---
title: "MEMORE_vs_wsMed"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{MEMORE_vs_wsMed}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

# introduction

The MEMORE reports below are stored reference output, not rerun by this
vignette. Compare estimates only after matching difference direction, model
structure, missing-data handling and interval settings. Standardized results
require matching the SD definition as well: wsMed uses marginal model-implied
difference-component SDs. Matching raw estimates does not imply matching
standardized estimates or confidence intervals.

For moderation, see [Standardized moderated mediation](StandardizedModeratedMediation.html).
This vignette does not establish agreement between the programs for moderated
standardized effects.

This document presents a comparison between the **MEMORE 3.0 (SPSS Plugin)** and **wsMed (R Package)** outputs.

## parallel mediation

We analyze a **three-mediator parallel mediation model**, comparing the results obtained from both methods.

### MEMORE 3.0 Analysis Report


````
## ```
##  
## Run MATRIX procedure:
## 
## *********************** MEMORE Procedure for SPSS Version 3.0 ***********************
## 
##                            Written by Amanda Montoya
## 
##                     Documentation available at github.com/akmontoya/MEMORE
## 
## **************************** ANALYSIS NOTES AND WARNINGS ****************************
## 
## Bootstrap confidence interval method used: Percentile bootstrap.
## 
## Number of bootstrap samples for bootstrap confidence intervals:
##   5000
## 
## The following variables were mean centered prior to analysis:
##  (        A2        +       A1       )        /2
##  (        B2        +       B1       )        /2
##  (        C2        +       C1       )        /2
## 
## Level of confidence for all confidence intervals in output:
##       95.00
## 
## **************************************************************************************
## 
## Model:
##   1
## 
## Variables:
## Y =   D2       D1
## M1 =  A2       A1
## M2 =  B2       B1
## M3 =  C2       C1
## 
## Computed Variables:
## Ydiff =           D2        -       D1
## M1diff =          A2        -       A1
## M2diff =          B2        -       B1
## M3diff =          C2        -       C1
## M1avg  = (        A2        +       A1       )        /2                         Centered
## M2avg  = (        B2        +       B1       )        /2                         Centered
## M3avg  = (        C2        +       C1       )        /2                         Centered
## 
## Sample Size:
##   100
## 
## **************************************************************************************
## Outcome: Ydiff =  D2        -       D1
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant     -.0316      .0170    -1.8586      .0661     -.0653      .0021
## 
## Degrees of freedom for all regression coefficient estimates:
##   99
## 
## **************************************************************************************
## Outcome: M1diff = A2        -       A1
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant     -.0271      .0176    -1.5385      .1271     -.0621      .0079
## 
## Degrees of freedom for all regression coefficient estimates:
##   99
## 
## **************************************************************************************
## Outcome: M2diff = B2        -       B1
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant      .0145      .0181      .8024      .4243     -.0213      .0503
## 
## Degrees of freedom for all regression coefficient estimates:
##   99
## 
## **************************************************************************************
## Outcome: M3diff = C2        -       C1
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant      .0153      .0163      .9404      .3493     -.0170      .0477
