[Mediation-information] possible bug in 'mediation-0.4'

[Liviu Andronic]

Hello
I am wondering whether I spotted a bug in latest 'mediation'. Consider
the following:
> require(mediation)
> summary(mod.m <- lm(EFFICACY ~ LEADER + AGE + SEX + DIPLOMA + DEPART + SUPTENURE, indir))  ##estimate m model

Call:
lm(formula = EFFICACY ~ LEADER + AGE + SEX + DIPLOMA + DEPART +
    SUPTENURE, data = indir)

Residuals:
     Min       1Q   Median       3Q      Max
-2.92860 -0.43824 -0.06034  0.49659  1.93870

Coefficients:
              Estimate Std. Error t value Pr(>|t|)
(Intercept)  4.6369421  0.8721587   5.317 7.92e-07 ***
LEADER       0.2229302  0.0944945   2.359   0.0205 *
AGE         -0.0224524  0.0107333  -2.092   0.0393 *
SEX          0.2862008  0.1745420   1.640   0.1046
DIPLOMA      0.1807359  0.0977275   1.849   0.0678 .
DEPART      -0.0154174  0.0102971  -1.497   0.1379
SUPTENURE   -0.0007209  0.0020428  -0.353   0.7250
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.7816 on 88 degrees of freedom
  (17 observations deleted due to missingness)
Multiple R-squared: 0.1959,	Adjusted R-squared: 0.1411
F-statistic: 3.574 on 6 and 88 DF,  p-value: 0.003242

> summary(mod.y <- lm(CREATIV ~ EFFICACY + LEADER + AGE + SEX + DIPLOMA + DEPART + SUPTENURE, indir))  ##estimate y model

Call:
lm(formula = CREATIV ~ EFFICACY + LEADER + AGE + SEX + DIPLOMA +
    DEPART + SUPTENURE, data = indir)

Residuals:
     Min       1Q   Median       3Q      Max
-1.20977 -0.44844 -0.09279  0.37973  1.29044

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept)  2.184317   0.784891   2.783 0.006606 **
EFFICACY     0.141007   0.083462   1.689 0.094707 .
LEADER       0.203025   0.076287   2.661 0.009268 **
AGE         -0.008247   0.008610  -0.958 0.340814
SEX          0.246680   0.138728   1.778 0.078871 .
DIPLOMA      0.037031   0.077987   0.475 0.636094
DEPART      -0.030152   0.008164  -3.693 0.000386 ***
SUPTENURE   -0.002973   0.001601  -1.857 0.066644 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.612 on 87 degrees of freedom
  (17 observations deleted due to missingness)
Multiple R-squared: 0.3114,	Adjusted R-squared: 0.256
F-statistic:  5.62 on 7 and 87 DF,  p-value: 2.275e-05

> med_a <- mediate(mod.m, mod.y, dropobs=T, treat='LEADER', mediator='EFFICACY', boot=T, sims=5000)  ##supply m and y models for mediation analysis

> summary(med_a)

Causal Mediation Analysis

Confidence Intervals Based on Nonparametric Bootstrap

                         Estimate 95% CI Lower 95% CI Upper p-value
Mediation Effect           0.0314      -0.0228       0.0842    0.23
Direct Effect              0.2030       0.0424       0.3672    0.01
Total Effect               0.2345       0.0765       0.3834    0.00
Proportion via Mediation   0.1341      -0.1035       0.4998    0.23

Sample Size Used: 95


Now the trouble is, I think, with the 'Mediation Effect' estimate: it
doesn't seem to be the bootstrap estimate, but the estimate obtained
directly from hte regressions. If you use the regression coefficients
you get this:
#a*b=0.0314
> (med_axb <- as.numeric(coef(mod.m)['LEADER'] * coef(mod.y)['EFFICACY'])) #data
[1] 0.03143479

And the 'medaite' object contains this:
> med_a$d0 #??bug
[1] 0.03143479

If, however, you compute the average over the bootstrap estimates as
stored in the object you get a different estimate, and this is what I
would expect printed in the summary() output above:
> mean(med_a$d0.sims) #boot/acme
[1] 0.02689732

Computing the bias worked fine with the previosu version of
'mediation', but now it yields zero:
> med_a$d0 - med_axb #bias
[1] 4.857226e-17


I may be wrong but I think there is a bug, and I am not sure if it
affects only the 'Mediation Effect' or some other coefficients (or the
CI).

Regards
Liviu


-- 
Do you know how to read?
http://www.alienetworks.com/srtest.cfm
http://goodies.xfce.org/projects/applications/xfce4-dict#speed-reader
Do you know how to write?
http://garbl.home.comcast.net/~garbl/stylemanual/e.htm#e-mail