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Qual Quant (2016) 50:21212140
DOI 10.1007/s11135-015-0254-5
Ross H. Taplin1
Published online: 29 July 2015 Springer Science+Business Media Dordrecht 2015
Abstract Despite previous recommendations for improvement, a literature review reveals a minority of recent papers in management journals provide correct interpretations of regression coefcients for analyses of limited dependent variables. Furthermore, the use of marginal effects to interpret relationships has resulted in confusing and inaccurate conclusions. This paper recommends simpler and more informative alternatives to the calculation and reporting of marginal effects. In particular, two key recommendations involve choosing and explicitly stating a suitable measurement scale for dependent variables and explicitly stating whether relationships with independent variables are multiplicative or additive effects. These recommendations for reporting hypotheses, analysis and interpretations will not only improve the precision of future research but also provide superior interpretations of past literature. Signicantly, this paper shows how standard regression coefcients can be used to interpret relationships between variables for any values of all variables. Other approaches such as the recommended inclusion of marginal effects and plots requires xing other variables to specic values (such as their mean value) and so are of less value to readers.
Keywords Logistic regression Logarithmic regression Multiplicative effects
Marginal effects Interaction effects
1 Introduction
The terminology limited dependent variable (LDV) is typically used to refer to dependent variables that are limited to a few (often two) possible values. Examples include whether a company goes bankrupt and whether a company makes a specic disclosure. Variables
& Ross H. [email protected]
1 School of Accounting, Curtin Business School, Curtin University, GPO Box U1987,
Perth 6845, Australia
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limited to positive values, such as CEO income, can also technically be considered LDVs. In these cases it is inappropriate to use ordinary least squares (OLS). Furthermore, interpreting results as if they resulted from OLS regression can lead to invalid conclusions.
Hoetker (2007) analysed 157 papers published between 2000 and 2005 in Strategic Management Journal (SMJ) and Academy of Management Journal (AMJ) using probit/ logit regression. Of these, 64.9 % provided no interpretation of the magnitude of a variables effect and 16 % provided incomplete or incorrect...