调节效应交互项检验显著后分析具体调节作用的方法

xinting.J

: J. K& t. t7 q& N" ?& L& v+ \4 E在《组织与管理研究的实证方法》的“中介作用和调节作用”一章中，我们对调节或交互作用分析（interaction analysis）部分的讲解有一些遗漏。在修订版中也来不及做补充了。受Kenny委托特在这里总结我们的讨论，说明他希望补充的内容，也请同学们互相转告。

下面的讨论中，我们以"X-->Y的关系受调节变量Z影响“为例。

+ n- S$ _% @. Z- l对于调节作用或交互作用的检验很多同学都已经熟悉，书里也讲得比较清楚了。在这一步结束后，我们可以得到一个关于交互项（X*Z）系数是否显著的结论。但这只能说明交互作用存在，分析还没有结束，下一步的问题是：Z是如何调节X-->Y的关系的？调节的方式是否与我们假设的一致？

+ W' E, {: A$ f' K+ v这里有两步工作要做：
一、画图。得到当Z在高值（一般取 Mean Z + 1sd）和低值（一般取Mean Z - 1sd）时的X与Y的关系，即两条回归线。
) ?# r0 ?4 t% W0 b二、分析两条回归线的斜率是否显著不为0。这也正是附件中要补充的难点。

( A$ C: N0 s5 g由于有图和公式，请参见附件。
) H0 d1 ?8 e' h+ @4 h& B（抱歉，好像系统自动设置付金币才能下载文件，取消不了。  只能劳烦大家发点帖子挣点钱来下载文件了。）
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rwxld

非常感谢，辛苦了！

jimmyzhaoxin

谢谢xinting.J，收藏了

mayecho

谢谢！需要好好学习！

allevon

很给力！

找天堂

太好了，谢谢！

mnczj

我来分享一个计算simple slope effect和画图的SPSS macro （https://people.ok.ubc.ca/brioconn/simple/simple.html）。大家只要自行修改下面Macro中b1,b2,b3的名称就可以了。
7 T6 l# V8 i/ k" x& h* s. u
: m. w/ O# c( ?, ^*****************.
desc b1 b2/save.
% ?4 x" e3 }4 v6 E% x% r, Ncompute idv = zb1.
: t, P! ^2 y) {' U0 P% a2 [& mcompute mod = zb2.
( q. p2 @8 V1 ]* bcompute x = idv * mod.
compute dv  = b3.
5 o* p1 ?# w& p( _
regression
/matrix out ('filename')
/var= idv mod x dv  
/statistics=defaults zpp bcov
3 K) T' w9 t0 [1 ^5 q /dependent=dv
/enter idv mod  
4 W# ~! I! p" e& R /test (x) .
' ?0 V; @7 ~3 u5 q: V9 j1 f
7 [% J+ J3 M  uset mxloops=65.
( w# w1 E) P& `  {matrix.
6 S! o& K: O1 ]2 X: c' Q8 A
compute multiMOD = 1.0   .
$ g) J! Y. O9 `; z/ b1 lcompute multiIDV = 1.0  .
$ ]5 Y6 f6 `$ P2 ]& bcompute dichotom = 0  .
compute dichotLo = 1  .
compute dichotHi = 2  .
; B+ o% i3 A$ K4 s' _4 z1 A( Amget /file='filename'.
0 v) @1 C4 e5 X5 R* ?% E6 D) l$ r/ y
; I1 w, [$ B* B: l* Overall regression coeffs.
8 [0 ^# J1 v, S: T& H# Ycompute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
* ~2 Q; s2 e. u  c; E' Tcompute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
compute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
+ ]$ f& I3 a) x( f* u7 U! ccompute r2all  = t(beta) * cr(1:3,4) .
  s8 Z7 Q' s% }2 Z5 vcompute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
7 C4 E# I) H+ s- v) ]& acompute r2chXn = r2all - r2main.
1 ]$ `% v. R4 K; a& M' z8 K! ]compute fsquare = (r2all - r2main) / (1 - r2all) .
compute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
compute dferror = nc(1,1) - 3 - 1.
compute pF = 1 - fcdf(F,1,dferror) .
  v7 q# k% `9 ^4 A
print {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
/clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
print {t(b),beta} /title="Beta weights for the full equation:"
. p* M& W* V8 h1 U  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
' r; H5 T/ I6 Oprint a /title="The intercept is:" .
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0 m1 x' Z7 _  ?3 {4 Q) m9 K' i
* simple slopes info .
  K+ m/ q9 W: N0 U! ]compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
1 B( N9 h7 v% Q$ C, ~4 |: |3 mcompute modmd = mn(1,2).
0 e1 B- p! m0 z* E+ X/ P, J! H( o3 [compute modhi = mn(1,2) + (sd(1,2) * multiMOD) .
compute slopes={(b(1,1)+(b(1,3)*modlo)) ;
* Q, L# J1 h0 R& O9 w0 \9 _                (b(1,1)+(b(1,3)*modmd)) ; (b(1,1)+(b(1,3)*modhi)) }.
compute aslopes={ (b(1,2)*modlo+a) ; (b(1,2)*modmd+a) ; (b(1,2)*modhi+a) }.
compute mse = (nc(1,1)/(nc(1,1)-3))*(sd(1,4)**2)*(1-r2all).
  M$ k6 s" S: f6 ^compute Sb=mse*inv((mdiag(sd(1,1:3))*cr(1:3,1:3)*mdiag(sd(1,1:3)))*(nc(1,1)-1)).
$ A9 L8 ]- I' F* \( ^$ ecompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
' H+ f" p1 R6 h3 P8 l" b                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
compute tslopes = slopes &/ SEslopes .
3 t# I$ w" A- i3 bcompute df = { (nc(1,1)-3-1) ; (nc(1,1)-3-1) ; (nc(1,1)-3-1) }.
1 ^3 q3 g/ \# Fcompute zslopes  = slopes &*  (sd(1,1)/sd(1,4)).
  w' W3 ^- V. P2 `5 ^2 Ecompute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
1 t4 @1 |1 }8 O) fcompute dfs =  nc(1,1)-3-1 .
compute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.

