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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6 ]  A, R, A3 {9 ^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。

* M/ X* ^& n! u1 {5 t. [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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这里有两步工作要做：
5 n' o6 p+ C/ \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。
! R2 A5 p. W% A* A( 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

5 G! W+ t! ]9 X, C' _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。

*****************.
desc b1 b2/save.
compute idv = zb1.
compute mod = zb2.
9 ^, ~) \% G# b) w! K1 X$ G5 bcompute x = idv * mod.
compute dv  = b3.
0 @7 J2 _( {; o% b. @+ E6 q
regression
/matrix out ('filename')
( W, d7 h9 U: c! F7 q /var= idv mod x dv  
/statistics=defaults zpp bcov
0 G6 W4 n; B7 h5 R' W. S /dependent=dv
4 D7 ?9 W5 A  \" f# P& ?3 } /enter idv mod  
/test (x) .

set mxloops=65.
: e, p; b0 L# {matrix.
$ g2 g' d" R) h+ i
, ?3 ~; a( F, N9 @compute multiMOD = 1.0   .
2 U. I9 i, D3 C) gcompute multiIDV = 1.0  .
7 W. J" T& N3 H0 Bcompute dichotom = 0  .
compute dichotLo = 1  .
compute dichotHi = 2  .
* d0 J- g0 y( {9 n0 mmget /file='filename'.

* Overall regression coeffs.
compute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
" t6 S* g' z' P3 \, @9 v. C- Pcompute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
compute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
! e7 r9 h. `0 acompute r2all  = t(beta) * cr(1:3,4) .
compute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
7 b* r7 U$ R7 {+ bcompute r2chXn = r2all - r2main.
compute fsquare = (r2all - r2main) / (1 - r2all) .
compute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
compute dferror = nc(1,1) - 3 - 1.
" _; g; t( H5 J9 Q! rcompute pF = 1 - fcdf(F,1,dferror) .
; f& ]3 F& ]+ \" C7 O
print {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
) B+ g5 E: u6 g7 s4 N  M: Z2 i /clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
; _: L- r7 Z* a) vprint {t(b),beta} /title="Beta weights for the full equation:"
  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
4 t, {  S! f. j; aprint a /title="The intercept is:" .

8 w$ |2 C0 |  b; s
* simple slopes info .
compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
' y+ W) i) v; d  e% g( q8 Hcompute 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+ R3 v) ?' i8 Y/ n0 jcompute 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)).
compute 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}) ))   }.
. q+ M* G' W' j9 q- V7 Bcompute 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))  .
compute dfs =  nc(1,1)-3-1 .
4 ~: e, N5 b8 O/ S+ _( scompute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.

0 K9 w. V2 C; J& G& o. [: G- _1 T* df & t values -- from Darlington p 516 & Howell 87 p 586 --  p = 05 two-tailed .
% }. ?. x: S! _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,
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;
# p1 g0 G7 q1 U0 q* I! Z+ s1 f3 [' D7 w 12.706,4.303,3.182,2.776,2.571,2.447,2.365,2.306,2.262,2.228,2.201,2.179,
7 n2 O: O, b- b# K7 k( | 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,
- f7 k2 g( C1 i3 B2 A6 E8 k 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.
1 t7 A, y: ~4 Gloop #a = 1 to 59  .
do if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
compute tabledT = dft(2,#a) .
' U- a8 j9 L* O7 ^! Q, k  i3 y3 ?end if.
end loop if (tabledT > 0).
1 z3 Z0 K: ]9 d- T7 ]compute confidLo = (zslopes - (tabledT &* zSE))   .
+ g# h1 X: h. W  \6 a, f2 dcompute confidHi = (zslopes + (tabledT &* zSE))  .
% V: e* I+ i$ g* {' W; {, r
print { aslopes , slopes , tslopes , df , pslopes}  
' B0 X( J: U8 W% E/ n: U2 g: E- y  /title="Simple Slope Coefficients for the DV on the IDV at 3"
+ " levels of the Moderator:"
  /rlabels="Mod=low" "Mod=med" "Mod=high"
) o" {4 S: Q: E/ h$ }. l  /clabels="a" "raw b" "t-test" "df" "Sig. T".
print { zslopes , zSE , confidLO, confidHI }
/title="Standardized Simple Slopes & 95% Confidence Intervals: "
* k5 n/ L  z6 t5 }  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
: j6 {9 c; Y; ~: x$ E; O1 mprint ((b(1,1)/b(1,3))*-1)/title="The simple slope for the DV on the IDV"
+ " is zero (flat) at Moderator =".
$ f5 {. c( z( A' A0 y7 [print ((b(1,2)/b(1,3))*-1)/title="The simple regression lines at "
5 N) a5 B) y& X1 L+ "Mod=high and Mod=low intersect at IDV =".


* S+ u; X/ T: `; i* data for plot.
1 f  i: {+ z( b1 M7 ccompute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
compute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
compute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
" U8 D/ I  ~. A$ edo if (dichotom = 1).
compute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
) Q5 V% s& ~, [2 ^end if.
/ v* j/ p4 _! E$ K0 I- [, _compute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
compute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
# J! p. o* H+ L( a% s2 Vcompute data = { idv , moder , dv }.
4 n. v/ V: I- u& ~" \
print data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
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save data /outfile=* / var=zb1 zb2 b3.
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end matrix.

plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
0 m7 q0 O, C* Qgraph   / 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