How to Interpret and Write-Up Parallel Mediation Output from PROCESS – Logistic Regression
by Jakob D. Jensen, Assistant Professor, University of Utah

In 2009, there was a flu called “H1N1 flu.” It was a terrible epidemic. In response to this flu, the CDCP created the H1N1a flu vaccine and ran media campaigns encouraging everyone to get vaccinated. After 8 months, the CDCP hired a team of researchers to survey adults across 7 counties in Indiana. They wanted to know two things:
(1)	Did exposure to the vaccination campaign increase vaccination behavior?
(2)	 All of the campaign messages focused on countering perceived barriers to vaccination, so they also wanted to know if that strategy was working. That is, did exposure to the campaign increase vaccination behavior via perceived barriers? Alternatively, the campaign could have impacted behavior via other health belief model (HBM) variables such as perceived benefits of vaccination, threat of the H1N1 flu, and self-efficacy to get the H1N1 flu vaccine.

The conceptual model above depicts the model to be tested. It is a parallel mediation model as all mediators are assumed to mediate the relationship equally.

Run MATRIX procedure:

************* PROCESS Procedure for SPSS Beta Release 120212 *************

        Written by Andrew F. Hayes, Ph.D.   http://www.afhayes.com

**************************************************************************

Note: The DV for this analysis is dichotomous (No, Yes) so this is logistic regression. The only aspect of the output that is different is the Logistic Regression Summary.

Model = 4
    Y = Behavior
    X = Exposure
   M1 = benefits
   M2 = threat
   M3 = barriers
   M4 = efficacy

Statistical Controls:
CONTROL= Age      Gender   Educatio FluSho_1 FluHist_

Sample size
       1201

**************************************************************************
Outcome: benefits

Model Summary
          R       R-sq          F        df1        df2          p
      .2643      .0699    14.9459     6.0000  1194.0000      .0000

Model

a1

              coeff         se          t          p
constant     2.1482      .2543     8.4463      .0000

Exposure      .0400      .0304     1.3176      .1879
Age          -.0003      .0018     -.1487      .8818
Gender        .0893      .0531     1.6824      .0928
Educatio      .0385      .0162     2.3731      .0178
FluSho_1      .1473      .0185     7.9794      .0000
FluHist_      .1438      .0879     1.6350      .1023

**************************************************************************
Outcome: threat

Model Summary
          R       R-sq          F        df1        df2          p
      .3155      .0995    21.9975     6.0000  1194.0000      .0000

Model

a2

              coeff         se          t          p

constant     1.8523      .2498     7.4165      .0000
Exposure      .0546      .0298     1.8282      .0678
Age           .0066      .0018     3.7503      .0002
Gender        .3314      .0522     6.3551      .0000
Educatio     -.0047      .0159     -.2951      .7680
FluSho_1      .1104      .0181     6.0901      .0000
FluHist_      .2136      .0864     2.4734      .0135

**************************************************************************
Outcome: barriers

Model Summary
          R       R-sq          F        df1        df2          p
      .2621      .0687    14.6795     6.0000  1194.0000      .0000

Model

a3

              coeff         se          t          p
constant     3.1206      .1766    17.6667      .0000

Exposure     -.0573      .0211    -2.7156      .0067
Age           .0000      .0012      .0159      .9873
Gender       -.0742      .0369    -2.0119      .0445
Educatio     -.0624      .0113    -5.5362      .0000
FluSho_1     -.0704      .0128    -5.4871      .0000
FluHist_     -.1114      .0611    -1.8246      .0683

**************************************************************************
Outcome: efficacy

Model Summary
          R       R-sq          F        df1        df2          p
      .2145      .0460     9.5973     6.0000  1194.0000      .0000

Model

a4

						 								

              coeff         se          t          p
constant     2.6472      .2503    10.5770      .0000
Exposure     -.0047      .0299     -.1588      .8739
Age          -.0056      .0018    -3.1577      .0016
Gender        .1661      .0523     3.1775      .0015
Educatio      .0828      .0160     5.1857      .0000
FluSho_1      .0684      .0182     3.7662      .0002
FluHist_      .0704      .0865      .8135      .4161

**************************************************************************

933.8426 – 798.0332 = 135.8094
χ2 = 135.8095
df = 10

χ2 table reveals this is significant at p < .001.

Outcome: Behavior

Coding of binary DV for analysis:

Where is the chi-square (χ2) and significance test for the model? You have to calculate this by hand using -2LLs.