## 
## Degrees of freedom for all regression coefficient estimates:
##   99
## 
## **************************************************************************************
## Outcome: Ydiff =  D2        -       D1
## 
## Model Summary
##           R       R-sq        MSE          F        df1        df2          p
##       .1978      .0391      .0296      .6312     6.0000    93.0000      .7049
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant     -.0315      .0176    -1.7875      .0771     -.0665      .0035
## M1diff       -.0501      .1009     -.4968      .6205     -.2505      .1502
## M2diff       -.0844      .1022     -.8252      .4114     -.2874      .1187
## M3diff       -.0167      .1084     -.1536      .8782     -.2320      .1987
## M1avg        -.0305      .1015     -.3002      .7647     -.2320      .1711
## M2avg        -.0060      .0945     -.0633      .9497     -.1936      .1816
## M3avg        -.1552      .1090    -1.4239      .1578     -.3716      .0612
## 
## Degrees of freedom for all regression coefficient estimates:
##   93
## 
## ************************* TOTAL, DIRECT, AND INDIRECT EFFECTS *************************
## 
## Total effect of X on Y
##      Effect         SE          t         df          p       LLCI       ULCI
##      -.0316      .0170    -1.8586    99.0000      .0661     -.0653      .0021
## 
## Direct effect of X on Y
##      Effect         SE          t         df          p       LLCI       ULCI
##      -.0315      .0176    -1.7875    93.0000      .0771     -.0665      .0035
## 
## Indirect Effect of X on Y through M
##           Effect     BootSE   BootLLCI   BootULCI
## Ind1       .0014      .0030     -.0049      .0078
## Ind2      -.0012      .0029     -.0088      .0035
## Ind3      -.0003      .0028     -.0072      .0050
## Total     -.0001      .0054     -.0130      .0092
## 
## Indirect Key
## Ind1  'X'      ->       M1diff   ->       Ydiff
## Ind2  'X'      ->       M2diff   ->       Ydiff
## Ind3  'X'      ->       M3diff   ->       Ydiff
## 
## Pairwise Contrasts Between Specific Indirect Effects
##           Effect     BootSE   BootLLCI   BootULCI
## (C1)       .0026      .0039     -.0053      .0113
## (C2)       .0016      .0043     -.0067      .0114
## (C3)      -.0010      .0038     -.0089      .0068
## 
## Contrast Key:
## (C1)  Ind1      -       Ind2
## (C2)  Ind1      -       Ind3
## (C3)  Ind2      -       Ind3
## 
## ------ END MATRIX -----
##  
## ```
````

### wsMed Analysis Report


```
## 
## 
## *************** VARIABLES ***************
## Outcome (Y):
##    Condition 1: D1 
##    Condition 2: D2 
## Mediators (M):
##   M1:
##     Condition 1: A1
##     Condition 2: A2
##   M2:
##     Condition 1: B1
##     Condition 2: B2
##   M3:
##     Condition 1: C1
##     Condition 2: C2
## Sample size (rows kept): 100 
## 
## 
## *************** MODEL FIT ***************
## 
## 
## |Measure   |  Value|
## |:---------|------:|
## |Chi-Sq    | 16.275|
## |df        | 12.000|
## |p         |  0.179|
## |CFI       |  0.000|
## |TLI       | -1.829|
## |RMSEA     |  0.060|
## |RMSEA Low |  0.000|
## |RMSEA Up  |  0.126|
## |SRMR      |  0.072|
## 
## 
## ************* TOTAL / DIRECT / TOTAL-IND (MC) *************
## 
## 
## |Label          | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:--------------|--------:|------:|---------:|----------:|
## |Total effect   |  -0.0316| 0.0170|   -0.0651|     0.0024|
## |Direct effect  |  -0.0315| 0.0170|   -0.0645|     0.0019|
## |Total indirect |  -0.0001| 0.0047|   -0.0099|     0.0096|
## 
## Indirect effects:
## 
## 
## |Label | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:-----|--------:|------:|---------:|----------:|
## |ind_1 |   0.0014| 0.0032|   -0.0046|     0.0090|
## |ind_2 |  -0.0012| 0.0026|   -0.0077|     0.0030|
## |ind_3 |  -0.0003| 0.0023|   -0.0054|     0.0045|
## 
## Indirect-effect key:
## 
## 
## |Ind   |Path                 |
## |:-----|:--------------------|
## |ind_1 |X -> M1diff -> Ydiff |
## |ind_2 |X -> M2diff -> Ydiff |
## |ind_3 |X -> M3diff -> Ydiff |
## 
## 
## *************** MODERATION EFFECTS (d-paths, MC) ***************
## 
## 
## |Coefficient | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:-----------|--------:|------:|---------:|----------:|
