Moderating effects of management control systems and innovation on performance. Simple methods for correcting the effects of measurement error for interaction effects in small samples

In the accounting literature, interaction or moderating effects are usually assessed by means of OLS regression and summated rating scales are constructed to reduce measurement error bias. Structural equation models and two-stage least squares regression could be used to completely eliminate this bias, but large samples are needed. Partial Least Squares are appropriate for small samples but do not correct measurement error bias. In this article, disattenuated regression is discussed as a small sample alternative and is illustrated on data of Bisbe and Otley (in press) that examine the interaction effect of innovation and style of use of budgets on performance. Sizeable differences emerge between OLS and disattenuated regression

Multilevel multitrait-multimethod model: application to the measurement of egocentered social networks

Our goal in this paper is to assess reliability and validity of egocentered network data using multilevel analysis (Muthen, 1989, Hox, 1993) under the multitrait-multimethod approach. The confirmatory factor analysis model for multitrait-multimethod data (Werts & Linn, 1970; Andrews, 1984) is used for our analyses. In this study we reanalyse a part of data of another study (Kogovšek et al., 2002) done on a representative sample of the inhabitants of Ljubljana. The traits used in our article are the name interpreters. We consider egocentered network data as hierarchical; therefore a multilevel analysis is required. We use Muthen's partial maximum likelihood approach, called pseudobalanced solution (Muthen, 1989, 1990, 1994) which produces estimations close to maximum likelihood for large ego sample sizes (Hox & Mass, 2001). Several analyses will be done in order to compare this multilevel analysis to classic methods of analysis such as the ones made in Kogovšek et al. (2002), who analysed the data only at group (ego) level considering averages of all alters within the ego. We show that some of the results obtained by classic methods are biased and that multilevel analysis provides more detailed information that much enriches the interpretation of reliability and validity of hierarchical data. Within and between-ego reliabilities and validities and other related quality measures are defined, computed and interpreted

Correcting Measurement Error Bias in Interaction Models with Small Samples

Several methods have been suggested to estimate non-linear models with interaction terms in the presence of measurement error. Structural equation models eliminate measurement error bias, but require large samples. Ordinary least squares regression on summated scales, regression on factor scores and partial least squares are appropriate for small samples but do not correct measurement error bias. Two stage least squares regression does correct measurement error bias but the results strongly depend on the instrumental variable choice. This article discusses the old disattenuated regression method as an alternative for correcting measurement error in small samples. The method is extended to the case of interaction terms and is illustrated on a model that examines the interaction effect of innovation and style of use of budgets on business performance. Alternative reliability estimates that can be used to disattenuate the estimates are discussed. A comparison is made with the alternative methods. Methods that do not correct for measurement error bias perform very similarly and considerably worse than disattenuated regression

Measurement Quality in Indicators of Compositions: a Compositional Multitrait-Multimethod Approach

Compositional data, also called multiplicative ipsative data, are common in survey research instruments in areas such as time use, budget expenditure and social networks. Compositional data are usually expressed as proportions of a total, whose sum can only be 1. Owing to their constrained nature, statistical analysis in general, and estimation of measurement quality with a confirmatory factor analysis model for multitrait-multimethod (MTMM) designs in particular are challenging tasks. Compositional data are highly non-normal, as they range within the 0-1 interval. One component can only increase if some other(s) decrease, which results in spurious negative correlations among components which cannot be accounted for by the MTMM model parameters. In this article we show how researchers can use the correlated uniqueness model for MTMM designs in order to evaluate measurement quality of compositional indicators. We suggest using the additive log ratio transformation of the data, discuss several approaches to deal with zero components and explain how the interpretation of MTMM designs di ers from the application to standard unconstrained data. We show an illustration of the method on data of social network composition expressed in percentages of partner, family, friends and other members in which we conclude that the faceto-face collection mode is generally superior to the telephone mode, although primacy e ects are higher in the face-to-face mode. Compositions of strong ties (such as partner) are measured with higher quality than those of weaker ties (such as other network members)