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。
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8 M7 b- z8 k' c4 L下面的讨论中，我们以"X-->Y的关系受调节变量Z影响“为例。

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？

2 V/ C* k9 }/ R' F  [% H9 o- N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。

由于有图和公式，请参见附件。
2 |: R7 Q) E5 g（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！
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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。

8 Z6 b) [' V% Z3 T$ _7 T- F*****************.
! ~* V5 C; {4 y+ [desc b1 b2/save.
compute idv = zb1.
compute mod = zb2.
* f2 P# F# j% Q# bcompute x = idv * mod.
compute dv  = b3.

9 M- L  h6 K% e% [/ |" Dregression
$ ]5 X) [* S+ f6 a1 E# i1 } /matrix out ('filename')
% J- w2 m3 q/ t8 w8 e /var= idv mod x dv  
* T4 [: q% p( u& x/ I' O /statistics=defaults zpp bcov
; i. a) h& T. O; x /dependent=dv
/enter idv mod  
/test (x) .

set mxloops=65.
0 q4 P/ j( Z& g( y7 U* ?matrix.

compute multiMOD = 1.0   .
, c6 b# R6 @- Gcompute multiIDV = 1.0  .
compute dichotom = 0  .
compute dichotLo = 1  .
4 k6 R  g0 U0 o* P) mcompute dichotHi = 2  .
mget /file='filename'.
9 v) X, l. c$ J8 m
9 J7 m; G, ^- U2 ^9 b5 J, E* Overall regression coeffs.
( k; c0 c9 d5 F- m4 h& Jcompute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
1 q& A- M0 s. ~- [) rcompute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
compute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
  j+ |& k) e9 M- e& d* @, L: Acompute r2all  = t(beta) * cr(1:3,4) .
1 b( H, M: n# {; P/ Rcompute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
  i: H) x( q" Z& e7 E. W2 Q% i# Tcompute r2chXn = r2all - r2main.
compute fsquare = (r2all - r2main) / (1 - r2all) .
* O. D9 o- L( y& T) x4 Y5 ^compute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
compute dferror = nc(1,1) - 3 - 1.
* j4 \4 O& y: L$ O5 ^. N. Ucompute pF = 1 - fcdf(F,1,dferror) .

print {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
* `- j6 R+ ?+ y- d( ` /clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
8 h3 n1 F* R2 {print {t(b),beta} /title="Beta weights for the full equation:"
  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
9 A" u7 Z7 H8 }; }9 Dprint a /title="The intercept is:" .
+ a$ W- R9 {) P- G! ], d
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# Z5 _1 x& V2 ~$ a- _) v; U' I4 w" ?* simple slopes info .
6 V9 v& E( ^* z7 _compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
  K+ ^( T# @& E. W7 Y; ]compute modmd = mn(1,2).
compute modhi = mn(1,2) + (sd(1,2) * multiMOD) .
; W. a9 m9 ?" X/ t) J; E6 o& Rcompute slopes={(b(1,1)+(b(1,3)*modlo)) ;
+ {$ O. w" o- T, l" x                (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).
compute Sb=mse*inv((mdiag(sd(1,1:3))*cr(1:3,1:3)*mdiag(sd(1,1:3)))*(nc(1,1)-1)).
  H0 e0 D# G4 L2 {9 ocompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
& G7 N' u: D6 s& ~& v                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
7 S" }  T* _- ?6 @: P1 w) X( d* [compute tslopes = slopes &/ SEslopes .
compute df = { (nc(1,1)-3-1) ; (nc(1,1)-3-1) ; (nc(1,1)-3-1) }.
/ ~  `% w+ t& z2 ]" }0 d8 f" h' mcompute zslopes  = slopes &*  (sd(1,1)/sd(1,4)).
compute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
compute dfs =  nc(1,1)-3-1 .
6 ]; ]7 g" B& \2 w- b, J  \compute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.

* df & t values -- from Darlington p 516 & Howell 87 p 586 --  p = 05 two-tailed .
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,
  X0 f" O0 l5 J' M1 f9 W/ o; m 30,32,34,36,38,40,43,46,49,52,56,60,65,70,75,80,85,90,95,100,110,120,130,
8 _* g6 M; c! N* A8 ]& m# r 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,
5 T( R7 Y" S. w( I$ h 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,
6 Q8 S; ~0 `& K6 L9 T) \& 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 }.
5 i( [, e8 w' |  F% y4 Vcompute tabledT = 0.
loop #a = 1 to 59  .
do if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
) w5 C$ e6 i7 ~4 H* u# R+ r# E$ ocompute tabledT = dft(2,#a) .
2 _( p4 d$ o2 n+ P, Uend if.
end loop if (tabledT > 0).
+ q. b, e3 k. H( J& W  b+ X! Rcompute confidLo = (zslopes - (tabledT &* zSE))   .
' u+ h5 q) R$ r6 w6 O( Icompute confidHi = (zslopes + (tabledT &* zSE))  .
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print { aslopes , slopes , tslopes , df , pslopes}  
  /title="Simple Slope Coefficients for the DV on the IDV at 3"
+ " levels of the Moderator:"
  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="a" "raw b" "t-test" "df" "Sig. T".
# d* u% u, F4 D4 {$ L9 X  Jprint { zslopes , zSE , confidLO, confidHI }
/title="Standardized Simple Slopes & 95% Confidence Intervals: "
  /rlabels="Mod=low" "Mod=med" "Mod=high"
6 m4 J: j3 n& ]: h3 V  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
& K- _* T* O: {1 d2 o' Sprint ((b(1,1)/b(1,3))*-1)/title="The simple slope for the DV on the IDV"
7 ~7 @0 k: r% A; y7 A. B+ " is zero (flat) at Moderator =".
9 K0 U/ L' C2 Wprint ((b(1,2)/b(1,3))*-1)/title="The simple regression lines at "
# E2 r  }/ K; g3 x+ "Mod=high and Mod=low intersect at IDV =".
+ d; _1 f6 K; y' b
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* data for plot.
compute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
; I8 e& o. G# Scompute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
+ |- B+ d: d" A5 a9 Q( i" r+ Xcompute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
$ L# c0 S+ j& a7 F1 e0 l$ xdo if (dichotom = 1).
" H+ W2 k+ h, w, u* q3 X& zcompute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
end if.
, D, P, h5 ~/ a. Q" Gcompute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
compute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
compute data = { idv , moder , dv }.
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print data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
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" [' e" N  x" m8 i! p$ c3 isave data /outfile=* / var=zb1 zb2 b3.
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$ N* R0 r' A; ?end matrix.

# r4 X" l9 }7 }! I+ K5 U. `plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
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