## |d1          |  -0.0305| 0.0974|   -0.2225|     0.1596|
## |d2          |  -0.0060| 0.0885|   -0.1801|     0.1655|
## |d3          |  -0.1552| 0.1038|   -0.3555|     0.0511|
## 
## 
## *************** MODERATION KEY (d-paths) ***************
## 
## 
## |Coefficient |Path           |Moderated       |
## |:-----------|:--------------|:---------------|
## |d1          |M1avg -> Ydiff |M1diff -> Ydiff |
## |d2          |M2avg -> Ydiff |M2diff -> Ydiff |
## |d3          |M3avg -> Ydiff |M3diff -> Ydiff |
## 
## UNSTANDARDIZED CONDITIONAL EFFECTS (mc)
## Percentile intervals; moderator probes and centering references are held fixed.
## 
## 
## *************** CONTRAST INDIRECT EFFECTS (No Moderator) ***************
## 
## 
## |Contrast                  | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:-------------------------|--------:|------:|---------:|----------:|
## |indirect_2  -  indirect_1 |  -0.0030| 0.0040|   -0.0120|     0.0050|
## |indirect_3  -  indirect_1 |  -0.0020| 0.0040|   -0.0110|     0.0060|
## |indirect_3  -  indirect_2 |   0.0010| 0.0030|   -0.0050|     0.0090|
## 
## 
## *************** C1-C2 COEFFICIENTS (No Moderator) ***************
## 
## 
## |Coeff | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:-----|--------:|------:|---------:|----------:|
## |X1_b1 |  -0.0650| 0.1060|   -0.2740|     0.1450|
## |X0_b1 |  -0.0350| 0.1070|   -0.2460|     0.1720|
## |X1_b2 |  -0.0870| 0.1030|   -0.2840|     0.1190|
## |X0_b2 |  -0.0810| 0.1040|   -0.2820|     0.1280|
## |X1_b3 |  -0.0940| 0.1150|   -0.3170|     0.1330|
## |X0_b3 |   0.0610| 0.1150|   -0.1590|     0.2830|
## 
## 
## *************** REGRESSION PATHS (MC) ***************
## 
## 
## |Path           |Label | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:--------------|:-----|--------:|------:|---------:|----------:|
## |Ydiff ~ M1diff |b1    |  -0.0501| 0.0947|   -0.2371|     0.1337|
## |Ydiff ~ M1avg  |d1    |  -0.0305| 0.0974|   -0.2225|     0.1596|
## |Ydiff ~ M2diff |b2    |  -0.0844| 0.0932|   -0.2628|     0.0966|
## |Ydiff ~ M2avg  |d2    |  -0.0060| 0.0885|   -0.1801|     0.1655|
## |Ydiff ~ M3diff |b3    |  -0.0167| 0.1024|   -0.2159|     0.1852|
## |Ydiff ~ M3avg  |d3    |  -0.1552| 0.1038|   -0.3555|     0.0511|
## 
## 
## *************** INTERCEPTS (MC) ***************
## 
## 
## |Intercept |Label | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:---------|:-----|--------:|------:|---------:|----------:|
## |Ydiff~1   |cp    |  -0.0315| 0.0170|   -0.0645|     0.0019|
## |M1diff~1  |a1    |  -0.0271| 0.0175|   -0.0613|     0.0073|
## |M2diff~1  |a2    |   0.0145| 0.0180|   -0.0206|     0.0502|
## |M3diff~1  |a3    |   0.0153| 0.0164|   -0.0172|     0.0470|
## |M1avg~1   |      |  -0.0000| 0.0184|   -0.0356|     0.0359|
## |M2avg~1   |      |   0.0000| 0.0203|   -0.0407|     0.0401|
## |M3avg~1   |      |  -0.0000| 0.0174|   -0.0337|     0.0339|
## 
## 
## *************** VARIANCES (MC) ***************
## 
## 
## |Variance       |Label | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:--------------|:-----|--------:|------:|---------:|----------:|
## |Ydiff~~Ydiff   |      |   0.0275| 0.0038|    0.0200|     0.0350|
## |M1diff~~M1diff |      |   0.0308| 0.0043|    0.0221|     0.0393|
## |M2diff~~M2diff |      |   0.0323| 0.0046|    0.0233|     0.0412|
## |M3diff~~M3diff |      |   0.0264| 0.0037|    0.0193|     0.0336|
## |M1avg~~M1avg   |      |   0.0339| 0.0048|    0.0246|     0.0431|
## |M2avg~~M2avg   |      |   0.0407| 0.0057|    0.0297|     0.0521|
## |M3avg~~M3avg   |      |   0.0306| 0.0043|    0.0225|     0.0392|
## 
## 
## *************** STANDARDIZED (MC) ***************
## 
## 
## |Parameter      | Estimate|     SE|         R|    2.5%|  97.5%|
## |:--------------|--------:|------:|---------:|-------:|------:|
## |cp             |  -0.1858| 0.0992| 5000.0000| -0.3786| 0.0107|
## |b1             |  -0.0519| 0.0953| 5000.0000| -0.2355| 0.1363|
## |d1             |  -0.0331| 0.1029| 5000.0000| -0.2376| 0.1723|
## |b2             |  -0.0894| 0.0958| 5000.0000| -0.2695| 0.1021|
## |d2             |  -0.0071| 0.1029| 5000.0000| -0.2105| 0.1928|
## |b3             |  -0.0160| 0.0956| 5000.0000| -0.1997| 0.1712|
## |d3             |  -0.1601| 0.1032| 5000.0000| -0.3552| 0.0511|
## |a1             |  -0.1546| 0.1015| 5000.0000| -0.3571| 0.0423|
## |a2             |   0.0806| 0.1014| 5000.0000| -0.1138| 0.2833|
## |a3             |   0.0945| 0.1024| 5000.0000| -0.1072| 0.2954|
## |Ydiff~~Ydiff   |   0.9578| 0.0458| 5000.0000|  0.8031| 0.9767|
## |M1diff~~M1diff |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M2diff~~M2diff |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M3diff~~M3diff |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M1avg~~M1avg   |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M1avg~~M2avg   |   0.2898| 0.0940| 5000.0000|  0.0942| 0.4589|
## |M1avg~~M3avg   |   0.3395| 0.0890| 5000.0000|  0.1530| 0.5019|
## |M2avg~~M2avg   |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M2avg~~M3avg   |   0.3240| 0.0916| 5000.0000|  0.1318| 0.4911|
## |M3avg~~M3avg   |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M1avg~1        |  -0.0000| 0.1010| 5000.0000| -0.1961| 0.1999|
## |M2avg~1        |   0.0000| 0.1019| 5000.0000| -0.2022| 0.2014|
## |M3avg~1        |  -0.0000| 0.1007| 5000.0000| -0.1941| 0.1917|
## |indirect_1     |   0.0080| 0.0183| 5000.0000| -0.0263| 0.0508|
## |indirect_2     |  -0.0072| 0.0151| 5000.0000| -0.0444| 0.0176|
## |indirect_3     |  -0.0015| 0.0132| 5000.0000| -0.0309| 0.0253|
## |total_indirect |  -0.0007| 0.0271| 5000.0000| -0.0558| 0.0550|
## |total_effect   |  -0.1865| 0.0993| 5000.0000| -0.3793| 0.0135|
```

```
## 
## Outcome Difference Model (Ydiff):
##  Ydiff ~ cp*1 + b1*M1diff + d1*M1avg + b2*M2diff + d2*M2avg + b3*M3diff + d3*M3avg 
## 
## Mediator Difference Model (Chained Mediator - M1diff):
## M1diff ~ a1*1 
## 
## Mediator Difference Model (Other Mediators):
## M2diff ~ a2*1
## M3diff ~ a3*1 
## 
## Indirect Effects:
## indirect_1 := a1 * b1
## indirect_2 := a2 * b2
## indirect_3 := a3 * b3 
## 
## Total Indirect Effect:
##  total_indirect := indirect_1 + indirect_2 + indirect_3 
## 
## Total Effect:
##  total_effect := cp + total_indirect
```

## chained/serial mediation

We analyze a **Serial Mediation (`Serial = 1`)**.

### MEMORE 3.0 Analysis Report


````
## ```
##  
## Run MATRIX procedure:
## 
## *********************** MEMORE Procedure for SPSS Version 3.0 ***********************
## 
##                            Written by Amanda Montoya
## 
##                     Documentation available at github.com/akmontoya/MEMORE
## 
## **************************** ANALYSIS NOTES AND WARNINGS ****************************
## 
## Bootstrap confidence interval method used: Percentile bootstrap.
## 
## Number of bootstrap samples for bootstrap confidence intervals:
##   5000
## 
## The following variables were mean centered prior to analysis:
##  (        A2        +       A1       )        /2
##  (        B2        +       B1       )        /2
## 
## Level of confidence for all confidence intervals in output:
##       95.00
## 
## **************************************************************************************
## 
## Model:
##   1
## 
## Variables:
## Y =   C2       C1
## M1 =  A2       A1
## M2 =  B2       B1
## 
## Computed Variables:
## Ydiff =           C2        -       C1
## M1diff =          A2        -       A1
## M2diff =          B2        -       B1
## M1avg  = (        A2        +       A1       )        /2                         Centered
## M2avg  = (        B2        +       B1       )        /2                         Centered
## 
## Sample Size:
##   100
## 
## **************************************************************************************
## Outcome: Ydiff =  C2        -       C1
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant      .0153      .0163      .9404      .3493     -.0170      .0477
## 
## Degrees of freedom for all regression coefficient estimates:
##   99
## 
## **************************************************************************************
## Outcome: M1diff = A2        -       A1
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant     -.0271      .0176    -1.5385      .1271     -.0621      .0079
## 
## Degrees of freedom for all regression coefficient estimates:
##   99
## 
## **************************************************************************************
## Outcome: M2diff = B2        -       B1
## 
## Model Summary
##           R       R-sq        MSE          F        df1        df2          p
##       .2351      .0553      .0314     2.8371     2.0000    97.0000      .0635
## 
## Model
##               coeff         SE          t          p       LLCI       ULCI
## constant      .0208      .0179     1.1603      .2488     -.0148      .0564
## M1diff        .2333      .1010     2.3086      .0231      .0327      .4338
## M1avg        -.0578      .0963     -.6002      .5498     -.2489      .1333
## 
## Degrees of freedom for all regression coefficient estimates:
##   97
## 
## **************************************************************************************
## Outcome: Ydiff =  C2        -       C1
## 
## Model Summary
##           R       R-sq        MSE          F        df1        df2          p
##       .1720      .0296      .0269      .7238     4.0000    95.0000      .5778
## 
## Model
##                Coef         SE          t          p       LLCI       ULCI
## constant      .0160      .0167      .9563      .3413     -.0172      .0492
## M1diff       -.0360      .0962     -.3744      .7089     -.2270      .1549
## M2diff       -.1123      .0967    -1.1607      .2487     -.3043      .0798
## M1avg        -.0617      .0931     -.6619      .5097     -.2466      .1233
## M2avg        -.0733      .0875     -.8374      .4044     -.2469      .1004
## 
## Degrees of freedom for all regression coefficient estimates:
##   95
## 
## ************************* TOTAL, DIRECT, AND INDIRECT EFFECTS *************************
## 
## Total effect of X on Y
##      Effect         SE          t         df          p       LLCI       ULCI
##       .0153      .0163      .9404    99.0000      .3493     -.0170      .0477
## 
## Direct effect of X on Y
##      Effect         SE          t         df          p       LLCI       ULCI
##       .0160      .0167      .9563    95.0000      .3413     -.0172      .0492
## 
## Indirect Effect of X on Y through M
##           Effect     BootSE   BootLLCI   BootULCI
## Ind1       .0010      .0031     -.0045      .0084
## Ind2      -.0023      .0036     -.0111      .0033
## Ind3       .0007      .0010     -.0008      .0034
## Total     -.0006      .0048     -.0109      .0095
## 
## Indirect Key
## Ind1  'X'      ->       M1diff   ->       Ydiff
## Ind2  'X'      ->       M2diff   ->       Ydiff
## Ind3  'X'      ->       M1diff   ->       M2diff   ->       YDiff
## 
## Pairwise Contrasts Between Specific Indirect Effects
##           Effect     BootSE   BootLLCI   BootULCI
## (C1)       .0033      .0042     -.0042      .0128
## (C2)       .0003      .0034     -.0063      .0083
## (C3)      -.0030      .0041     -.0132      .0035
## 
## Contrast Key:
## (C1)  Ind1      -       Ind2
## (C2)  Ind1      -       Ind3
## (C3)  Ind2      -       Ind3
## 
## ------ END MATRIX -----
##  
## ```
````

### wsMed Analysis Report


``` r
result2 <- wsMed(
  data = example_data, #dataset
  M_C1 = c("A1","B1"), # A1/B1 is A/B mediator variable in condition 1
  M_C2 = c("A2","B2"), # A2/B2 is A/B mediator variable in condition 2
  Y_C1 = "C1", # C1 is outcome variable in condition 1
  Y_C2 = "C2", # C2 is outcome variable in condition 2
  form = "CN", # Serial mediation
  standardized = TRUE,
  Na = "DE", ci_method = "mc", R = 5000, seed = 123
)
print(result2,digits=4)
```

```
## 
## 
## *************** VARIABLES ***************
## Outcome (Y):
##    Condition 1: C1 
##    Condition 2: C2 
## Mediators (M):
##   M1:
##     Condition 1: A1
##     Condition 2: A2
##   M2:
##     Condition 1: B1
##     Condition 2: B2
## Sample size (rows kept): 100 
## 
## 
## *************** MODEL FIT ***************
## 
## 
## |Measure   |  Value|
## |:---------|------:|
## |Chi-Sq    |  5.751|
## |df        |  3.000|
## |p         |  0.124|
## |CFI       |  0.494|
## |TLI       | -0.518|
## |RMSEA     |  0.096|
## |RMSEA Low |  0.000|
## |RMSEA Up  |  0.214|
## |SRMR      |  0.050|
## 
## 
## ************* TOTAL / DIRECT / TOTAL-IND (MC) *************
## 
## 
## |Label          | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:--------------|--------:|------:|---------:|----------:|
## |Total effect   |   0.0153| 0.0164|   -0.0160|     0.0487|
## |Direct effect  |   0.0160| 0.0165|   -0.0158|     0.0487|
## |Total indirect |  -0.0006| 0.0044|   -0.0099|     0.0082|
## 
## Indirect effects:
## 
## 
## |Label   | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:-------|--------:|------:|---------:|----------:|
## |ind_1   |   0.0010| 0.0030|   -0.0048|     0.0079|
## |ind_2   |  -0.0023| 0.0032|   -0.0102|     0.0025|
## |ind_1_2 |   0.0007| 0.0010|   -0.0005|     0.0033|
## 
## Indirect-effect key:
## 
## 
## |Ind     |Path                           |
## |:-------|:------------------------------|
## |ind_1   |X -> M1diff -> Ydiff           |
## |ind_2   |X -> M2diff -> Ydiff           |
## |ind_1_2 |X -> M1diff -> M2diff -> Ydiff |
## 
## 
## *************** MODERATION EFFECTS (d-paths, MC) ***************
## 
## 
## |Coefficient | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:-----------|--------:|------:|---------:|----------:|
