Linear Mixed Measurement Error Models Research Articles

Estimation of Linear Mixed Measurement Error Models in the Presence of Multicollinearity

Estimation of Linear Mixed Measurement Error Models in the Presence of Multicollinearity

Ölçüm Hatalı Kısmi Lineer Karma Modellerde Modified Kernel Ridge Öntahmin Edicilerin Covid-19 Veri Analizi Yoluyla Performans Değerlendirmesi

In this article we describe new predictors under multicollinearity situation in the partially linear mixed measurement error models. In order to achieve this aim, we refer to some preliminary information and use it in order to suggest the modified Kernel ridge predictors in the partially linear mixed measurement error models. In addition, we also attain some mean square error comparisons between our new described modified Kernel ridge predictors and predictors previously described in literature for the partially linear mixed measurement error model. In conclusion, the article showcases real data analysis and a simulation study to illusrate our theoretical findings.

Kernel mixed and Kernel stochastic restricted ridge predictions in the partially linear mixed measurement error models: an application to COVID-19

ABSTRACT In this article, we define mixed predictor and stochastic restricted ridge predictor of partially linear mixed measurement error models by taking advantage of Kernel approximation. Under matrix mean square error criterion, we make the comparison of the superiorities the linear combinations of the new defined predictors. Then we investigate the asymptotic normality characteristics and the situation of the unknown covariance matrix of measurement errors. Finally, the study is ended with a Monte Carlo simulation study and COVID-19 data application.

Local influence in linear mixed measurement error models with ridge estimation

This paper deals with the assessment of the effects of minor perturbations of data in the linear mixed measurement error models with Ridge estimation, based on the corrected score function. The local influence approach is used for assessing the influence of small perturbations on the parameter estimates. We examine different types of perturbation schemes including the covariance matrix of the conditional errors, case weight, response, and explanatory perturbation, to identify influential observations. A real data application and a simulation study illustrate the performance of the proposed diagnostics.

Kernel Liu prediction approach in partially linear mixed measurement error models

ABSTRACT In this paper, we put forward ‘kernel Liu prediction approach’ instead of ‘kernel prediction approach’ under multicollinearity case in partially linear mixed measurement error model. We obtain the necessary and sufficient condition for the superiority of the linear combinations of the predictors in the sense of the matrix mean square error criterion and give the selection of the Liu biasing parameter via the Conceptual Prediction () criterion. The asymptotic normality condition is examined and the unknown covariance matrix of measurement errors circumstance is derived. We study a numerical example together with a Monte Carlo simulation study to evaluate the performance of the kernel Liu prediction approach at the end of this paper.

Influence measures and outliers detection in linear mixed measurement error models with Ridge estimation

In this article, we have concentrated on the influence diagnostics based on the mean shift outlier models (MSOM) and case deletion methods in the linear mixed measurement error models with Ridge estimation using the corrected likelihood of Nakamura (1990). We have derived the corrected score test statistic for outliers detection according to MSOM. Then, several case deletion measures are constructed as a tool for influence diagnostics. A parametric bootstrap procedure is used to obtain empirical distributions of the test statistics, and a simulation study has been used to show the performance of the proposed score test statistic and cook distance. Finally, a numerical example is given to illustrate the theoretical results.

Improved estimation in elliptical linear mixed measurement error models

In this paper, we propose a set of improved estimators for the fixed effect parameters in the linear mixed models when the covariates are measured with additive errors and prior information for the parameters is available. When it is suspected that the parameter vector may be the null-vector with some degree of uncertainty, we define improved estimators which including the preliminary test estimator, the Stein-type estimator and the postive-rule Stein-type estimator. It is assumed that the measurement error distributed according to the law belonging to the class of elliptically contoured distributions. The asymptotic properties of resulting estimators such as the asymptotic distributional quadratic biases and the asymptotic distributional quadratic risks are examined. A simulation study is also performed to illustrate the finite sample performance of the proposed procedures and finally Boston housing data set is analysed.

Ridge estimation in linear mixed measurement error models with stochastic linear mixed restrictions

This article is concentrated on the problem of multicollinearity in linear mixed models (LMMs) with measurement error in the fixed effects variables. After introducing a ridge estimator (RE) in these models, we propose a new estimator called the stochastic restricted ridge estimator (SRRE) by combining the ridge estimator (RE) and the stochastic restricted estimator (SRE). Moreover, asymptotic properties of these estimators will be derived and the necessary and sufficient conditions for the superiority of the SRRE over the RE and SRE are obtained using the mean squared error matrix (MSEM). Finally, the theoretical findings of the proposed estimators are also evaluated with a Monte Carlo simulation study and a numerical example.

Stochastic restricted Liu estimator in linear mixed measurement error models

This paper is concerned with the Liu estimator, stochastic restricted estimator and stochastic restricted Liu estimator of fixed and random effects in the linear mixed measurement error models. We compare the proposed estimators under the criterion of mean squared error matrix (MSEM). Furthermore, the selection of the Liu biasing parameter is discussed. A real data analysis is provided to illustrate the theoretical results and a simulation study is conducted to characterize the performance of estimators in the linear mixed measurement error model.

Influence Diagnostics in Semiparametric Linear Mixed Measurement Error Models

Semiparametric linear mixed measurement error models are extensions of linear mixed measurement error models to include a nonparametric function of some covariate. They have been found to be useful in both cross-sectional and longitudinal studies. In this paper first we propose a penalized corrected likelihood approach to estimate the parametric component in semiparametric linear mixed measurement error model and then using the case deletion and subject deletion analysis we survey the influence diagnostics in such models. Finally, the performance of our influence diagnostics methods are illustrated through a simulated example and a real data set.

