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。

9 Y% j4 n" \! Z6 t7 Z8 v下面的讨论中，我们以"X-->Y的关系受调节变量Z影响“为例。
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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？
% Q1 o- Q# i7 U  w/ I  y
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。
0 R2 {  g8 |: P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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$ T& O$ R$ Q4 t/ i( n2 ^8 Q6 w  N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

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。

5 z: o0 D; I9 {, s& m8 E7 i. q/ i*****************.
$ g# K) ]# n' odesc b1 b2/save.
compute idv = zb1.
compute mod = zb2.
- w! V/ {; U+ x* p$ t1 ^compute x = idv * mod.
compute dv  = b3.
* B- L4 [8 \* }! L7 j) g
regression
; r& @- |# K  G3 Z3 _4 A /matrix out ('filename')
/var= idv mod x dv  
$ ~  L' `4 {' T7 ~ /statistics=defaults zpp bcov
/dependent=dv
/enter idv mod  
8 \! z/ s# |* H8 T7 c: w /test (x) .

set mxloops=65.
& m5 b& V2 y& }: ]3 u1 w+ m- o1 D, Lmatrix.

compute multiMOD = 1.0   .
; x* u- G: H' f* Q+ G, ?' t- V0 Bcompute multiIDV = 1.0  .
compute dichotom = 0  .
compute dichotLo = 1  .
compute dichotHi = 2  .
& }! g8 X4 `0 x7 V0 y% p% |, Pmget /file='filename'.

; }3 f! E" l/ j* Overall regression coeffs.
- s' S3 O/ K3 B$ Jcompute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
compute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
/ |" u' W7 E* n# I+ s$ d. Bcompute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
5 t5 ?# Z( l7 p6 }# y% h* ^% mcompute 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.
compute fsquare = (r2all - r2main) / (1 - r2all) .
compute F = (r2all-r2main) / ((1-r2all)/(nc(1,1)-3-1)).
  r9 C  U- z/ T' c: G6 j5 \compute dferror = nc(1,1) - 3 - 1.
compute pF = 1 - fcdf(F,1,dferror) .
  }2 m  ~! x- v& S0 j
print {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
; G( i0 p8 W- k+ c7 k /clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
print {t(b),beta} /title="Beta weights for the full equation:"
  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
; C# M3 y* ?- Q5 i( C4 T" cprint a /title="The intercept is:" .

: a) \6 n+ u. l( I6 p
* simple slopes info .
compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
) l; o0 W: f/ N0 W- Hcompute modmd = mn(1,2).
* J# M( e6 L8 Lcompute 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)) }.
. S' h$ i. u1 Y" O) @2 {compute aslopes={ (b(1,2)*modlo+a) ; (b(1,2)*modmd+a) ; (b(1,2)*modhi+a) }.
3 L( R7 V% b& o2 c0 ^: i: hcompute 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)).
0 T$ G8 m- f: K0 wcompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
2 y7 F* j6 Q* z; S: \$ m5 a8 E                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
) C8 M0 |0 n& k4 @* @6 T                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
8 J  _( E( M  fcompute tslopes = slopes &/ SEslopes .
  V5 @1 A- l( g* T7 {+ r. t' Scompute df = { (nc(1,1)-3-1) ; (nc(1,1)-3-1) ; (nc(1,1)-3-1) }.
# x) S4 q, m: g+ A0 Pcompute zslopes  = slopes &*  (sd(1,1)/sd(1,4)).
compute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
compute dfs =  nc(1,1)-3-1 .
compute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.

! k0 L8 ~  j1 p' o, g* 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,
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;
/ C% y2 g6 w& \8 o/ k 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,
$ z8 V: d2 `% I, K+ Q8 u/ { 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 k3 C/ y8 E9 Q1 L+ mcompute tabledT = 0.
6 F; n2 |9 _- o' I+ [loop #a = 1 to 59  .
do if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
+ V3 N# Y) `2 U2 E1 ?- y6 S3 r8 Tcompute tabledT = dft(2,#a) .
& H3 v6 H/ f3 n& Aend if.
  C% k' `7 E. I; Q0 j: ^end loop if (tabledT > 0).
% v4 [2 m( i3 v$ ]; z5 wcompute confidLo = (zslopes - (tabledT &* zSE))   .
compute confidHi = (zslopes + (tabledT &* zSE))  .

print { aslopes , slopes , tslopes , df , pslopes}  
7 D1 A+ ?) s' a, q/ ^/ x  L3 K- v  /title="Simple Slope Coefficients for the DV on the IDV at 3"
' y; e3 E% A$ S* U+ ^) R  N+ " levels of the Moderator:"
1 K! w9 H; F. Z- S+ K8 X  /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: "
3 h/ p5 V) p% ^3 m  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
print ((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 =".
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# m; S" f% _: p1 K' C* data for plot.
! c. Y! D+ U7 P4 m; g% v% Jcompute 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 } .
do if (dichotom = 1).
7 K# o1 y" o& O: L; ecompute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
7 D# l! o6 b/ {1 T4 f( H/ oend if.
" e! _5 K7 {8 G; V2 X$ P3 Ecompute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
compute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
* ~7 g# u, y0 y6 ^( _compute data = { idv , moder , dv }.

print data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .

+ U0 d2 C# F' D, E/ i3 Osave data /outfile=* / var=zb1 zb2 b3.

. h* k: n8 e$ l$ l, Yend matrix.

plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
8 c2 W" T, @. V8 w! ~" U  ?7 r/ ]7 P+ ^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