  FluShot_  Analysis
       .00       .00
      1.00      1.00

Logistic Regression Summary

       -2LL   Model LL   McFadden   CoxSnell   Nagelkrk          n
   798.0332   482.0696      .3766      .3306      .5043  1201.0000

Model
              coeff         se          Z          p
constant    -8.7047     1.2016    -7.2441      .0000
benefits      .6833      .1205     5.6727      .0000
threat        .2833      .1158     2.4453      .0145

c’

barriers    -1.0091      .1706    -5.9138      .0000

efficacy      .0949      .1142      .8305      .4063
Exposure      .2443      .1090     2.2407      .0250
Age          -.0243      .0065    -3.7527      .0002
Gender       -.1948      .1922    -1.0137      .3107
Educatio      .0930      .0590     1.5751      .1152
FluSho_1      .8012      .0760    10.5412      .0000
FluHist_     2.1281      .2667     7.9794      .0000

************************** TOTAL EFFECT MODEL ****************************
Outcome: Behavior

Logistic Regression Summary
       -2LL   Model LL   McFadden   CoxSnell   Nagelkrk          n
   933.8426   346.2602      .2705      .2505      .3821  1201.0000

Is the total effect model significant? Calculate base -2LL. This can be obtained by running binary logistic regression using the same variables and requesting iteration history. Subtract total effect model -2LL from base -2LL and compare to χ2 table.

Model

c

              coeff         se          Z          p
constant    -8.8903      .9017    -9.8590      .0000

Exposure      .3338      .0991     3.3680      .0008
Age          -.0175      .0056    -3.1202      .0018
Gender        .0860      .1727      .4980      .6185
Educatio      .1852      .0531     3.4869      .0005
FluSho_1      .8992      .0702    12.8019      .0000
FluHist_     2.0844      .2413     8.6370      .0000

***************** TOTAL, DIRECT, AND INDIRECT EFFECTS ********************

To make comparison easier, the output provides you (once again) with c’ and c. These are the same numbers as above. 

Total effect of X on Y
     Effect         SE          Z          p
      .3338      .0991     3.3680      .0008

Direct effect of X on Y
     Effect         SE          Z          p
      .2443      .1090     2.2407      .0250

Indirect effect of X on Y

Bootstrap tests of indirect effects – i.e., tests of mediation

             Effect    Boot SE   BootLLCI   BootULCI
TOTAL         .1002      .0406      .0235      .1820

benefits      .0274      .0221     -.0153      .0734
threat        .0155      .0116      .0002      .0491
barriers      .0578      .0246      .0168      .1154
efficacy     -.0005      .0049     -.0118      .0085

******************** ANALYSIS NOTES AND WARNINGS *************************

Number of bootstrap samples for bias corrected bootstrap confidence intervals:
     1000

Level of confidence for all confidence intervals in output:
    95.00

NOTE: Some cases were deleted due to missing data.  The number of such cases was:
  176

------ END MATRIX -----

Sample Write-Up of this Analysis:	
	In the current analysis, the first question is whether encoded exposure is significantly related to behavior (i.e., the c path). It was hypothesized that exposure would be positively related to behavior (H1). PROCESS tested this hypothesis by regressing exposure on behavior with education, gender, age, flu shot history, and H1N1 flu history as covariates. The exposure model was significantly better than the null model, Cox & Snell R2 = .25, -2 Log Likelihood = 933.84, χ2 = 346.26, df = 6, p < .001. Consistent with H1, exposure was a significant predictor of behavior, b = .33, SE = .10, Z = 3.37, p < .001, Exp(B) = 1.40. In other words, controlling for covariates, a one unit increase in encoded exposure increased the odds of vaccination by 40%. 
	Parallel mediation assumes that all four HBM constructs mediate the relationship between exposure and behavior in a comparable manner. To test this model, behavior was entered as the outcome variable, exposure as the predictor variable, education, gender, age, flu shot history, and H1N1 flu history as covariates, and all four HBM constructs as mediators. The parallel mediation model was significantly better than the exposure model, Cox & Snell R2 = .33, -2 Log Likelihood = 798.03, χ2 = 135.81, df = 10, p < .001. Exposure was still related to behavior after mediators were taken into account although the relationship was weaker, b = .24, SE = .11, Z = 2.24, p = .025. The direct effect was reduced as exposure indirectly effected behavior via perceived barriers, b = .06, SE = .03, 95% bootstrap confidence interval: .0168, .1154 , and threat, b = .02, SE = .01, 95% bootstrap confidence interval: .0002, .0491. Participants with greater exposure perceived fewer barriers and greater threat; perceptions related to increased vaccination (see Figure 1). 

Figure 1. Parallel Mediation Model. †p < .10 *p < .05 **p < .01
Total effect of exposure: b = .33, SE = .10
Direct effect of exposure: b = .24, SE = .11
Indirect effect via barriers: b = .06, SE = .03, 95% bootstrap confidence interval: .0168, .1154
Indirect effect via threat: b = .02, SE = .01, 95% bootstrap confidence interval: .0002, .0491