on the benefits of using the process macro to · pdf fileon the benefits of using the process...

ON THE BENEFITS OF USING THE PROCESS MACRO TO TEST STATISTICAL MODELS IN DATA
ANALYSIS CLASSES
Renaud Lunardo, PhD, HDR
Kedge Business School, Bordeaux
[email protected]
Xlstat Conference, Bordeaux, Juin 2017

What students learn in statistical classes
X Y
Basic tests :- T-tests, ANOVAs- Correlations, regressions
1/ Descriptive statistics: - means, medians, quartiles, proportions, confidence intervals
2/ Bivariate / Multivariate statistics:

Beyond main effects: moderation and mediation
X
Z
Y X
M
Y
GOAL: identify the conditions under which:- X has an effect on Y- or the effect of X on Y changes
GOAL: identify the mechanism that explainswhy X has an effect on Y

A step further: Moderated medations
X
M
Y
Z

Testing main effects using SEMs: General principles and vocabulary
Latent variable
Indicator 1E 1
Indicator 2
Indicator 3
Indicator 4
E 2
E 3
E 4
1
2
3
4
1

SEMs enable the inclusion of second-ordervariables (multidimensional scales)
Constructive
X11
X2
X3
X4
11
21
31
41
12
3
4
Offensive
X55
X6
X7
X8
52
62
72
82
26
7
8
Humor

Xlstat Conference, Bordeaux, Juin 2017 7
Notations : Independent variable Dependent variable
Indicator X Y
Latent variable (ksi) (ta)
Error in the measure of
indicators (delta) (epsilon)
Loadings (PCA) (lambda)
Relation (gamma) (bta)
Covariance (phi) (psi)
Error of specification of
the model- (zta)
General principles of SEMs

Testing models using SEMS
11
21
12
22
12
Performance
Y1 1
Y2
Y3
Y4
11
21
31
41
12
3
4
1
Trust
Y5 5
Y6
Y7
Y8
52
62
72
82
26
7
82
Humor
X11
X2
X3
X4
11
21
31
41
12
3
4
Competence
X55
X6
X7
X8
52
62
72
82
26
7
8

Testing moderations using SEMs: the multigroups analyses
11
21
12
22
12
Benevolence
Integrity
Purchase
Attitude
Past experience with the brand

the (numerous) assumptions behind them
Measurement invariance Goal: is the latent factor structure underlying the items measures the same across groups (Judd and Kenny 2010).Configural invariance: same structure across groups
Error variance invariance: same error variance across groups
Metric invariance: same factor loadings across groups
Factor variance invariance: same factor variance across groups
Scalar invariance: same item intercepts across groups
Factor covariance invariance: same factor covariance across groups
Factor mean invariance: same factor mean across groups

and its drawbacks
1. Boostrap
2. Often need to perform a split (median- or mean-based)
Huge controversy around this method due to, among others, arbitrary value of the split and insensitive analysis to the pattern of local covariation between X and Y within groups defined by the median split
We know of no statistical argument in favor of median splits to counterbalance the chorus of statistical critiques against them (Mc Lelland et al., 2015, p.680).

The need to check the fit of the model
Fit Formula
Bentler-Bonett (NFI)2(Null Model) - 2(Proposed Model)
----------------------------------------------------2(Null Model)
Tucker-Lewis Index (TLI)2/df(Null Model) - 2/df(Proposed Model)
---------------------------------------------------------------2/df(Null Model) - 1
CFId(Null Model) - d(Proposed Model)
-----------------------------------------------------d(Null Model)
RMSEA(2 - df)
---------------------[df(N - 1)]

