Strategies for dealing with measurement error in multiple regression

ABSTRACT

modes for handling measurement error in regression analysis range from assuming that measures are consummately reliable to explicitly modeling measurement error end the use of multiple indicators. In sum of two units simulation studies, we examined the effectiveness of several strategies for incorporating measurement error in regression. First, we compared four strategies: (1) multiple indicator structural equation modeling, (2) a composite indicator structural equation (CISE) type with adjustment for measurement error based upon Cronbach's alpha of the composite, (3) a composite indicator structural equation pattern with no adjustment for measurement error, and (4) a single indicator design with no adjustment for measurement error. The next to the first study explored the consequences of either over- or under- estimating measurement error while using the CISE alpha method

Keywords: Structural Equation Modeling, Measurement Error, Monte-Carlo Simulation, Multiple Regression

1 INTRODUCTION

Multiple regression has become an important multivariate data analytic technique in the management and industrial organizational fields. above the past two decades, increased attention has been paid to the issue of measurement error (Anderson, Stone-Romero & Tisak, 1996) and representation of builds as latent variables (Bagozzi & Edwards, 1998) The recognition that virtually all social science be pendents on fallible measures is extremely important because biased parameter estimates and standard errors can be met with when measurement error is ignored in regression analysis (Hayduk, 1987)

2 HANDLING MEASUREMENT ERROR

Strategies designed to address the measurement error issue in regression situations include simultaneous estimation of measurement error and regression parameters, estimation of measurement error and regression parameters in separate analyses, and fixing measurement error to an a priori value. Multiple indicator structural equation (MISE) modeling using maximum likelihood estimation is an example of a commonly used strategy for simultaneously estimating measurement error and regression parameters (Joreskog & Sorbom, 1993) The major advantage of this technique is that all the information in the variance-covariance matrix of the variables beneath consideration is used in the simultaneous estimation of measurement error and regression parameters. Using all available information can increase the efficiency of parameter estimates. However, specification errors or estimation errors in individual part of the model can cause biased parameter estimates completely through the model as well as gradual approach problems (Bollen, 1996). A next to the first approach is the estimation of measurement error of an indicator independent of the estimation of the regression parameters (Bagozzi & Edwards, 1998 p 57) Specifically, the estimation of measurement error associated with each indicator is done upon an indicator-by-indicator basis, not simultaneously. Mis-specification or mis-estimation of measurement error for single indicator will not affect estimates of measurement error for another indicator. A third approach for dealing with measurement error is to fix the proportion of measurement error for an indicator to an a priori value (Hayduk, 1987 p 120) This approach has the advantage that the estimation of measurement error is based upon a different sample than the sample used for the estimation of the regression parameters. Thus, the estimation of the measurement error and the regression parameters are independent. In this inquiry several methods for handling measurement error are compared.

21 Single-Indicator Approach

With traditional standard regression managements variables are assumed to be exquisitely reliable without contamination from measurement error. The enigma with this assumption is that measurement error can attenuate estimated relationships among latent variables and bias standard error terminuss associated with the estimated relationships. The overall consequence of not incorporating measurement error in data analysis can be a reduction in statistical power for detecting relationships among variables. Since this technique has many known drawbacks, many have advocated for alternate rules that incorporate measurement error.

22 Multiple Indicator Structural Equation Modeling

individual commonly used data analytic technique for the simultaneous estimation of measurement error and regression parameters is multiple indicator structural equation modeling (MISE) with maximum likelihood estimation. This prototype is the total disaggregation type in the construct framework propos by dint of Baggozi and Edwards (1998). MISE is a powerful data analytic technique for estimating simultaneous linear regression equations for latent variables in the connected thought [i]or[/i] thoughts of a measurement error theory (Joreskog & Sorbom, 1993) With the MISE approach, structural and measurement archetypes are specified. The structural original specifies the relationship among the latent variables and the measurement protoplast specifies the relationship of the latent variables with the indicators and the error manner of making of the indicators. For example, the structural type specifying a situation with three latent exogenous variables related to a latent endogenous variable is defined as: