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多元迴歸的自變數比較與多元共線性之影響：效果量、優勢性與相對權數指標的估計與應用
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2. Research Design
Following a simulation demonstrating these effects, a sample of 2,325 Taiwanese
individuals selected from the 2011 Panel Study of Family Dynamics is used to show the use
of those statistics and effect sizes in explaining salary differences.
Simulation
A simulated dataset of one dependent variable and four independent variables (with
different correlations with the dependent variable) are drawn from a multivariate normal
distribution. Based on six possible correlations between a pair of predictors, this study
conducts three cases of simulations to distinguish the three different effects of
multicollinearity.
Case1:
Uncorrelated predictors
. The four predictors are perfectly uncorrelated with
each other. This is the baseline model for comparisons.
Case2:
Correlated predictors and a decreased R
2
. A simulation of the
suppression
effect
is created by a positive inter-correlation between two predictors, and the
redundancy
effect is created by a lower inter-correlation.
Case3:
Correlated predictors and an increased R
2
. A simulation of the
enhancement
effect is created by a strong positive inter-correlation or a negative inter-
correlation between two predictors.
Depending on the values of inter-correlation between two predictors (
r
12
), Friedman and
Wall (2005) defines four regions to reflect the effects of multicollinearity: (R1)
enhancement: with an increasing R
2
and
r
12
< 0; (R2) redundancy: with a decreasing R
2
and 0
<
r
12
<
r
’; (R3) suppression: with an increasing R
2
and
r
’ <
r
12
<
r
”; and (R4) enhancement:
with an increasing R
2
and
r
” <
r
12
, where the critical values
r
’ and
r
” define the three different
effects of multicollinearity.
Survey Data Analysis
A sample of 2,325 (53% of males) Taiwanese individuals selected from the 2011 Panel
Study of Family Dynamics (PSFD) is used to demonstrate the performances of the index
statistics of effect sizes in predicting salary difference. Seven predictors implied by the
human capital theory are selected: gender, age, marital status, number of kids, years on the
job, weekly working hours, and years of formal education.