A variance shift model for detection of outliers in the linear mixed measurement error models

ABSTRACTIn this paper, we extend a variance shift model, previously considered in the linear mixed models, to the linear mixed measurement error models using the corrected likelihood of Nakamura (1990). This model assumes that a single outlier arises from an observation with inflated variance. We derive the score test and the analogue of the likelihood ratio test, to assess whether the ith observation has inflated variance. A parametric bootstrap procedure is implemented to obtain empirical distributions of the test statistics. Finally, results of a simulation study and an example of real data are presented to illustrate the performance of proposed tests.

Estimation in skew-normal linear mixed measurement error models

In this paper we define a class of skew-normal linear mixed measurement error models. This class provides a useful generalization of normal linear mixed models with measurement error in fixed effects variables. It is assumed that the random effects, model errors and measurement errors follow a skew-normal distribution, extending usual symmetric normal model in order to avoid data transformation. We find the likelihood function of the observed data, which can be maximized by using standard optimization techniques. Next, an EM-type algorithm is proposed for estimating the parameters that seems to provide some advantages over a direct maximization of the likelihood. Finally, we propose results of a simulation study and an example of real data for illustration.

Residuals and leverages in the linear mixed measurement error models

Residuals are frequently used to evaluate the validity of the assumptions of statistical models and may also be employed as tools for model selection. In this paper, we consider residuals and their limiting properties in the linear mixed measurement error models. Also, we develop types of residuals for these models and then review some of the residual analysis techniques. Further, by using the definition of generalized leverage, we derive generalized leverage matrices for identification of high-leverage points for these models. Finally, we analyse a real data set.

Likelihood inference in generalized linear mixed measurement error models

The generalized linear mixed models (GLMMs) for clustered data are studied when covariates are measured with error. The most conventional measurement error models are based on either linear mixed models (LMMs) or GLMMs. Even without the measurement error, the frequentist analysis of LMM, and particularly of GLMM, is computationally difficult. On the other hand, Bayesian analysis of LMM and GLMM is computationally convenient in both cases without and with the measurement error. Recent introduction of the method of data cloning has made frequentist analysis of mixed models also equally computationally convenient. As an application of data cloning, we conduct a frequentist analysis of GLMM with covariates subject to the measurement error model. The performance of the proposed approach which yields the maximum likelihood estimation is evaluated by two important real data types, Normal and logistic linear mixed measurement error models, and also through simulation studies.

Estimation of variance components in linear mixed measurement error models

In this paper, we consider a linear mixed model with measurement errors in fixed effects. We find the corrected score function estimators for the variance components. An iterative algorithm is proposed for estimating the parameters. The computations on each iteration of this algorithm are those associated with computing estimates of fixed and random effects for given values of the variance components. We also derive the consistency of the estimators under regularity conditions. The simulation study shows that for relatively small sample size the corrected estimators perform very well. Finally, an example of real data is given for illustration.

On Estimation and Influence Diagnostics in Linear Mixed Measurement Error Models

SYNOPTIC ABSTRACTIt is not uncommon that the independent variables of linear mixed models are subject to measurement errors in practice. In this paper, we suggest a method for parameter estimation in linear mixed measurement error models, based on the corrected score function. The proposed parameter estimates are shown to be statistically consistent to the order of n−½ and normally distributed asymptotically. Diagnostic measures for the model such as the leverage measure, Cook's distance and local influence measures are constructed. A data set on hedonic housing price is analyzed.

SIMEX variance component tests in generalized linear mixed measurement error models.

In the analysis of clustered data with covariates measured with error, a problem of common interest is to test for correlation within clusters and heterogeneity across clusters. We examined this problem in the framework of generalized linear mixed measurement error models. We propose using the simulation extrapolation (SIMEX) method to construct a score test for the null hypothesis that all variance components are zero. A key feature of this SIMEX score test is that no assumptions need to be made regarding the distributions of the random effects and the unobserved covariates. We illustrate this test by analyzing Framingham heart disease data and evaluate its performance by simulation. We also propose individual SIMEX score tests for testing the variance components separately. Both tests can be easily implemented using existing statistical software.

A bias correction regression calibration approach in generalized linear mixed measurement error models

Two major topics are discussed when a fixed effect covariate is measured with error in a generalized linear mixed effects model: (i) the applicability of a direct regression calibration approach in various situations and (ii) a bias correction regression calibration approach. When the fixed and random effect structures are both misspecified, we find that a direct bias correction to the naive estimators is often not feasible due to lack of analytical bias expressions. While the direct regression calibration approach still often leads to inconsistent estimators, a combination of using the regression calibration to correct for the misspecified fixed effects and applying direct bias correction to correct for the misspecified random effects provides a simple, fast, and easy to implement method. Applications of this approach to linear, loglinear, probit and logistic mixed models arc discussed in detail A small simulation study is presented for the logistic normal mixed model.

Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models

We consider generalized linear mixed models (GLMMs) for clustered data when one of the predictors is measured with error. When the measurement error is additive and normally distributed and the error-prone predictor is itself normally distributed, we show that the observed data also follow a GLMM but with a different fixed effects structure from the original model, a different and more complex random effects structure, and restrictions on the parameters. This characterization enables us to compute the biases that result in common GLMMs when one ignores measurement error. For instance, in one common situation the biases in parameter estimates become larger as the number of observations within a cluster increases, both for regression coefficients and for variance components. Parameter estimation is described using the SIMEX method, a relatively new functional method that makes no assumptions about the structure of the unobservable predictors. Simulations and an example illustrate the results.

Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models

Bias Analysis and SIMEX Approach in Generalized Linear Mixed Measurement Error Models