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Investigating bias in squared regression structure coefficients.

Nimon KF, Zientek LR, Thompson B - Front Psychol (2015)

Bottom Line: The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented.Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections.While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients.

View Article: PubMed Central - PubMed

Affiliation: Department of Human Resource Development, University of Texas at Tyler Tyler, TX, USA.

ABSTRACT
The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients.

No MeSH data available.


Related in: MedlinePlus

Bias of uncorrected squared structure coefficients (top panel) and corrected squared structure coefficients (bottom panel). k, number of predictors; n, sample size.
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Figure 1: Bias of uncorrected squared structure coefficients (top panel) and corrected squared structure coefficients (bottom panel). k, number of predictors; n, sample size.

Mentions: The ANOVA η 2 values (see Table 2) suggest that the negative bias in r2x appeared to be mostly a function of the study's main effects as well as number of interaction effects including n:ρ2y, ρ2y:ρ2xx, ρ2y:k, and ρ 2xx:k. However, the ANOVA estimated marginal means tell somewhat of a different story (see Figure 1). When ρ2y = 0.80, bias was minimal as long as the level of multicollinearity = 0.30 or 0.10. When ρ2y = 0.50 and ρ2y = 0.20, bias was minimal as long as the level of multicollinearity = 0.10. In other instances, bias appeared to be a factor of k and n, with the greatest impact being seen in the case when ρ2y = 0.20 and ρ2xx = 0.50. The role that k and n plays in the bias of r2x appears to stem from related bias in R2y, where the interaction between k and n appears to be a function of ρ2y (see Figure 2). It would also appear that the role that sample size play in the bias of r2xy contributes to the bias of r2x (see Figure 3).


Investigating bias in squared regression structure coefficients.

Nimon KF, Zientek LR, Thompson B - Front Psychol (2015)

Bias of uncorrected squared structure coefficients (top panel) and corrected squared structure coefficients (bottom panel). k, number of predictors; n, sample size.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4495312&req=5

Figure 1: Bias of uncorrected squared structure coefficients (top panel) and corrected squared structure coefficients (bottom panel). k, number of predictors; n, sample size.
Mentions: The ANOVA η 2 values (see Table 2) suggest that the negative bias in r2x appeared to be mostly a function of the study's main effects as well as number of interaction effects including n:ρ2y, ρ2y:ρ2xx, ρ2y:k, and ρ 2xx:k. However, the ANOVA estimated marginal means tell somewhat of a different story (see Figure 1). When ρ2y = 0.80, bias was minimal as long as the level of multicollinearity = 0.30 or 0.10. When ρ2y = 0.50 and ρ2y = 0.20, bias was minimal as long as the level of multicollinearity = 0.10. In other instances, bias appeared to be a factor of k and n, with the greatest impact being seen in the case when ρ2y = 0.20 and ρ2xx = 0.50. The role that k and n plays in the bias of r2x appears to stem from related bias in R2y, where the interaction between k and n appears to be a function of ρ2y (see Figure 2). It would also appear that the role that sample size play in the bias of r2xy contributes to the bias of r2x (see Figure 3).

Bottom Line: The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented.Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections.While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients.

View Article: PubMed Central - PubMed

Affiliation: Department of Human Resource Development, University of Texas at Tyler Tyler, TX, USA.

ABSTRACT
The importance of structure coefficients and analogs of regression weights for analysis within the general linear model (GLM) has been well-documented. The purpose of this study was to investigate bias in squared structure coefficients in the context of multiple regression and to determine if a formula that had been shown to correct for bias in squared Pearson correlation coefficients and coefficients of determination could be used to correct for bias in squared regression structure coefficients. Using data from a Monte Carlo simulation, this study found that squared regression structure coefficients corrected with Pratt's formula produced less biased estimates and might be more accurate and stable estimates of population squared regression structure coefficients than estimates with no such corrections. While our findings are in line with prior literature that identified multicollinearity as a predictor of bias in squared regression structure coefficients but not coefficients of determination, the findings from this study are unique in that the level of predictive power, number of predictors, and sample size were also observed to contribute bias in squared regression structure coefficients.

No MeSH data available.


Related in: MedlinePlus