' x5 A4 a! p) y% o# s* m5 x( Q# g* df & t values -- from Darlington p 516 & Howell 87 p 586 --  p = 05 two-tailed .
& x$ Z  M9 s6 X0 G" \; O0 Y: vcompute dft={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,22,24,26,28,
! {& F: f5 m( Y; i8 v1 u- A 30,32,34,36,38,40,43,46,49,52,56,60,65,70,75,80,85,90,95,100,110,120,130,
$ q- K+ {: _. M9 {. X! G7 |1 z8 D 150,175,200,250,300,400,500,600,700,800,900,1000,1000000000;
12.706,4.303,3.182,2.776,2.571,2.447,2.365,2.306,2.262,2.228,2.201,2.179,
# F- C0 |. @! a6 g- ]' B  g 2.160,2.145,2.131,2.120,2.110,2.101,2.093,2.086,2.074,2.064,2.056,2.048,
6 \$ k# v% E- W% l. M 2.042,2.037,2.032,2.028,2.024,2.021,2.017,2.013,2.010,2.007,2.003,2.000,
+ D2 v0 ~) B8 b 1.997,1.994,1.992,1.990,1.988,1.987,1.985,1.984,1.982,1.980,1.978,1.976,
& j# h% X( U3 b* `7 s7 H 1.974,1.972,1.969,1.968,1.966,1.965,1.964,1.963,1.963,1.963,1.962,1.962 }.
compute tabledT = 0.
$ X# n$ F  q1 ^+ ~# Bloop #a = 1 to 59  .
do if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
compute tabledT = dft(2,#a) .
: U1 W# K: o  b' ]+ ~. |end if.
end loop if (tabledT > 0).
compute confidLo = (zslopes - (tabledT &* zSE))   .
- Z; d  {7 K8 u5 Z9 R7 i" e8 K& Ecompute confidHi = (zslopes + (tabledT &* zSE))  .
6 d% d8 g4 p" l- A; h; Z% u
print { aslopes , slopes , tslopes , df , pslopes}  
0 @$ M3 p% J* l: b  /title="Simple Slope Coefficients for the DV on the IDV at 3"
+ " levels of the Moderator:"
% P3 g# s1 e: D  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="a" "raw b" "t-test" "df" "Sig. T".
+ q! L) q! @  g- f) F' E' Yprint { zslopes , zSE , confidLO, confidHI }
6 _+ }6 u7 w" g$ `; ` /title="Standardized Simple Slopes & 95% Confidence Intervals: "
. ?$ t& d- p9 a, |" y) M8 W  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
print ((b(1,1)/b(1,3))*-1)/title="The simple slope for the DV on the IDV"
+ " is zero (flat) at Moderator =".
print ((b(1,2)/b(1,3))*-1)/title="The simple regression lines at "
+ "Mod=high and Mod=low intersect at IDV =".
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" Q: D. O; R( f1 e1 o7 K* data for plot.
compute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
+ r; n* `5 `! I4 M/ s; j+ hcompute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
6 d5 b& B" f9 ~" zcompute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
1 d- a6 F( ^/ t2 ado if (dichotom = 1).
1 [9 w4 T) X1 s" Y5 I5 Wcompute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
end if.
compute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
9 X) f, I+ {- l" @. y/ e6 ]compute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
compute data = { idv , moder , dv }.
6 ]& T( j, u0 s, T
8 }5 q" F/ i- R- z: a5 C" x8 R" Kprint data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
8 p5 o: t/ G* O* B8 y/ k
$ g5 Y+ c  y7 u* ksave data /outfile=* / var=zb1 zb2 b3.

# J. `6 ?! w+ e2 L# ~% |, M* n6 ?end matrix.

plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
. Z8 m- w" W, n3 p  ^# G" |graph   / line = mean (b3) by b1 by b2.

sobing

有帮助，谢谢！

reddyrunny

非常感谢，学习收获不少，谢谢！

snryjj

好东西 学习中