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

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。

4 p0 E7 B8 S0 L7 _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？
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  _. }1 ~7 O" z7 L* p; S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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8 ~* F' m  `& N0 h: {2 E2 h! A由于有图和公式，请参见附件。
: @/ c& E: Q1 p; S1 Z（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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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。
& S: h1 p7 L5 \% Q0 Q% K3 g
7 c5 Z3 W2 y/ Q2 m6 f& F*****************.
! w% H1 u" e0 t( b% \desc b1 b2/save.
  z5 C$ e0 X% h2 ?1 S  Tcompute idv = zb1.
compute mod = zb2.
  B9 D, I2 }+ ccompute x = idv * mod.
compute dv  = b3.
8 j& A/ n2 F9 A9 v& P& k' R0 x4 p
regression
/matrix out ('filename')
/var= idv mod x dv  
9 K9 K& V  s8 O" ]7 |0 d" {9 j /statistics=defaults zpp bcov
" r- M7 ^3 M" }' V /dependent=dv
% |* W7 P  K+ g5 J /enter idv mod  
+ q4 ~* D5 s1 O9 ` /test (x) .
, l3 z! b" o+ ^2 j& d+ u3 |/ t
" O* Q+ g9 K) k- V+ i5 [5 kset mxloops=65.
5 N' \1 i' j# ?8 M# Cmatrix.

8 {% G$ t' N- g" s" Qcompute multiMOD = 1.0   .
compute multiIDV = 1.0  .
compute dichotom = 0  .
8 n! g# j, u; Scompute dichotLo = 1  .
5 y- a, a  x, E' }$ O% Hcompute dichotHi = 2  .
$ l6 [1 ^' h- [* I9 X' imget /file='filename'.
; p! k, u) E3 P, i5 U2 {
* |* d7 x" Q4 U. I0 X1 v4 }! B1 \* Overall regression coeffs.
7 y% w5 V! P6 ]% A: a8 ucompute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
2 L/ ~* G) \. Z& J  Rcompute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
$ Z2 j1 w4 b  e2 }- _) a8 A& ~  E2 Xcompute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
2 P. d- P# @6 k* Z; ycompute r2all  = t(beta) * cr(1:3,4) .
compute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
compute r2chXn = r2all - r2main.
( z: F4 M- D* |/ Zcompute fsquare = (r2all - r2main) / (1 - r2all) .
compute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
7 |6 ]+ |% X' ?8 W+ S7 Acompute dferror = nc(1,1) - 3 - 1.
compute pF = 1 - fcdf(F,1,dferror) .

print {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
) ?6 m/ Q% Z/ D+ v: K& _ /clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
! t" B' q6 f( A  N& S- \print {t(b),beta} /title="Beta weights for the full equation:"
  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
print a /title="The intercept is:" .

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. |. X, P, a) C3 A* simple slopes info .
compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
, c: `1 }* l+ D' ccompute modmd = mn(1,2).
compute modhi = mn(1,2) + (sd(1,2) * multiMOD) .
compute slopes={(b(1,1)+(b(1,3)*modlo)) ;
/ h0 @4 X# g( C" V                (b(1,1)+(b(1,3)*modmd)) ; (b(1,1)+(b(1,3)*modhi)) }.
6 N. z9 {- f0 K2 y% ~7 O4 L" pcompute 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).
! q5 B3 Q* O7 J2 ^3 F0 Wcompute Sb=mse*inv((mdiag(sd(1,1:3))*cr(1:3,1:3)*mdiag(sd(1,1:3)))*(nc(1,1)-1)).
7 V9 L7 Y: c3 {  ncompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
% d8 G3 w, U8 P( m                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
# j7 d% z( [9 v, W/ M) lcompute tslopes = slopes &/ SEslopes .
8 ^% {; r* B+ rcompute df = { (nc(1,1)-3-1) ; (nc(1,1)-3-1) ; (nc(1,1)-3-1) }.
: |% c9 U+ {* W1 Pcompute zslopes  = slopes &*  (sd(1,1)/sd(1,4)).
% O! W- K! \- P+ Vcompute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
compute dfs =  nc(1,1)-3-1 .
4 y; W) m: G9 r0 L* J6 V3 Wcompute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.
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, o- f% A$ p" M3 \7 f. h8 H3 m* df & t values -- from Darlington p 516 & Howell 87 p 586 --  p = 05 two-tailed .
, y0 y6 m& G! {6 [, a# D+ w7 ?$ Tcompute 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,
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,
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,
+ h  }7 y/ G3 ~- B7 l/ P; \ 1.974,1.972,1.969,1.968,1.966,1.965,1.964,1.963,1.963,1.963,1.962,1.962 }.
* `; |0 @* c; V8 S! }compute tabledT = 0.
7 v. k0 Z6 B! c! Y9 o/ N8 \" ^( oloop #a = 1 to 59  .
1 }4 @( v4 S, Bdo if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
1 P* c2 P# U  S' I$ g) Kcompute tabledT = dft(2,#a) .
9 i# J3 u6 |1 ~/ k) {end if.
end loop if (tabledT > 0).
% ]/ s9 o7 T/ {4 ^/ f8 ~; pcompute confidLo = (zslopes - (tabledT &* zSE))   .
compute confidHi = (zslopes + (tabledT &* zSE))  .

% _* `% ^7 R1 k' h% ~* @5 B& G9 Oprint { aslopes , slopes , tslopes , df , pslopes}  
  /title="Simple Slope Coefficients for the DV on the IDV at 3"
5 B. {& y# _" H$ h$ U5 e+ " levels of the Moderator:"
  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="a" "raw b" "t-test" "df" "Sig. T".
print { zslopes , zSE , confidLO, confidHI }
/title="Standardized Simple Slopes & 95% Confidence Intervals: "
: L7 _8 ], u" o# ~: O  /rlabels="Mod=low" "Mod=med" "Mod=high"
" h8 [. k4 i8 @( V: }  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
7 s1 m7 V3 Z) v" ?: `: Aprint ((b(1,1)/b(1,3))*-1)/title="The simple slope for the DV on the IDV"
; `  w9 u+ E1 c* f+ " 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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* data for plot.
0 H9 G9 B# e0 e" dcompute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
  u$ d# i, m! }& Q7 k3 n! t, Ucompute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
2 f/ \: `  c9 x) @/ W1 g+ Ycompute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
3 r" z+ }/ j+ i; z6 bdo if (dichotom = 1).
  f/ J7 y( \& W. jcompute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
/ G; g% j  K! R4 N& dend 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.
  Z. K2 S- u7 n! E6 bcompute data = { idv , moder , dv }.
+ \3 w4 s# ~6 |' I1 x5 [
: o' U+ }: p0 q. f! Y% uprint data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
; ]0 M/ R# C1 p- c1 r+ o
save data /outfile=* / var=zb1 zb2 b3.
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; e8 {0 J8 r5 m' Y" x1 Jend matrix.
' l) ?! ]) u. e0 V1 q% y
plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
graph   / line = mean (b3) by b1 by b2.
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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