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

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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。

! |6 E& a) E+ ^, H( U+ p2 \下面的讨论中，我们以"X-->Y的关系受调节变量Z影响“为例。

" Y+ a$ t2 J& w8 F" C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？

这里有两步工作要做：
# L1 I0 k% B9 `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。
. X2 K6 P+ e0 Z; s. F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。
1 B" n" T) X' `
由于有图和公式，请参见附件。
7 o$ @/ m$ }* C（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

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' m* u2 U9 l  M' D- F9 A3 I谢谢！需要好好学习！
3 R+ _2 G7 U- S/ \  b

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  j4 h$ L! J, o% {$ b3 g*****************.
3 o" Z( e) ?1 d- idesc b1 b2/save.
& i. k6 m  Z& `7 X: }6 J3 Vcompute idv = zb1.
compute mod = zb2.
3 D) y# x* ?$ g3 b9 w4 V; scompute x = idv * mod.
- S" g. ~2 w6 D3 V6 o4 Ocompute dv  = b3.

0 R, I, P3 i, X% a' v" c# ?regression
/matrix out ('filename')
/var= idv mod x dv  
/statistics=defaults zpp bcov
/dependent=dv
% e# e" g, S" v0 K. u% p /enter idv mod  
0 ~  {$ q, U/ e5 g /test (x) .
# d1 j; A! n; t- v5 F' A7 P9 K
set mxloops=65.
matrix.

) f' K& h) w0 S; v0 ucompute multiMOD = 1.0   .
2 G' c: U; }. @, B  B4 _$ x8 m$ [compute multiIDV = 1.0  .
compute dichotom = 0  .
compute dichotLo = 1  .
compute dichotHi = 2  .
mget /file='filename'.
1 [8 ^( p# F2 I9 F
* Overall regression coeffs.
# z8 c0 N! r* W9 R( k& w0 Ccompute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
compute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
compute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
compute r2all  = t(beta) * cr(1:3,4) .
compute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
* q' _( t  k0 e" `& r% l3 i6 ^compute r2chXn = r2all - r2main.
compute fsquare = (r2all - r2main) / (1 - r2all) .
: n0 t6 c9 m4 B  n% qcompute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
" o; B& r) T4 E0 l# Ycompute dferror = nc(1,1) - 3 - 1.
0 i5 B% |- m2 y: L4 _: Qcompute pF = 1 - fcdf(F,1,dferror) .

; L, V/ w% v1 }print {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
6 ]3 H0 u  ?1 u, H /clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
3 P8 h( B: r% O, h  S& I& @print {t(b),beta} /title="Beta weights for the full equation:"
7 l5 k% J+ t( ~7 N; [! V* R; m7 g/ A  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
3 I( F8 _3 [9 @4 ~5 v2 Fprint a /title="The intercept is:" .
  A% O7 C7 G. A" a0 k; L' |; ?

3 y- b; z. ?! V* simple slopes info .
compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
: O7 p4 w  _0 mcompute modmd = mn(1,2).
compute modhi = mn(1,2) + (sd(1,2) * multiMOD) .
compute slopes={(b(1,1)+(b(1,3)*modlo)) ;
                (b(1,1)+(b(1,3)*modmd)) ; (b(1,1)+(b(1,3)*modhi)) }.
$ d* ]0 A' h- z: K0 E' ncompute 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).
) z6 ?* m9 v6 {; |compute Sb=mse*inv((mdiag(sd(1,1:3))*cr(1:3,1:3)*mdiag(sd(1,1:3)))*(nc(1,1)-1)).
. n- L# i% u* w, c- ~7 fcompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
% P* {5 @# Y/ i4 p: E6 f0 ^! }2 Qcompute tslopes = slopes &/ SEslopes .
8 _2 x" |0 o. y  [# L/ Ycompute 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))  .
compute dfs =  nc(1,1)-3-1 .
2 T; y3 N( \/ scompute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.

* df & t values -- from Darlington p 516 & Howell 87 p 586 --  p = 05 two-tailed .
5 i# i) `' Z% M5 D3 m+ h- q% N: |compute 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,
. h& @4 d+ Z% u4 O' i+ K' i) h 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;
12.706,4.303,3.182,2.776,2.571,2.447,2.365,2.306,2.262,2.228,2.201,2.179,
' y, l5 }1 Q1 j& 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,
; [" U* a2 B8 o- I& n. m$ ~. j. r 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.
loop #a = 1 to 59  .
  p. K! g  X( r' ?do if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
4 w# s+ Y: o* e- K8 Q/ mcompute tabledT = dft(2,#a) .
end if.
end loop if (tabledT > 0).
compute confidLo = (zslopes - (tabledT &* zSE))   .
, {1 B* _0 E$ ^compute confidHi = (zslopes + (tabledT &* zSE))  .

print { aslopes , slopes , tslopes , df , pslopes}  
  /title="Simple Slope Coefficients for the DV on the IDV at 3"
3 e4 ~* R) p3 Q) p* v: O+ " levels of the Moderator:"
7 C. g: s7 T) V$ r; F. h  U& a  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="a" "raw b" "t-test" "df" "Sig. T".
9 N% B" h9 j( n, N7 z" `print { zslopes , zSE , confidLO, confidHI }
/title="Standardized Simple Slopes & 95% Confidence Intervals: "
  /rlabels="Mod=low" "Mod=med" "Mod=high"
& T5 [( T& a9 M/ B: k  a. G# u  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
) `1 E9 |( L" T' W( wprint ((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 =".

0 D" h6 R* y6 R$ r9 b0 f
% J& ?: ]8 A: o3 {% x* data for plot.
  [) H& X* F+ F4 R: d2 A* v1 ocompute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
0 i% ]4 N) @6 [" ]/ j, P7 Q8 ]compute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
$ Z9 q( H# M& }# ?* acompute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
do if (dichotom = 1).
compute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
end if.
- R; T8 c( B( N/ [2 E2 c9 c) ?* l0 Tcompute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
' A2 X6 |% I' e6 N* Z) Mcompute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
0 \9 P; H# R* S: Icompute data = { idv , moder , dv }.

print data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
6 E2 }  X. l! p0 C$ U
/ q6 z* }3 Z2 C6 |: E' vsave data /outfile=* / var=zb1 zb2 b3.
1 L% {7 x. F$ x
" L1 n0 N7 f$ }' [end matrix.
) `. R* V+ w' d/ K
plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
3 s* f2 j* e8 j% K) vgraph   / line = mean (b3) by b1 by b2.
! T3 J; t( d2 v4 F& U5 ?

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