C++ Klassen zur Linearen Regression bei fehlenden Kovariablen

In diesem Bericht werden C++ Klassen zu linearen Modellen mit fehlenden Werten in der Kovariablenmatrix X vorgestellt. Diese Klassen implementieren erste verwendbare Modelle wie Zero Order Regression, First Order Regression oder modified First Order Regression und dienen als Ausgangsbasis für weitere Modellklassen. Die hier vorgestellten Klassen können in Simulationsstudien oder für konkrete Datensätze verwendet werden

Modified First Order Regression, eine Simulationsstudie

In diesem Bericht werden verschiedene Imputationsmechanismen fuer fehlende Kovariablen in einem linearen Regressionsmodell mit zwei Kovariablen untersucht. Hierbei ist eine der Kovariablen vollstaendig beobachtet, die andere nur teilweise. Die betrachteten Imputationsmechanismen sind Zero Order Regression (ZOR), First Order Regression (FOR), First Order Regression plus random noise (FOR+) und Modified First Order Regression (MFOR)

Using diagnostic measures to detect non-MCAR processes in linear regression models with missing covariates

This paper presents methods to analyze and detect non-MCAR processes that lead to missing covariate values in linear regression models. First, the data situation and the problem is sketched. The next section provides an overview of the methods that deal with missing covariate values. The idea of using outlier methods to detect non-MCAR processes is described in section 3. Section 4 uses these ideas to introduce a graphical method to visualize the problem. Possible extensions conclude the presentation

Regression modelling with fixed effects - missing values and other problems

The paper considers new devices to predict the response variable using a convex target function weighting the response and its expectation. A MDEP-matrix superiority condition is given concerning BLUE, RLSE and mixed estimator where the latter is used in case of imputation for missing values. A small simulation study compares the alternative estimators. Finally the detection of non-MCAR processes in linear regression is discussed

MAREG and WinMAREG

This paper describes a software tool for marginal regression methods. MAREG currently handles binary, categorical and continious data with several link functions. Although intended for the analysis of correlated data, uncorrelated data can be analysed. We supplies two different approaches for these problems-Maximum Likelihood and GEE methods. Handling of missing data is also provided. [ Published in: Computational Statistics and Data Analysis, 24, 235-241

WinMAREG Quick Start

This paper is a short introduction into the usage of WinMAREG. Two examples are used to illustrate the most common options and features of the software

Shrinkage Estimation of Incomplete Regression Models by Yates Procedure

The problem of estimating the coefficients in a linear regression model is considered when some of the response values are missing. The conventional Yates procedure employing least squares predictions for missing values does not lead to any improvement over the least squares estimator using complete observations only. However, if we use Stein-rule predictions, it is demonstrated that some improvement can be achieved. An unbiased estimator of the mean squared error matrix of the proposed estimator of coefficient vector is also presented. Some work on the application of the proposed estimation procedure to real-world data sets involving some discrete variables in the set of explanatory variables is under way and will be reported in future

Approximate Confidence Regions for Minimax-Linear Estimators

Minimax estimation is based on the idea, that the quadratic risk function for the estimate β is not minimized over the entire parameter space R^K, but only over an area B(β) that is restricted by a priori knowledge. If all restrictions define a convex area, this area can often be enclosed in an ellipsoid of the form B(β) = { β : β' Tβ ≤ r }. The ellipsoid has a larger volume than the cuboid. Hence, the transition to an ellipsoid as a priori information represents a weakening, but comes with an easier mathematical handling. Deriving the linear Minimax estimator we see that it is biased and non-operationable. Using an approximation of the non-central χ^2-distribution and prior information on the variance, we get an operationable solution which is compared with OLSE with respect to the size of the corresponding confidence intervals

C++ Utilities zur Implementierung statistischer Verfahren unter Berücksichtigung fehlender Werte

Die hier vorgestellten Erweiterungen der bereits bestehenden generischen Bibliothek zur linearen Algebra (Fieger, A., Heumann, C., Kastner, C., Watzka, K., 1997:(Discussion Paper 63) stellen Funktionen bereit, die bei der Implementierung statistischer Verfahren benötigt werden. Besondere Beachtung findet der Umgang mit fehlenden Daten