New techniques in testing the significance of mediated effects

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New techniques in testing the significance of
mediated effects

• Rob Dvorak Ryan Engdahl
• Department of Psychology
• The University of South Dakota

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Outline

• Introduction
• What is a mediator?
• How do you test for mediation?
• Problems with traditional tests of mediated
  effects?
• New techniques in testing mediated effects.
• Examples

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Introduction
4
What is a mediator?
5
What is a mediator? The mechanism by which one
variable affects another variable
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What is a mediator? The mechanism by which one
variable affects another variable
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Testing Mediation

• Baron Kenny (1986)
• Step 1 IV DV
• Step 2 IV Mediator
• Step 3 Mediator DV
• Step 4 Effect of IV on DV is significantly
  reduced by controlling for the mediator.

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Testing Mediated Effects

• Goodman (1960) test
• z-value ab/SQRT(b2sa2 a2sb2 - sa2sb2)
• Sobel (1982) test
• z-value ab/SQRT(b2sa2 a2sb2)
• Aroian (1944/1947) test
• z-value ab/SQRT(b2sa2 a2sb2 sa2sb2)

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Problems with Traditional Tests

• The traditional tests are simply z-tests
• ME arent normally distributed
• /- 1.96 may, or may not, actually be significant

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Heres Our Model
Blood Glucose
a
b
Control
Gender Video T1 Blood Glucose Trait Self-control
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Heres Our Model
Blood Glucose
a
b
c
Control
Gender Video T1 Blood Glucose Trait Self-control
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For our data
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Three ways to go from here

• You can use re-sampling techniques to bootstrap
  the standard error of your path coefficients.
• You can refer to MacKinnons technique to correct
  for the distribution of Mediated effects
  (PRODCLIN).
• You can utilize computationally intensive
  techniques that will boot strap the standard
  error of the Mediated effect based on your
  particular distribution.

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Bootstrapped standard error of path Coefficients
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Using PRODCLIN

• Distribution of the PROduct Confidence Limits for
  INdirect effects (PRODCLIN)
• http//www.public.asu.edu/davidpm/ripl/Prodclin/
  

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PRODCLIN Results

• OUTPUT
• a-2.455927 sea1.168241 b12.322910 seb
  3.005995
• ab -30.264167 sobelse 16.178686
• rho 0.000000 Type1 error .050000
• Normlow -61.973810 Normup 1.445475
• Prodclin lower critical value -2.821298
• Prodclin upper critical value 1.534485
• Prodlow -75.909062 Produp -5.438211

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Bootstrapping the Standard Error of Mediated
Effects

• This is the most computationally intensive method
  for generating an accurate mediated effect.
• Utilizes the bootstrap for the SE of the mediated
  effect.

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Using the Bootstrap method

• AMOS, EQS, LISREL, and Mplus are all capable of
  conducting bootstrap resampling
• A recent program was written for STATA that can
  do it regardless of variable type for the IV MV
  or DV.

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STATA Bootstrap ME

• Search sgmediation

Sobel-Goodman Mediation Tests Coef
Std Err Z PgtZ Sobel
-30.264161 16.178689 -1.871
.06139792 Goodman-1 -30.264161 16.555428
-1.828 .06754195 Goodman-2 -30.264161
15.792965 -1.916 .0553261 Pecent of total
effect that is mediated 8.92 Ratio of
indirect to direct effect
0.0979 Percentile and Bias-corrected bootstrap
results for Sobel 1000 replications Observed
Bootstrap Coef. Bias
Std. Err. 95 Conf IV
-30.264161 -.3649974 16.53234
-66.39647 -2.462249 (P)
-69.26264 -3.368593
(BC) (P) percentile confidence interval (BC)
bias-corrected confidence interval
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Conclusions

• Mediation is becoming increasingly more important
• There are several new ways to test for mediated
  effects that help to reduce the error associated
  with product distribution problems
• The use of these new will likely become
  standard procedures in the near future so you
  might as well start using them now.

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References

• Aroian, L. A. (1944/1947). The probability
  function of the product of two normally
  distributed variables. Annals of Mathematical
  Statistics, 18, 265-271.
• Baron, R. M., Kenny, D. A. (1986). The
  moderator-mediator variable distinction in
  social psychological research Conceptual,
  strategic, and statistical considerations.
  Journal of Personality and Social Psychology, 51,
  1173-1182.
• Goodman, L. A. (1960). On the exact variance of
  products. Journal of the American Statistical
  Association, 55, 708-713.
• Hoyle, R. H., Kenny, D. A. (1999). Sample size,
  reliability, and tests of statistical mediation.
  In R. Hoyle (Ed.) Statistical Strategies for
  Small Sample Research. Thousand Oaks, CA Sage
  Publications.
• MacKinnon, D. P., Fritz, M. S., Williams, J.,
  Lockwood, C. M. (2007). A comparison of methods
  to test mediation and other intervening variable
  effects. Behavior Research Methods, 39, 384-389.
• MacKinnon, D. P., Lockwood, C. M., Hoffman, J.
  M., West, S. G., Sheets, V. (2002). A
  comparison of methods to test mediation and other
  intervening variable effects. Psychological
  Methods, 7, 83-104.
• MacKinnon, D. P., Warsi, G., Dwyer, J. H.
  (1995). A simulation study of mediated effect
  measures. Multivariate Behavioral Research,
  30(1), 41-62.
• Preacher, K. J., Hayes, A. F. (2004). SPSS and
  SAS procedures for estimating indirect effects
  in simple mediation models. Behavior Research
  Methods, Instruments, Computers, 36(4),
  717-731.
• Sobel, M. E. (1982). Asymptotic intervals for
  indirect effects in structural equations models.
  In S. Leinhart (Ed.), Sociological methodology
  1982 (pp.290-312). San Francisco Jossey-Bass.