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。

& I+ C- W% L0 B7 I( d3 Q5 s下面的讨论中，我们以"X-->Y的关系受调节变量Z影响“为例。

$ f( _; M4 o8 w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：
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。
  d% C: ^& I! \! \* U% I) B+ T* n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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由于有图和公式，请参见附件。
（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

! y( ]1 c( T( E* Z. e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。

  S8 ^% A6 _: e! M*****************.
9 R3 K; Q# q! [desc b1 b2/save.
compute idv = zb1.
compute mod = zb2.
# P+ }5 i& V9 ncompute x = idv * mod.
compute dv  = b3.
, r* A. Y; ^7 T& {' @: O
regression
; P# j/ N# q- y* u, k  [ /matrix out ('filename')
/var= idv mod x dv  
3 {/ G4 v$ u& x2 `2 K- x4 C% H /statistics=defaults zpp bcov
/dependent=dv
/enter idv mod  
/test (x) .
: [4 T) e+ G) F5 V8 S9 V
set mxloops=65.
matrix.
& l/ S, R4 Y# f& h
compute multiMOD = 1.0   .
compute multiIDV = 1.0  .
compute dichotom = 0  .
compute dichotLo = 1  .
4 O# X0 G) S: y' C3 ncompute dichotHi = 2  .
mget /file='filename'.
/ Y3 d8 V: @% i1 D  g
* Overall regression coeffs.
  ~% ^% k) s  X) w8 Fcompute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
compute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
, U: Y8 F. a- `+ I) u( }9 ?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).
2 I+ f* b/ k" d+ acompute r2chXn = r2all - r2main.
+ {1 `- N3 O$ }, q  `compute fsquare = (r2all - r2main) / (1 - r2all) .
compute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
compute dferror = nc(1,1) - 3 - 1.
compute pF = 1 - fcdf(F,1,dferror) .
. C1 S, `/ o+ p2 T- r1 y4 n
& U1 ~* w% O1 Dprint {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
/clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
% h1 G. F5 c9 _8 B8 }print {t(b),beta} /title="Beta weights for the full equation:"
  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
- E9 O1 _4 G" l3 K2 b) Oprint a /title="The intercept is:" .
! S1 U& a0 b/ p

9 Q0 H! r9 D, J2 @* simple slopes info .
compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
2 f6 q1 n6 J& S7 b0 _compute 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)) }.
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)).
* T, G; r3 i8 Y: A0 d4 Zcompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
, W$ y" u' J( ^6 H& t$ C                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
compute tslopes = slopes &/ SEslopes .
# D2 H1 U6 P# l& W2 {4 r" d3 \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)).
: w. D* ~, K# O" a- gcompute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
compute dfs =  nc(1,1)-3-1 .
compute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.

. m, W  W5 \) m* [  J* 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,
2 q* D5 B( E, }" H! T 30,32,34,36,38,40,43,46,49,52,56,60,65,70,75,80,85,90,95,100,110,120,130,
* K/ a# t7 X: X 150,175,200,250,300,400,500,600,700,800,900,1000,1000000000;
* b" j, `  ~7 d6 i 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,
8 o, u1 ?3 F- F 2.042,2.037,2.032,2.028,2.024,2.021,2.017,2.013,2.010,2.007,2.003,2.000,
! L. o7 R5 K& ^, G0 j, W 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 }.
compute tabledT = 0.
9 t4 Y/ h& A4 D; R6 Lloop #a = 1 to 59  .
" K* e% |5 ?7 ~% z+ H& M4 \% rdo if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
+ ~: n$ M9 q4 M4 Y9 U4 O. Scompute tabledT = dft(2,#a) .
& y6 k3 L# ?5 g+ M* \* ?9 aend if.
end loop if (tabledT > 0).
( X# m5 |' k! Z1 g4 hcompute confidLo = (zslopes - (tabledT &* zSE))   .
compute confidHi = (zslopes + (tabledT &* zSE))  .

print { aslopes , slopes , tslopes , df , pslopes}  
  /title="Simple Slope Coefficients for the DV on the IDV at 3"
. B1 h- g$ p$ }& x& `/ U; B( m  O6 F+ " levels of the Moderator:"
  /rlabels="Mod=low" "Mod=med" "Mod=high"
. }6 Y& @' z# d) R. x/ k5 f# D  /clabels="a" "raw b" "t-test" "df" "Sig. T".
print { zslopes , zSE , confidLO, confidHI }
4 \$ x. a1 L% ?5 p8 H /title="Standardized Simple Slopes & 95% Confidence Intervals: "
  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
5 R& K4 c: O  k# j" j2 uprint ((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 "
" h! S8 `3 C. B+ "Mod=high and Mod=low intersect at IDV =".
* x* l$ Z: R0 o: f

* data for plot.
compute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
compute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
( \; M5 o8 n- ^7 w% @8 b2 B2 M3 [compute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
1 e9 E) }. @# G' i5 c/ O  \1 x7 D& Ldo if (dichotom = 1).
compute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
  W! D% c9 l- }. i/ ~; o2 gend if.
! L, e' n% J- |9 z0 ~compute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
3 I/ M4 z1 Y0 k1 Vcompute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
compute data = { idv , moder , dv }.

4 [$ T" b( d9 E1 J0 Z. W4 Wprint data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
, P9 g% g5 C1 D: h
+ I: i, s8 G6 `" r. k1 ^/ V" O$ qsave data /outfile=* / var=zb1 zb2 b3.

% G5 w& z3 L6 I7 xend matrix.

8 Q0 p' P  X5 Q; xplot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
$ o/ I; U+ d* c. A: U) ~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