And the light comes: the Process macro

How to use it: easy

An easy-to-interpret output
Outcome: CONF
coeff se t p LLCI ULCIconstant 2,6147 ,2505 10,4367 ,0000 2,1206 3,1088EXPLOR 1,5231 ,7383 2,0630 ,0404 ,0670 2,9793HUMOR ,3109 ,0653 4,7635 ,0000 ,1822 ,4396int_1 -,4290 ,1910 -2,2460 ,0258 -,8057 -,0523
R-square increase due to interaction(s):R2-chng F df1 df2 p
int_1 ,0231 5,0443 1,0000 195,0000 ,0258
*************************************************************************
Conditional effect of X on Y at values of the moderator(s):EXPLOR Effect se t p LLCI ULCI,0000 ,3109 ,0653 4,7635 ,0000 ,1822 ,43961,0000 -,1181 ,1795 -,6581 ,5113 -,4722 ,2359
1
1,5
2
2,5
3
3,5
4
4,5
1 2 3 4 5 6 7
Tru
st
Use of humor
Not exploration phase Exploration phase

Moderations using Process: Floodlight analyses

A concrete example of floodlight analysis
1
2
3
4
5
6
7
1 2 3 4 5 6 7
Po
siti
ve R
ein
terp
reta
tio
n
Rumination
Low Guilt
High Guilt
Outcome: REINTERP
coeff se t p
constant 2,1844 ,3294 6,6324 ,0000
RUMIN ,5474 ,1158 4,7283 ,0000
GUILTMAN 2,9101 ,5617 5,1805 ,0000
int_1 -,5843 ,1736 -3,3651 ,0009
******************************************************
Effect of X on Y at values of the moderator(s):
RUMIN Effect se t p
1,4270 2,0764 ,3551 5,8471 ,0000
2,8340 1,2542 ,2439 5,1414 ,0000
4,2411 ,4320 ,3351 1,2893 ,1990
********** JOHNSON-NEYMAN TECHNIQUE *****************
Moderator value(s) defining Johnson-Neyman significance
region(s):
Value % below % above
3,9561 78,5311 21,4689

More in details
Conditional effect of X on Y at values of the moderator (M)
RUMIN Effect se t p LLCI ULCI
1,0000 2,3258 ,4122 5,6424 ,0000 1,5122 3,1394
1,3000 2,1505 ,3715 5,7895 ,0000 1,4174 2,8837
1,6000 1,9753 ,3339 5,9161 ,0000 1,3163 2,6342
1,9000 1,8000 ,3007 5,9869 ,0000 1,2065 2,3934
2,2000 1,6247 ,2734 5,9429 ,0000 1,0851 2,1643
2,5000 1,4494 ,2540 5,7065 ,0000 ,9481 1,9507
2,8000 1,2741 ,2444 5,2141 ,0000 ,7918 1,7564
3,1000 1,0988 ,2456 4,4734 ,0000 ,6140 1,5836
3,4000 ,9235 ,2577 3,5843 ,0004 ,4150 1,4321
3,7000 ,7482 ,2790 2,6813 ,0080 ,1974 1,2990
3,9561 ,5986 ,3033 1,9738 ,0500 ,0000 1,1971
4,0000 ,5729 ,3079 1,8610 ,0644 -,0347 1,1806
4,3000 ,3976 ,3422 1,1620 ,2468 -,2778 1,0731

Turning to mediations : Focus on CIsOutcome: MPERF
coeff se t p
constant 2,9574 ,2648 11,1676 ,0000
MCONF ,2241 ,0741 3,0259 ,0029
*******************************************************
Outcome: MBAO
Coeff se t p
constant 1,6966 ,2740 6,1919 ,0000
MPERF ,2674 ,0598 4,4738 ,0000
MCONF ,3590 ,0601 5,9764 ,0000
******************** DIRECT AND INDIRECT EFFECTS ******
Direct effect of X on Y
Effect SE t p
,3590 ,0601 5,9764 ,0000
Indirect effect of X on Y
Effect Boot SE BootLLCI BootULCI
MPERF ,0599 ,0285 ,0181 ,1327

Mediations using Process: Even with 2 mediators
*************** DIRECT AND INDIRECT EFFECTS ******************
Direct effect of X on Y
Effect SE t p LLCI ULCI
-,0588 ,2515 -,2340 ,8154 -,5567 ,4390
Indirect effect(s) of X on Y
Effect Boot SE BootLLCI BootULCI
Total: -,0956 ,1362 -,4039 ,1294
Ind1 : ,1383

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