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

- d& W/ V0 \: @4 r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。
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下面的讨论中，我们以"X-->Y的关系受调节变量Z影响“为例。
* Z, X& P" J5 R# z% \% O& X+ s
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？

3 p/ ]$ b8 n' Z- S* U( p: |8 |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。
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。
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4 D, _4 D* Y+ V* F& H. [! F% l由于有图和公式，请参见附件。
* d, D. b2 B6 d6 A（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

. ^" }. c# F4 k3 ^
/ }6 ~5 C0 o7 M; ^# d3 H谢谢！需要好好学习！
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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。
. E- b8 M* ^' e- P' e
*****************.
desc b1 b2/save.
compute idv = zb1.
+ `8 N; i9 l  |9 y2 _3 G8 L. Qcompute mod = zb2.
$ L2 [  C, Y! D% a: h! ecompute x = idv * mod.
) _  p; x2 L9 F( i$ u$ Y$ x3 H6 F1 bcompute dv  = b3.
% a4 V6 c) O* u( d/ w7 G
regression
; E2 [3 A" H$ ~, P% L  V /matrix out ('filename')
/ H! f1 a0 N' W- s /var= idv mod x dv  
! _* D7 U8 t" v! K$ O5 w /statistics=defaults zpp bcov
0 @: Z7 X$ ]/ p /dependent=dv
1 F7 F! p+ n% S, w7 M /enter idv mod  
! h( c4 Z6 S, Y3 _ /test (x) .

8 q9 x8 O% r, i+ ~" w2 ]7 H8 zset mxloops=65.
$ x% A! F0 `3 x- n) {& E5 nmatrix.

