Accommodating Outliers and Nonlinearity in Decision Models

Abstract

This paper describes and compares six procedures that can be used in a regression model to adjust for outliers in the data and nonlinearities in the relationship between the dependent and independent variables. The data accommodation procedures are: (1) noadjustment; (2) winsorizing ; (3) trimming; (4) regression on ranks; (5) nonlinear regression; and (6) piecewise linear regression. The results show that the choice of data accommodation procedure has a major impact on the predictive ability and coeficient estimates of the regression model. The winsorizing and ranking procedures produce a regression model that jits the data well and has a low level of prediction error.Decision models based on financial variables have been applied in a variety of situations, including predicting bankruptcy (Altman [ 1968]), explaining and estimating firm systematic risk (Beaver, Kettler, and Scholes [ 1970]), predicting bond ratings (Pinches and Mingo [ 1973]), and in evaluating the information content of accrual versus cash flow measures (Bowen, Burgstahler and Daley [1987]). When constructing such a model, a researcher is confronted with several decisions that can have a dramatic and distortive impact on the results. A researcher must decide which variables are "important" in explaining the dependent variable, and then choose surrogates to represent these variables. The researcher also must determine the functional relationship between the dependent and independent variables.

Longitudinal Analysis of Relationships between Planning and Performance in Small Firms

“…The use of different tests ensures that the relationships identified are not influenced by the statistical procedure employed and helps control for the effects of the distributions of the data (Kennedy, Lakonishok and Shaw, 1992;Camp, Nenide, Pricer and Sexton, 1999). Each of the tests applied for both employment and sales measures of performance are described below:…”

The Effect of Small Business Managers’ Growth Motivation on Firm Growth: A Longitudinal Study

“…Several techniques exist to normalize data (e.g., logarithmic transformation). We relied on the Winsor technique (e.g., Kennedy, Lakonishok, & Shaw, 1992), where a fixed percentage (in our case 5%) of the outlier cases at the tale of the distribution receive the same values as the observations at the truncation point (i.e., the 95 percentile). This transformation led to a distribution that was acceptable, with a minimum change in the data.…”

Cash Conversion Cycle Management in Small Firms: Relationships with Liquidity, Invested Capital, and Firm Performance

“…This technique has been recommended as an effective method for addressing outliers and obtaining normal distributions without the loss of data (Kennedy, Lakonishok, and Shaw, 1992). Firms with negative equity were excluded from analyses that included return on invested capital, as negative equity could provide mis- …”