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

( ]. b) J( s" c8 R$ [
- P, j+ g$ b$ x8 X$ p. `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。

/ {0 ?7 p7 A0 e" }! O  g$ @( U下面的讨论中，我们以"X-->Y的关系受调节变量Z影响“为例。

- n* f; H6 t1 S/ ^1 @2 x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？

1 G% g6 }( m" I. f+ K  d这里有两步工作要做：
0 q. J- D5 d" ~0 ]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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0 k! _1 K9 D; `5 t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

1 E2 T' L/ p7 N- ~0 R6 j
& m8 y% C0 o% t/ b2 F# F! c3 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。

/ V* r2 }/ M( S8 b*****************.
desc b1 b2/save.
$ j5 S8 c( ^8 Q' H1 [! A7 kcompute idv = zb1.
compute mod = zb2.
! j' s3 P# [5 D) xcompute x = idv * mod.
  j+ q/ M- R4 [; ]( ]. n4 tcompute dv  = b3.

0 V( m; q; J3 v2 u7 sregression
+ s7 o* a& i2 D6 @8 r /matrix out ('filename')
/var= idv mod x dv  
$ Q4 |9 C' I7 z9 K /statistics=defaults zpp bcov
1 T+ {( P1 F. M2 E6 r- j' O /dependent=dv
/enter idv mod  
6 V& L" m/ z* m$ F$ a. ? /test (x) .

$ p& J9 I  E* r! g' B1 A! n8 Lset mxloops=65.
matrix.
+ n5 h2 I' j2 A+ G
' i" r3 l+ o2 S' Tcompute multiMOD = 1.0   .
compute multiIDV = 1.0  .
4 Z& G$ H' }& H: V* U% K! Pcompute dichotom = 0  .
compute dichotLo = 1  .
compute dichotHi = 2  .
mget /file='filename'.
4 O: f& F; |2 d6 v
; m1 z! w! L: T/ C. q* Overall regression coeffs.
0 `! t) e. h- \) g* n4 \compute beta = inv(cr(1:3,1:3)) * cr(1:3,4) .
compute b = (sd(1,4) &/ sd(1,1:3))   &* t(beta) .
compute a = mn(1,4) - ( rsum ( mn(1,1:3) &* b ) ) .
compute r2all  = t(beta) * cr(1:3,4) .
% Z( @( K$ w3 h" p6 jcompute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
compute r2chXn = r2all - r2main.
9 N7 i+ C8 m) `8 \( Rcompute 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) .

6 f& J: P( v& B  \- a3 B" u& qprint {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
/clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
print {t(b),beta} /title="Beta weights for the full equation:"
8 Z& F# `8 }) H3 d3 d# {  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
print a /title="The intercept is:" .
7 L! n( g, ~' Z( _! H, T  Q
& I+ k( O4 v' @) r, a/ T* `
: E4 Q0 L, B% t% [8 w$ @" c* simple slopes info .
compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
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)) }.
, B, ^$ o; e, T0 N/ R8 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).
0 \; ?6 ~5 I4 \" @7 s5 ?9 _compute Sb=mse*inv((mdiag(sd(1,1:3))*cr(1:3,1:3)*mdiag(sd(1,1:3)))*(nc(1,1)-1)).
/ B% O: {. n8 N. Q; i6 z5 ccompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
! d0 l& H# v$ h& t# j% w                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
$ r+ Y: e) V8 y. z7 Z3 ycompute tslopes = slopes &/ SEslopes .
' u9 \, ^" ~) L7 hcompute 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)).
. d8 k5 M0 W( a# F2 x0 S6 k1 ~1 c" rcompute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
compute dfs =  nc(1,1)-3-1 .
compute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.

/ t/ y! Q( ?$ q: X! @1 e* 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,
1 u$ H/ w. h  b7 a% m 30,32,34,36,38,40,43,46,49,52,56,60,65,70,75,80,85,90,95,100,110,120,130,
- Z, ^7 X/ W5 { 150,175,200,250,300,400,500,600,700,800,900,1000,1000000000;
% U4 U3 ~7 y. N2 u 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,
: K) g8 N2 m* B 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,
1.974,1.972,1.969,1.968,1.966,1.965,1.964,1.963,1.963,1.963,1.962,1.962 }.
1 w1 j1 [3 r8 z0 o! ~1 xcompute tabledT = 0.
1 i$ ]* ]' v4 oloop #a = 1 to 59  .
+ m9 s- o0 Z8 R$ |/ q" y9 e$ odo if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
compute tabledT = dft(2,#a) .
" H4 ?2 O0 h0 l- y1 J' u3 v" F% Send if.
end loop if (tabledT > 0).
: L& [7 F& @) q  j% B6 scompute confidLo = (zslopes - (tabledT &* zSE))   .
2 y9 h" [$ d% T7 N) n3 _# D9 ]compute confidHi = (zslopes + (tabledT &* zSE))  .

; n  ^2 t* f! L' Q; @- pprint { aslopes , slopes , tslopes , df , pslopes}  
  /title="Simple Slope Coefficients for the DV on the IDV at 3"
+ " levels of the Moderator:"
3 P2 v8 ?. ?: c0 L! C  /rlabels="Mod=low" "Mod=med" "Mod=high"
$ W& f9 A2 e2 T3 z/ \7 }& w9 J  /clabels="a" "raw b" "t-test" "df" "Sig. T".
4 C" m0 \( [; X. E( L4 k  Yprint { zslopes , zSE , confidLO, confidHI }
/title="Standardized Simple Slopes & 95% Confidence Intervals: "
# W* d4 u" [3 e; M$ k+ I4 m/ t. u  /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"
& i5 i! |3 Y, b+ " is zero (flat) at Moderator =".
# `0 d. T6 Y' H) m4 |% @- E# ~# l+ |print ((b(1,2)/b(1,3))*-1)/title="The simple regression lines at "
1 m0 |8 I8 f5 z8 x+ r: b  e+ "Mod=high and Mod=low intersect at IDV =".


" g- J1 C8 [( _& F+ }* data for plot.
compute 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).
compute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
end if.
compute moder = { modlo;modlo;modmd;modmd;modhi;modhi }.
$ h: d0 L' H0 T- t% k$ E* U; pcompute dv = (b(1,1)&*idv)+(b(1,2)&*moder)+(b(1,3)&*idv&*moder)+a.
" u/ p, F% G6 ^$ Wcompute data = { idv , moder , dv }.
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, _  n" ~: `0 a; Y/ w4 ^print data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
0 d+ a. E4 [6 a  x. s' j$ v4 Y
save data /outfile=* / var=zb1 zb2 b3.

! z- F9 i+ O- u# L4 f8 Dend matrix.

plot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
8 I8 i- x1 r1 _9 W# y! q, agraph   / line = mean (b3) by b1 by b2.
, y. r+ \5 ?! Z2 O/ S! J

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