessment scores.

Bootstrap inference on variance component functions in the unbalanced two-way random effects model

In this paper, we consider the one-sided hypothesis testing problems for variance component functions in the unbalanced two-way random effects model. Firstly, using the Bootstrap approach and generalized approach, the test statistics and confidence intervals for the sum and ratio of variance components are constructed respectively. Next, the Monte Carlo simulation results indicate that the Bootstrap approach is better than the generalized approach in most cases. Finally, the above approaches are applied to the real data example of the efficiency of assembly lines workers in a manufacturing plant.

Forecasting with unbalanced panel data

AbstractThis paper derives the best linear unbiased prediction (BLUP) for an unbalanced panel data model. Starting with a simple error component regression model with unbalanced panel data and random effects, it generalizes the BLUP derived by Taub (Journal of Econometrics, 1979, 10, 103–108) to unbalanced panels. Next it derives the BLUP for an unequally spaced panel data model with serial correlation of the AR(1) type in the remainder disturbances considered by Baltagi and Wu (Econometric Theory, 1999, 15, 814–823). This in turn extends the BLUP for a panel data model with AR(1) type remainder disturbances derived by Baltagi and Li (Journal of Forecasting, 1992, 11, 561–567) from the balanced to the unequally spaced panel data case. The derivations are easily implemented and reduce to tractable expressions using an extension of the Fuller and Battese (Journal of Econometrics, 1974, 2, 67–78) transformation from the balanced to the unbalanced panel data case.

Nonconformance probability of an air quality index

Air pollution is one of the most important global environmental issues. Taiwan Environmental Protection Agency (EPA) is currently using an Air Quality Index (AQI) to measure and monitor its national air quality. The main objective of this study is to assess the air quality per hour every month in Taichung City of Taiwan from 2014 to 2016 based on the nonconformance probability of the AQI index. The nonconformance probability is defined as the probability that a characteristic of interest falls outside of an acceptance region. A lower confidence bound for the nonconformance probability is applied to test whether the AQI index value exceeds a warning threshold, and then the government could issue warnings according to the decision made by such statistical inference. An unbalanced two-way random effects model is presented for fitting the AQI index values. We evaluate three different lower confidence bound construction methods, including a t-based, an adjusted t-based and a generalized pivotal quantity (GPQ) based methods, through a detailed simulation study. Finally, a hybrid method of the t-based and the adjusted t-based estimators is recommended for practical use.

Multinational Subsidiary Performance: Evidence from the Ghanaian Banking Sector

The global economic volatility has given rise to diverse firm operational strategies including internationalization through subsidiary establishment. This has aroused the interest of scholars to the study of multinational firm performance. The study seeks to ascertain the factors that contribute to the performance of multinational subsidiary banks in Ghana. Using an unbalanced random effects panel regression estimation following the Hausman specification test, the study found that increasing bank size does not necessarily lead to performance. As it stands, the Multinational Subsidiary (MNS) banks under perform as they increase in size. It was further noted that the banks are inefficient and so shift their costs and risks to customers in the form of high interest charges on credit. Notwithstanding, it appears that older MNSs perform better than the relatively younger ones. The study found that leadership origin does not have any significant impact on bank performance. Evidence was, however, found about the significant influence of the host country economic conditions on MNS performance.

Unilateral Conformance Proportions in Balanced and Unbalanced Normal Random Effects Models

Conformance proportion is the proportion of a performance characteristic of interest that falls within a prespecified acceptance region, which has been used in various applications. In this article, a simple closed-form interval estimation, based on Student’s t statistic, is proposed for unilateral conformance proportions in balanced and unbalanced random-effects models. Two real datasets are analyzed to illustrate the proposed method, whose performance is also evaluated through detailed simulation studies. The simulation results reveal that the empirical coverage probabilities for upper confidence limits of the method are sufficiently close to the nominal values, but those for lower confidence limits appear to be slightly less than the nominal level. Furthermore, a bootstrap-based calibration for both upper and lower confidence limits is provided to have empirical coverage probabilities closer to the nominal level. This article has supplementary material online.

On Computing Maximum-Likelihood Estimates of the Unbalanced Two-Way Random-Effects Model

This article applies the ECME algorithm to derive an easily implemented iterative feasible generalized least squares procedure for calculating maximum-likelihood estimates of the parameters of the unbalanced two-way random-effects model. The algorithm increases the log-likelihood monotonically and the fitted variance components are guaranteed to be non negative. This article applies the algorithm in an example.

