Detecting and Assessing the Problems Caused by Multi-Collinearity: A Useof the Singular-Value Decomposition

This paper presents a means for detecting the presence of multicollinearity and for assessing the damage that such collinearity may cause estimated coefficients in the standard linear regression model. The means of analysis is the singular value decomposition, a numerical analytic device that directly exposes both the conditioning of the data matrix X and the linear dependencies that may exist among its columns. The same information is employed in the second part of the paper to determine the extent to which each regression coefficient is being adversely affected by each linear relation among the columns of X that lead to its ill conditioning.

Multicollinearity: Diagnosing its Presence and Assessing the Potential Damage It Causes Least Squares Estimation

This paper suggests and examines a straightforward diagnostic test procedure that 1) provides numerical indexes whose magnitudes signify the presence of one or more near dependencies among columns of a data matrix X, and 2) provides a means for determining, within the linear regression model, the extent to which each such near dependency is degrading the least- squares estimation of each regression coefficient. In most instances this latter information also enables the investigator to determine specifically which columns of the data matrix are involved in each near dependency. The diagnostic test is based on an interrelation between two analytic devices, the singular-value decomposition (closely related to eigensystems) and a matching regression-variance decomposition. Both these devices are developed in full. The test is successfully given empirical content through a set of experiments that examine its behavior when applied to several different series of data matrices having one or more known near dependencies that are weak to begin with and are made to became systematically more nearly perfectly collinear. The general diagnostic properties of the test that result from these experiments and the steps required to carry out the test are summarized, and then exemplified by application to real economic data.

Estimation of Econometric Model Using Nonlinear Full Information Maximum Likelihood: Preliminary Computer Results

This working paper provides some preliminary results on the computational feasibility of nonlinear full information maximum likelihood (NECML) estimation. Severa1 of the test cases presented were also subjected to nonlinear three stage least square (NLBSLS) estimation in order to illustrate the relative performance of the two estimation techniques. In addition, certain other aspects central to practical implementation are highlighted. These include the effect of various computers on the efficiency of the code, as well as the relative merits of numerical and analytical generation of gradient information. Broadly speaking, NLFIML appears competitive in cost and superior in statistical properties to NL3SLS.

Is peace a missing value or a zero? On selection models in political science

Sample selection models, variants of which are the Heckman and Heckit models, are increasingly used by political scientists to accommodate data in which censoring of the dependent variable raises concerns of sample selectivity bias. Beyond demonstrating several pitfalls in the calculation of marginal effects and associated levels of statistical significance derived from these models, we argue that many of the empirical questions addressed by political scientists would – for both substantive and statistical reasons – be more appropriately addressed using an alternative but closely related procedure referred to as the two-part model (2 PM). Aside from being simple to estimate, one key advantage of the 2 PM is its less onerous identification requirements. Specifically, the model does not require the specification of so-called exclusion restrictions, variables that are included in the selection equation of the Heckit model but omitted from the outcome equation. Moreover, we argue that the interpretation of the marginal effects from the 2 PM, which are in terms of actual outcomes, are more appropriate for the questions typically addressed by political scientists than the potential outcomes ascribed to the Heckit results. Drawing on data from the Correlates of War database, we present an empirical analysis of conflict intensity illustrating that the choice between the sample selection model and 2 PM can bear fundamentally on the conclusions drawn.Dieser Beitrag ist mit Zustimmung des Rechteinhabers aufgrund einer (DFG-geförderten) Allianz- bzw. Nationallizenz frei zugänglich. - This publication is with permission of the rights owner freely accessible due to an Alliance licence and a national licence (funded by the DFG, German Research Foundation) respectively