## |d1          |  -0.0617| 0.0908|   -0.2381|     0.1148|
## |d2          |  -0.0733| 0.0826|   -0.2402|     0.0862|
## |d_1_2       |  -0.0578| 0.0950|   -0.2449|     0.1272|
## 
## 
## *************** MODERATION KEY (d-paths) ***************
## 
## 
## |Coefficient |Path            |Moderated        |
## |:-----------|:---------------|:----------------|
## |d1          |M1avg -> Ydiff  |M1diff -> Ydiff  |
## |d2          |M2avg -> Ydiff  |M2diff -> Ydiff  |
## |d_1_2       |M1avg -> M2diff |M1diff -> M2diff |
## 
## UNSTANDARDIZED CONDITIONAL EFFECTS (mc)
## Percentile intervals; moderator probes and centering references are held fixed.
## 
## 
## *************** CONTRAST INDIRECT EFFECTS (No Moderator) ***************
## 
## 
## |Contrast                    | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:---------------------------|--------:|------:|---------:|----------:|
## |indirect_2    -  indirect_1 |  -0.0030| 0.0040|   -0.0130|     0.0040|
## |indirect_1_2  -  indirect_1 |  -0.0000| 0.0030|   -0.0070|     0.0070|
## |indirect_1_2  -  indirect_2 |   0.0030| 0.0040|   -0.0020|     0.0120|
## 
## 
## *************** C1-C2 COEFFICIENTS (No Moderator) ***************
## 
## 
## |Coeff    | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:--------|--------:|------:|---------:|----------:|
## |X1_b1    |  -0.0670| 0.1030|   -0.2680|     0.1320|
## |X0_b1    |  -0.0050| 0.1040|   -0.2040|     0.1980|
## |X1_b2    |  -0.1490| 0.1010|   -0.3470|     0.0500|
## |X0_b2    |  -0.0760| 0.1010|   -0.2770|     0.1210|
## |X1_b_1_2 |   0.2040| 0.1100|   -0.0120|     0.4170|
## |X0_b_1_2 |   0.2620| 0.1110|    0.0500|     0.4760|
## 
## 
## *************** REGRESSION PATHS (MC) ***************
## 
## 
## |Path            |Label | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:---------------|:-----|--------:|------:|---------:|----------:|
## |Ydiff ~ M1diff  |b1    |  -0.0360| 0.0930|   -0.2178|     0.1468|
## |Ydiff ~ M1avg   |d1    |  -0.0617| 0.0908|   -0.2381|     0.1148|
## |Ydiff ~ M2diff  |b2    |  -0.1123| 0.0924|   -0.2915|     0.0688|
## |Ydiff ~ M2avg   |d2    |  -0.0733| 0.0826|   -0.2402|     0.0862|
## |M2diff ~ M1diff |b_1_2 |   0.2333| 0.0998|    0.0368|     0.4267|
## |M2diff ~ M1avg  |d_1_2 |  -0.0578| 0.0950|   -0.2449|     0.1272|
## 
## 
## *************** INTERCEPTS (MC) ***************
## 
## 
## |Intercept |Label | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:---------|:-----|--------:|------:|---------:|----------:|
## |Ydiff~1   |cp    |   0.0160| 0.0165|   -0.0158|     0.0487|
## |M1diff~1  |a1    |  -0.0271| 0.0176|   -0.0620|     0.0072|
## |M2diff~1  |a2    |   0.0208| 0.0176|   -0.0139|     0.0552|
## |M1avg~1   |      |  -0.0000| 0.0184|   -0.0360|     0.0371|
## |M2avg~1   |      |   0.0000| 0.0201|   -0.0391|     0.0398|