/ F) z% C3 S; o3 S0 z  v1 T& zcompute multiMOD = 1.0   .
compute multiIDV = 1.0  .
compute dichotom = 0  .
, K2 x& ?& Z% l* O/ B* j/ n! Y7 V  acompute dichotLo = 1  .
compute dichotHi = 2  .
mget /file='filename'.
1 d5 b2 M5 Y5 X' v
4 z' s1 J) \* G1 K4 ^* Overall regression coeffs.
compute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
compute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
  x2 W1 }/ k* c( _6 h) Vcompute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
) X) L/ K* c  icompute r2all  = t(beta) * cr(1:3,4) .
; T5 `( D7 {, H# m; z! tcompute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
7 e- _4 D; F& `  d; D" Kcompute r2chXn = r2all - r2main.
compute fsquare = (r2all - r2main) / (1 - r2all) .
2 p7 H6 O9 {8 F0 P" o; z7 o* Ccompute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
compute dferror = nc(1,1) - 3 - 1.
' h1 c( f" y/ a0 y# Zcompute pF = 1 - fcdf(F,1,dferror) .
" m$ j4 Q; L" n4 G5 F1 b
4 b" P) f* i9 O) g$ ^0 Dprint {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
/ r- t9 o4 m' C! D; ` /clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
0 O2 L/ e6 w! N9 a7 }+ tprint {t(b),beta} /title="Beta weights for the full equation:"
$ z2 z/ f  ^: M4 \# e6 T  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
1 O/ m# m' _' n+ k1 b) lprint a /title="The intercept is:" .
: }2 d( B9 c  g& k
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* simple slopes info .
5 u. Z9 G  m% S" |5 p% f; ncompute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
# \2 V3 W6 j) g9 `/ X/ m2 Ycompute modmd = mn(1,2).
compute modhi = mn(1,2) + (sd(1,2) * multiMOD) .
: [% z' ]7 `) w, Scompute slopes={(b(1,1)+(b(1,3)*modlo)) ;
4 y! R, R7 x# M# v5 ^                (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: N" A! z8 x/ L1 zcompute Sb=mse*inv((mdiag(sd(1,1:3))*cr(1:3,1:3)*mdiag(sd(1,1:3)))*(nc(1,1)-1)).
compute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
& o: y: ], H3 g0 ]( C2 p                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
' o6 K$ K6 A1 Y% y1 c9 F5 ^  t+ |7 s                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
compute tslopes = slopes &/ SEslopes .
compute df = { (nc(1,1)-3-1) ; (nc(1,1)-3-1) ; (nc(1,1)-3-1) }.
compute zslopes  = slopes &*  (sd(1,1)/sd(1,4)).
compute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
$ u- ~  S" `% w9 w* Q! H- Acompute dfs =  nc(1,1)-3-1 .
5 \' X+ g: }: k+ R) zcompute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.
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* df & t values -- from Darlington p 516 & Howell 87 p 586 --  p = 05 two-tailed .
5 N5 Q% `: g  F3 g/ c5 p) I# o6 c0 wcompute 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,
) z, _- [6 ]1 Z9 V$ E 30,32,34,36,38,40,43,46,49,52,56,60,65,70,75,80,85,90,95,100,110,120,130,
150,175,200,250,300,400,500,600,700,800,900,1000,1000000000;
$ v( l. @* r& B+ a7 M 12.706,4.303,3.182,2.776,2.571,2.447,2.365,2.306,2.262,2.228,2.201,2.179,
/ _" D4 B6 R- f$ s8 i 2.160,2.145,2.131,2.120,2.110,2.101,2.093,2.086,2.074,2.064,2.056,2.048,
2.042,2.037,2.032,2.028,2.024,2.021,2.017,2.013,2.010,2.007,2.003,2.000,
1.997,1.994,1.992,1.990,1.988,1.987,1.985,1.984,1.982,1.980,1.978,1.976,
1.974,1.972,1.969,1.968,1.966,1.965,1.964,1.963,1.963,1.963,1.962,1.962 }.
( Y2 t+ p/ z" T( s8 C) acompute tabledT = 0.
, X/ N" K; i! x; R7 a) `2 n' Y" eloop #a = 1 to 59  .
do if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
; k1 [4 L! n3 Rcompute tabledT = dft(2,#a) .
( I. T% E1 c# P. Y/ ~0 M3 Kend if.
end loop if (tabledT > 0).
5 X! }3 @4 I( u7 Acompute confidLo = (zslopes - (tabledT &* zSE))   .
& L- E9 g) v" s# \' e  @, @$ Rcompute confidHi = (zslopes + (tabledT &* zSE))  .
& S3 d9 {( M. O5 k( ~. L1 q) I
* Y$ t  _  @# ^8 ^" K$ Eprint { aslopes , slopes , tslopes , df , pslopes}  
  /title="Simple Slope Coefficients for the DV on the IDV at 3"
+ " levels of the Moderator:"
! w' ], G# n& z  x0 c; A# T/ g  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="a" "raw b" "t-test" "df" "Sig. T".
print { zslopes , zSE , confidLO, confidHI }
, T+ J1 T) U3 U( W% e2 z2 y /title="Standardized Simple Slopes & 95% Confidence Intervals: "
  _4 E6 Z' L! o9 k  /rlabels="Mod=low" "Mod=med" "Mod=high"
& I. ~' ]: w: k$ J  /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 =".
* v7 B" }/ i0 z

* data for plot.
compute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
# f! q1 ?* R1 I. R& f- b" Ccompute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
8 [/ _) M+ p& h+ g" D! A, M" }compute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
do if (dichotom = 1).
& }9 D- E: i' Q3 e9 f1 [1 F4 q* Mcompute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
+ M/ S4 X! Y; ?& _: Q; d9 m' M0 V- _end if.
compute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
compute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
; q% C2 N2 H8 K; ?' E) icompute data = { idv , moder , dv }.

# x7 ]$ B9 _1 D  k2 g( K+ rprint data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
& q( o% B( h  ?+ z& ]; l
save data /outfile=* / var=zb1 zb2 b3.

end matrix.
$ v% |7 M) G1 }8 {
plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
+ {; h5 k; h/ U0 [( J; Egraph   / 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