Heteroscedastic Random Effects Research Articles

Technical efficiency and firm heterogeneity in stochastic frontier models: application to smallholder maize farms in Ethiopia

This study estimates the technical efficiency measures of maize producing farm households in Ethiopia using stochastic frontier (SF) panel models that take different approaches to model firm heterogeneity. The efficiency measures are found to vary depending on how the estimation model treats both unobserved and observed firm heterogeneity. Estimates from the ‘true’ random effects (TRE) models that treat firm effects as heterogeneity are found to be identical to those from pooled SF models. Those results differ from the ones generated from the basic random effects (RE) models that treat firm effects as part of overall technical inefficiency. The more flexible generalised ‘true’ random effects (GTRE) model that splits the error term into firm effects, persistent inefficiency, transient inefficiency, and a random noise component indicates the presence of higher levels of persistent inefficiency than transient inefficiency. The basic truncated-normal RE model and heteroscedastic RE model yields similar efficiency estimates. The GTRE model predict persistent efficiency measures similar to those from the basic RE and flexible RE model with environmental variables incorporated in the variance function as well as in the deterministic production frontier. These results imply that the RE and GTRE panel models provide reliable efficiency estimates for our data compared to the TRE models. All the estimated SF models generate comparable production function parameters in terms of magnitude and sign. Overall, the results underscore the importance of scrutinising stochastic frontier models for their reliability of analytical results before drawing policy inferences.

Specification of Random Effects in Multilevel Models: A Review

The analysis of highly structured data requires models with unobserved components (random effects) able to adequately account for the patterns of variances and correlations. The specification of the unobserved components is a key and challenging task. In this paper, we first review the literature about the consequences of misspecifying the distribution of the random effects and the related diagnostic tools; we then outline the main alternatives and generalizations, also considering some issues arising in Bayesian inference. The relevance of suitably structuring the unobserved components is illustrated by means of an application exploiting a model with heteroscedastic random effects.

Decision-theoretic issues in heterogeneity variance estimation

Motivated by a heteroscedastic random effects setting of meta-analysis, a general model for the between-study variance is studied from the decision-theoretic point of view. This model leads to estimation of a linear in the variance reciprocals, random function or to simultaneous inference on curve-confined natural parameters of independent heterogeneous \(\chi ^2\)-random variables with given degrees of freedom. A form of the Stein phenomenon for the suggested loss functions is noted; the exact minimax value is determined, and minimax estimators are derived.

Specification of random effects in multilevel models: a review

The analysis of highly structured data requires models with unobserved compo- nents (random effects) able to adequately account for the patterns of variances and corre- lations. The specification of the unobserved components is a key and challenging task. In this paper, we first review the literature about the consequences of misspecifying the dis- tribution of the random effects and the related diagnostic tools; we then outline the main alternatives and generalizations, also considering some issues arising in Bayesian inference. The relevance of suitably structuring the unobserved components is illustrated by means of an application exploiting a model with heteroscedastic random effects.

Approximate interval for the between-group variance under heteroscedasticity

The paper presents an approximate confidence interval for the between-group variance in a one-way heteroscedastic random-effects model. Derivation of the interval is inspired by the ideas in Williams [A confidence intervals for variance components, Biometrika 49 (1962), pp. 278–281] for the homoscedastic case. Simulations suggest that the proposed interval performs better than or comparably to the other available procedures as studied in Wimmer and Witkovský [Between group variance component interval estimation for the unbalanced heteroscedastic one-way random effects model, J. Stat. Comput. Simul. 73 (2003), pp. 333–346], Hartung and Knapp [On confidence intervals for the among-group variance in the one-way random effects model with unequal error variances, J. Statist. Plann. Inference 127 (2005), pp. 157–177], Li [Comparison of confidence intervals on between group variance in unbalanced heteroscedastic one-way random models, Comm. Statist. Simulation Comput. 36 (2007), pp. 381–390]. Moreover, it is relatively easy to compute.

Tests concerning a nested mixed model with heteroscedastic random effects

Abstract The purpose of this article is to present tests concerning the fixed and random effects for a two-fold nested mixed model under the following conditions: 1. (i) The nesting effect is fixed. 2. (ii) The nested effect is random with an unknown variance component assumed to depend only on the levels of the nesting effect. 3. (iii) All random effects, including the random errors, are independently distributed as normal variates. 4. (iv) The subclass frequencies in the last stage are equal (last-stage uniformity). An example is given to illustrate the proposed tests.