# Heteroskedasticity Question

I have a model that's affected by Heteroskedasticity:

bptest(m1)

studentized Breusch-Pagan test


data: m1 BP = 65.055, df = 6, p-value = 4.205e-12

In this model I had 2 variables (yrs.since.phd and yrs.service) that have significant coefficients:

summary(m1)

Call:
lm(formula = salary ~ ., data = data)

Residuals:
Min     1Q Median     3Q    Max
-65248 -13211  -1775  10384  99592

Coefficients:
Estimate        Std.Error       tvalue        Pr(>|t|)

(Intercept)    78862.8     4990.3  15.803  < 2e-16 ***

rankAsstProf  -12907.6     4145.3  -3.114  0.00198 **

rankProf       32158.4     3540.6   9.083  < 2e-16 ***

disciplineB    14417.6     2342.9   6.154 1.88e-09 ***

yrs.since.phd    535.1      241.0   2.220  0.02698 *

yrs.service     -489.5      211.9  -2.310  0.02143 *

sexMale         4783.5     3858.7   1.240  0.21584
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 22540 on 390 degrees of freedom
Multiple R-squared:  0.4547,    Adjusted R-squared:  0.4463
F-statistic:  54.2 on 6 and 390 DF,  p-value: < 2.2e-16


I tried to fix this model by using robust standard errors, and now the two variables mentioned above (yrs.since.phd and yrs.service) are not significant (or barely significant):

coeftest(m1, df = Inf, vcovHC(m1, omega = NULL, type = "HC4"))


z test of coefficients:

     Estimate Std. Error z value  Pr(>|z|)

(Intercept)    78862.82    3936.67 20.0329 < 2.2e-16 ***

rankAsstProf  -12907.59    2229.92 -5.7884 7.108e-09 ***

rankProf       32158.41    2343.04 13.7251 < 2.2e-16 ***

disciplineB    14417.63    2320.44  6.2133 5.188e-10 ***

yrs.since.phd    535.06     320.96  1.6670   0.09551 .

yrs.service     -489.52     315.23 -1.5529   0.12045

sexMale         4783.49    2457.27  1.9467   0.05157 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


Could anyone please explain me what's happened? All other variables Std.errors decreased, while happened the opposite for these two...

Thanks!

James

• It's an interesting question. Note that this phenomenon could be anticipated before even collecting the data: one would not expect salaries that cover such a wide range to exhibit a homoscedastic response. You certainly would have seen that during your initial exploratory analysis of these data, right? Using log salary as a response could make a better model. If you must use salary itself (which might better reflect an additive salary increase associated with rank), choose a suitable weighted regression. – whuber May 25 '16 at 17:59

One sensitivity analysis you should consider is histograms of the dfbetas, called using dfbeta. We would be concerned if the trends were being driven by a single observation, leading to irregular DF beta plots. Then we would consider presenting analyses which do and do not include the high influence observation.