Modifying the rebound: It depends! Explaining mobility behavior on the basis of the German socio-economic panel

We address the empirical question of the extent to which higher fuel efficiency of cars affects additional travel and the way this behavioral aspect is modified by additional variables. The data set used to estimate a theoretical model of the rebound effect covers two panel waves, 1998 and 2003, taken from the German Socio-Economic Panel (SOEP). To take full advantage of the information in the data available, and to avoid problems due to possible selection effects, we estimated an unbalanced two-wave random effects panel model. Our results suggest that in line with the rebound hypothesis, car efficiency has a negative effect on the kilometers driven. That is, the lower the fuel consumption, the greater the distance driven. However, contrasting recent empirical literature about the rebound effect in the transportation sector, this seems to be true only for cars with a consumption of more than roughly 8l per 100km. In addition, we find a positive diesel effect, which implies that owning a diesel engine car is positively correlated with the distance driven. Both effects can be interpreted as support for the rebound hypothesis, although not in a simple linear way. Moreover, it can be shown that some “soft” variables such as certain attitudes towards the environment tend to amplify this non-linear rebound effect.

One-Sided Tolerance Limits for Balanced and Unbalanced Random Effects Models

A simple analytical approach for constructing one-sided β-content, γ-confidence tolerance limits is proposed for general random effects models with normal data in both balanced and unbalanced data scenarios. The approach is based on an approximation to the noncentral t distribution and modified large sample methods for constructing confidence bounds on functions of variance components. An alternative bootstrap-adjusted limit is also proposed. The performance of the analytical and bootstrap-adjusted limits is assessed via simulation techniques. The results indicate that the analytical limit is generally somewhat conservative, but is often less conservative than an existing analytical approach and may provide substantially shorter interval lengths, particularly for smaller sample sizes and larger values of γ. The bootstrap-adjusted limit generally maintains the nominal confidence level and yields shorter interval lengths, though it can be anticonservative for small sample sizes. This article has supplementary material online.

Modifying the Rebound: It depends! Explaining Mobility Behaviour on the Basis of the German Socio-Economic Panel

We address the empirical question to which extent higher fuel efficiency of cars affects additional travel and how this behavioural aspect is modified by additional variables. The data set used to estimate a theoretical model of the rebound effect covers two panel waves, 1998 and 2003, taken from the German Socio-Economic Panel (SOEP). To take full advantage of the information in the data available, and to avoid problems due to possible selection effects, we estimated an unbalanced two-wave random effects panel model. Our results suggest that in line with the rebound hypothesis, there is a negative effect of car efficiency on the kilometers driven. That is, the lower the fuel consumption, the larger the driven distance. However, contrasting recent empirical literature about the rebound effect in the transportation sector, this seems to be true only for cars with a consumption of more than roughly eight liters per hundred kilometers. In addition, we find a positive diesel effect, which implies that owning a diesel engined car, has a positive effect on the driven distance. Both effects can be interpreted as support for the rebound hypothesis, although not in a simple linear way. Moreover, it can be shown that some “soft” variables such as certain attitudes towards the environment tend to amplify this non-linear rebound effect. Our results support the general direction of the rebound effect on households travel activities. But because of the remaining political relevance of the rebound effect, they also highlight the importance of accounting for additional behavioural variables which tend to influence individual mobility behaviour. Hence, the classical interpretation of the rebound as a linear effect of advances in fuel economy on individual travel has to be questioned.

One-sided tolerance limits for unbalanced one-way random effects models: a generalized Mee and Owen procedure

This article proposes a new procedure for obtaining one-sided tolerance limits in unbalanced random effects models. The procedure is a generalization of that proposed by Mee and Owen for the balanced situation, and can be easily implemented, because it only needs a non-central-t table. Two simulation studies are carried out to assess the performance of the new procedure and to compare it with one of the other procedures laid out in previous statistical literature. The article findings show that the new procedure is much simpler to compute and performs better than the previous ones, having inferior values of the gamma bias in a wide range of situations, representative of many actual industrial applications, and behaving also reasonably well in more extreme sampling situations. The use of the new limits is illustrated by an application to an actual example from the steel industry.

Inferences on the intraclass correlation coefficients in the unbalanced two-way random effects model with interaction

In this paper, the hypothesis testing and interval estimation for the intraclass correlation coefficients are considered in a two-way random effects model with interaction. Two particular intraclass correlation coefficients are described in a reliability study. The tests and confidence intervals for the intraclass correlation coefficients are developed when the data are unbalanced. One approach is based on the generalized p-value and generalized confidence interval, the other is based on the modified large-sample idea. These two approaches simplify to the ones in Gilder et al. [2007. Confidence intervals on intraclass correlation coefficients in a balanced two-factor random design. J. Statist. Plann. Inference 137, 1199–1212] when the data are balanced. Furthermore, some statistical properties of the generalized confidence intervals are investigated. Finally, some simulation results to compare the performance of the modified large-sample approach with that of the generalized approach are reported. The simulation results indicate that the modified large-sample approach performs better than the generalized approach in the coverage probability and expected length of the confidence interval.