## 
## 
## *************** VARIANCES (MC) ***************
## 
## 
## |Variance       |Label | Estimate|     SE| 2.5%CI.Lo| 97.5%CI.Up|
## |:--------------|:-----|--------:|------:|---------:|----------:|
## |Ydiff~~Ydiff   |      |   0.0256| 0.0037|    0.0185|     0.0327|
## |M2diff~~M2diff |      |   0.0305| 0.0043|    0.0218|     0.0391|
## |M1diff~~M1diff |      |   0.0308| 0.0043|    0.0224|     0.0388|
## |M1avg~~M1avg   |      |   0.0339| 0.0049|    0.0245|     0.0434|
## |M2avg~~M2avg   |      |   0.0407| 0.0058|    0.0292|     0.0518|
## 
## 
## *************** STANDARDIZED (MC) ***************
## 
## 
## |Parameter      | Estimate|     SE|         R|    2.5%|  97.5%|
## |:--------------|--------:|------:|---------:|-------:|------:|
## |cp             |   0.0983| 0.1005| 5000.0000| -0.0947| 0.2980|
## |b1             |  -0.0388| 0.0986| 5000.0000| -0.2278| 0.1595|
## |d1             |  -0.0697| 0.1004| 5000.0000| -0.2633| 0.1288|
## |b2             |  -0.1239| 0.1004| 5000.0000| -0.3148| 0.0758|
## |d2             |  -0.0908| 0.1006| 5000.0000| -0.2915| 0.1062|
## |a1             |  -0.1546| 0.1016| 5000.0000| -0.3562| 0.0398|
## |a2             |   0.1159| 0.0978| 5000.0000| -0.0779| 0.3045|
## |b_1_2          |   0.2278| 0.0947| 5000.0000|  0.0379| 0.4048|
## |d_1_2          |  -0.0592| 0.0963| 5000.0000| -0.2496| 0.1286|
## |Ydiff~~Ydiff   |   0.9656| 0.0420| 5000.0000|  0.8312| 0.9897|
## |M2diff~~M2diff |   0.9446| 0.0466| 5000.0000|  0.8192| 0.9929|
## |M1diff~~M1diff |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M1avg~~M1avg   |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M1avg~~M2avg   |   0.2898| 0.0931| 5000.0000|  0.0953| 0.4603|
## |M2avg~~M2avg   |   1.0000| 0.0000| 5000.0000|  1.0000| 1.0000|
## |M1avg~1        |  -0.0000| 0.1011| 5000.0000| -0.1988| 0.2006|
## |M2avg~1        |   0.0000| 0.1010| 5000.0000| -0.1952| 0.2005|
## |indirect_1     |   0.0060| 0.0183| 5000.0000| -0.0298| 0.0483|
## |indirect_2     |  -0.0144| 0.0191| 5000.0000| -0.0606| 0.0152|
## |indirect_1_2   |   0.0044| 0.0058| 5000.0000| -0.0033| 0.0196|
## |total_indirect |  -0.0040| 0.0265| 5000.0000| -0.0593| 0.0500|
## |total_effect   |   0.0943| 0.1005| 5000.0000| -0.0974| 0.2946|
```

``` r
printGM(result2)
```

```
## 
## Outcome Difference Model (Ydiff):
##  Ydiff ~ cp*1 + b1*M1diff + d1*M1avg + b2*M2diff + d2*M2avg 
## 
## Mediator Difference Model (Chained Mediator - M1diff):
## M1diff ~ a1*1 
## 
## Mediator Difference Model (Other Mediators):
## M2diff ~ a2*1 + b_1_2*M1diff + d_1_2*M1avg 
## 
## Indirect Effects:
## indirect_1 := a1 * b1
## indirect_2 := a2 * b2
## indirect_1_2 := a1 * b_1_2 * b2 
## 
## Total Indirect Effect:
##  total_indirect := indirect_1 + indirect_2 + indirect_1_2 
## 
## Total Effect:
##  total_effect := cp + total_indirect
```