The regression dilemma

Hocking, R. R.; Pendleton, O J

doi:10.1080/03610928308828477

Cited by 114 publications

(42 citation statements)

References 18 publications

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“…However, the idea of having many highly correlated variables of egg measurements entered into a regression model can lead to multicollinearity (MC) problems. Multicollinearity refers to a situation in which there is an exact (or nearly exact) linear relation among two or more of the input variables (Hawking and Pendleton, 1983). This has a potentially serious effect on the standard errors of the coefficients, which may mislead the interpretation of the results.…”

Section: Introductionmentioning

confidence: 99%

Dealing with Multicollinearity in Predicting Egg Components from Egg Weight and Egg Dimension

Shafey

Mahmoud

Abouheif

2014

Italian Journal of Animal Science

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Measurements of 174 eggs from meat-type breeder flock (Ross) at 36 weeks of age were used to study the problem of multicollinearity (MC) instability in the estimation of egg components of yolk weight (YKWT), albumen weight (ALBWT) and eggshell weight (SHWT). Egg weight (EGWT), egg shape index (ESI)=egg width (EGWD)*100/egg length (EGL) and their interaction (EGWTESI) were used in the context of un-centred vs centred data and principal components regression (PCR) models. The pairwise phenotypic correlations, variance inflation factor (VIF), eigenvalues, condition index (CI), and variance proportions were examined. Egg weight had positive correlations with EGWD and EGL (r=0.56 and 0.50, respectively; P<0.0001) and EGL had a negative correlation with ESI (r=-0.79; P<0.0001). The highest correlation was observed between EGWT and ALBWT (r=0.94; P<0.0001), while the lowest was between EGWD and SHWT (r=0.33; P<0.0001). Multicollinearity problems were found in EGWT, ESI and their interaction as shown by VIF (>10), eigenvalues (near zero), CI (>30) and high corresponding proportions of variance of EGWT, ESI and EGWTESI with respect to EGWTESI. Results from this study suggest that mean centring and PCR were appropriate to overcome the MC instability in the estimation of egg components from EGWT and ESI. These methods improved the meaning of intercept values and produced much lower standard error values for regression coefficients than those from un-centred data.

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Section: Introductionmentioning

confidence: 99%

Dealing with Multicollinearity in Predicting Egg Components from Egg Weight and Egg Dimension

Shafey

Mahmoud

Abouheif

2014

Italian Journal of Animal Science

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“…The estimated temperature effects on the amount of precipitation can therefore be biased. Another point is the rather strong correlation between T and D. This correlation inflates the standard errors of the predicted mean precipitation amounts in situations where the changes in T and D differ from those expected from the observed statistical relationship between T and D (Hocking & Pendleton 1983), such as a positive change in T and no change in D. Rather long records are then required to keep these standard errors within reasonable limits.…”

Section: Discussionmentioning

confidence: 99%

Dependence of precipitation on temperature at Florence and Livorno (Italy)

Buishand¹,

Brandsma²

1999

Clim. Res.

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Papers dealing with precipitation scenarios for a potentially warmer climate have often ignored the relationship between precipitation and temperature. Although the atmosphere has a larger capacity to hold water vapour at higher temperatures, plots of the mean wet-day precipitation amounts versus temperature may not reveal a clear positive relationship. This phenomenon is studied in detail for Florence and Livorno (Italy). Vorticity and the difference between the land and sea surface temperatures are 2 important factors that determine precipitation at these sites. The wet-day precipitation amount is explored as a function of these 2 variables and temperature using an iterative smoothing technique. The estimated functions show a marked increase in the mean wet-day precipitation amount with increasing temperature (~6% °C -1 ). The differences between the smoothed relations for Florence and Livorno are small and the smooths for the winter and summer halves of the year are also quite similar. Besides the mean wet-day precipitation amounts, the mean wet-hour amounts (mean rainfall intensities) of each day with rain are also analysed. These show a much stronger increase with increasing temperature (~11% °C -1 ), which is partly due to a decrease of rainfall duration with increasing temperature.

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“…Belsley et al (1980) pointed out that there is not a clear cutoff point to distinguish between "high" and "low" VIFs. Several researchers (e.g., Hocking and Pendelton 1983;Craney and Surles 2002) have suggested that the "typical" cutoff values (or rules of thumb) for "large" VIFs of 5 or 10 are based on the associated R i 2 of 0.80 or 0.90, respectively. O'Brien (2007) recommended that well-known VIF rules of thumb (e.g., VIFs greater than 5 or 10 or 30) should be treated with caution when making decisions to reduce collinearity (like eliminating one or more predictors) and indicated that researchers should also consider other factors (e.g., sample size) which influence the variability of regression coefficients.…”

Section: A Brief Review Of Variance Inflation Factorsmentioning

confidence: 99%

Variance Inflation Factors in Regression Models With Dummy Variables

Murray¹,

Nguyen²,

Lee³

et al. 2012

Conference on Applied Statistics in Agriculture

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Variance Inflation Factors (VIFs) are used to detect collinearity among predictors in regression models. Textbook explanation of collinearity and diagnostics such as VIFs have focused on numeric predictors as being "co-linear" or "co-planar", with little attention paid to VIFs when a dummy variable is included in the model. This work was motivated by two regression models with high VIFs, where "standard' interpretations of causes of collinearity made no sense. The first was an alfalfa-breeding model with two numeric predictors and two dummy variables. The second was an economic model with one numeric predictor, one dummy and the numeric x dummy cross-product. This paper gives formulas for VIFs for several regression models with a dummy variable which indicate that these VIFs are functions of the numeric predictors' means, sums of squares and sample sizes within the two dummy groups. The economic regression model is also presented to illustrate how high VIFs occurred in this data. Researchers should be cautious in using high VIFs as a reason for deleting predictors in general but especially if dummy variables are involved. It is recommended that collinearity diagnostics be applied to the numeric predictors first to check for collinearity without the influence of any dummies, then add dummy variables in one at a time to see their effect on VIFs.

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The regression dilemma

Cited by 114 publications

References 18 publications

Dealing with Multicollinearity in Predicting Egg Components from Egg Weight and Egg Dimension

Dealing with Multicollinearity in Predicting Egg Components from Egg Weight and Egg Dimension

Dependence of precipitation on temperature at Florence and Livorno (Italy)

Variance Inflation Factors in Regression Models With Dummy Variables

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