DAnTE: a statistical tool for quantitative analysis of -omics data

Data Analysis Tool Extension (DAnTE) is a statistical tool designed to address challenges associated with quantitative bottom-up, shotgun proteomics data. This tool has also been demonstrated for microarray data and can easily be extended to other high-throughput data types. DAnTE features selected normalization methods, missing value imputation algorithms, peptide-to-protein rollup methods, an extensive array of plotting functions and a comprehensive hypothesis-testing scheme that can handle unbalanced data and random effects. The graphical user interface (GUI) is designed to be very intuitive and user friendly. DAnTE may be downloaded free of charge at http://omics.pnl.gov/software/. An example dataset with instructions on how to perform a series of analysis steps is available at http://omics.pnl.gov/software/

The pigeonhole bootstrap

Recently there has been much interest in data that, in statistical language, may be described as having a large crossed and severely unbalanced random effects structure. Such data sets arise for recommender engines and information retrieval problems. Many large bipartite weighted graphs have this structure too. We would like to assess the stability of algorithms fit to such data. Even for linear statistics, a naive form of bootstrap sampling can be seriously misleading and McCullagh [Bernoulli 6 (2000) 285--301] has shown that no bootstrap method is exact. We show that an alternative bootstrap separately resampling rows and columns of the data matrix satisfies a mean consistency property even in heteroscedastic crossed unbalanced random effects models. This alternative does not require the user to fit a crossed random effects model to the data.

The Expected Sample Variance of Uncorrelated Random Variables with a Common Mean and Some Applications in Unbalanced Random Effects Models

There is a little-known but very simple generalization of the standard result that for uncorrelated random variables with common mean and variance , the expected value of the sample variance is . The generalization justifies the use of the usual standard error of the sample mean in possibly heteroscedastic situations, and motivates elementary estimators in even unbalanced linear random effects models. The latter both provides nontrivial examples and exercises concerning method-of-moments estimation, and also helps “demystify” the whole matter of variance component estimation. This is illustrated in general for the simple one-way context and for a specific unbalanced two-factor hierarchical data structure.

Maximum Likelihood Analysis for Heteroscedastic One‐Way Random Effects ANOVA in Interlaboratory Studies

This article presents results for the maximum likelihood analysis of several groups of measurements made on the same quantity. Following Cochran (1937, Journal of the Royal Statistical Society 4(Supple), 102-118; 1954, Biometrics 10, 101-129; 1980, in Proceedings of the 25th Conference on the Design of Experiments in Army Research, Development and Testing, 21-33) and others, this problem is formulated as a one-way unbalanced random-effects ANOVA with unequal within-group variances. A reparametrization of the likelihood leads to simplified computations, easier identification and interpretation of multimodality of the likelihood, and (through a non-informative-prior Bayesian approach) approximate confidence regions for the mean and between-group variance.

Do Reuters spreads reflect currencies' differences in global trading activity?

A new estimation of the long-run impact of trading activity on bid–ask spreads in the foreign exchange markets is undertaken with a short panel containing around-the-clock Reuters quotes and global transaction volumes. Individual and time effects are accounted for in an unbalanced random effects model. In line with liquidity effect explanations the volume parameter is found to have a (weakly) significant negative sign, whereas the volatility parameter is positive. Structural parameters are stable over time, while residuals are groupwise heteroscedastic. Reuters quoting (`tick') frequency is also tested as a measure of trading activity with very similar results.)

Harmonic mean approach to uunbalanced random effects models under heteroscedasticity

In this paper we consider unbalanced random effects models under heteroscedastic variances. By using' the harmonic mean approach, it is shown that the problems are analogous to those from balanced random effects models under horaoscedastic variances. Thus, by using the harmonic mean approach, statistical inferences about variance components are derived by using procedures from balanced models under homoscedastic variances. Laguerre polynomial expansion is used to approximate the sampling distributions of relevant statistics.

On maximum likelihood and restricted maximum likelihood approaches to estimation of variance components

Two variations of the dispersion-mean correspondence model for varince components lead to the ML and REML equations. This formulation provides for addition of a nonnegativity constraint to the computational method of T. W. Anderson (1971, 1973), an iterative procedure for obtaining ML and REML estimates, which not only assures that estimates will be within the parameter space, but contributes to the stability of the algorithm as well. Estimates of the variance components obtained in this way (which includes MINQUE) are simulated for four balanced and two unbalanced random effects designs. The effect of the nonnegativity constraint on mean squared error is compared to the alternative of replacing negative values of unconstrained estimates to zero, for both the REML and ML approaches. For the two unbalanced designs, the effect of initial starting values and the significance of iterating are also assessed. The simulation results are an extension of those reported by Rich and Brown (1979) for the REML approac...

Cumulants of bilinear forms and quadratic forms and their applications

In this paper, mixed cumulants of general bilinear forms, quadratic forms and linear forms are given up to order 4. These results are useful in deriving approximations to the distributions of sums of squares and F-ratios from unbalanced analysis of variance models from non-normal universes. As an illustration, the results are applied to derive mixed cumulants of sums of squares in a three stages nested unbalanced random effects models from non-normal universes.