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

# g: Z- X: H2 r/ D, {9 `0 B/ f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。

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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1 S/ u+ A) w9 ?: l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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, e0 U' A% O) h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。
) q0 H2 S$ R! X5 _) x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。
（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

: q" `, l9 X7 V$ S* s" n/ Q. n. w; s) L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。
) O+ u" q' ]8 Q: U: p
, Q5 n, J2 w: Z* h/ k/ y*****************.
, [  D) L6 o2 d& \) o) idesc b1 b2/save.
compute idv = zb1.
compute mod = zb2.
compute x = idv * mod.
0 B4 M- p! m# j/ f1 W  \. Vcompute dv  = b3.
( l9 ~8 u( {* U+ |  `) l
$ \/ O% Z) L, K& {. D% n9 nregression
/matrix out ('filename')
* t5 J, x3 ?7 k  e3 {; t/ `# Y /var= idv mod x dv  
: i" \7 M, `0 s /statistics=defaults zpp bcov
/dependent=dv
/enter idv mod  
/test (x) .

2 t' ?2 c: E$ `3 d1 y3 N. ^: nset mxloops=65.
% t$ v) H! m, H7 c/ f9 n9 imatrix.
& _6 ]- j( r! p. l& A
compute multiMOD = 1.0   .
/ a+ m& Z' B+ E$ X6 l4 ]% h6 b% Jcompute multiIDV = 1.0  .
compute dichotom = 0  .
4 Q$ _/ L& k& S3 Gcompute dichotLo = 1  .
1 N' M) J' V* ?( d3 k* g: [. A2 @compute dichotHi = 2  .
mget /file='filename'.

/ E) j" q3 z9 `& E* Overall regression coeffs.
$ ^) S" V7 X; d! I- W. Vcompute 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) .
% ?6 h2 K& h& ~6 a! mcompute r2main = t(inv(cr(1:2,1:2))*cr(1:2,4))*cr(1:2,4).
3 @( C" A9 O$ m" p: Dcompute r2chXn = r2all - r2main.
- V+ g9 [- d7 K6 gcompute 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) .

2 c/ B; i7 Q0 b, {& uprint {r2chXn,F,{1},dferror,fsquare,pF} /title="Coefficients for the Interaction"
/clabels="Rsq. ch." "F" "df num." "df denom." "f-squared" "Sig. F".
- O1 o; S( m/ h: e! z! Lprint {t(b),beta} /title="Beta weights for the full equation:"
  /rlabels="idv" "mod" "Xn" /clabels="raw b" "std.beta"  .
) J$ ?- t7 d; E% H7 S6 z) ?% Uprint a /title="The intercept is:" .


( f7 B4 f; u+ s5 g* simple slopes info .
compute modlo = mn(1,2) - (sd(1,2) * multiMOD) .
, I; j5 F( K( G( {2 acompute modmd = mn(1,2).
: N1 _  }0 t: |: Z! _6 Jcompute modhi = mn(1,2) + (sd(1,2) * multiMOD) .
compute slopes={(b(1,1)+(b(1,3)*modlo)) ;
" {5 y# g; g) B: f  d9 ^& }                (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).
% l( b  c( c  ^8 c7 A5 \compute Sb=mse*inv((mdiag(sd(1,1:3))*cr(1:3,1:3)*mdiag(sd(1,1:3)))*(nc(1,1)-1)).
5 T- }: f% t% ]! |( x9 xcompute SEslopes={ (sqrt ( {1,0,modlo} * Sb * t({1,0,modlo}) )) ;
/ X3 ~0 j0 Z3 f' [, ^                   (sqrt ( {1,0,modmd} * Sb * t({1,0,modmd}) )) ;
, |/ f7 p5 a+ K6 e' A                   (sqrt ( {1,0,modhi} * Sb * t({1,0,modhi}) ))   }.
compute tslopes = slopes &/ SEslopes .
+ w5 u+ r1 r7 L( s0 ycompute df = { (nc(1,1)-3-1) ; (nc(1,1)-3-1) ; (nc(1,1)-3-1) }.
; }  O4 V5 W% h( C( G8 zcompute zslopes  = slopes &*  (sd(1,1)/sd(1,4)).
compute zSE = SEslopes &* (sd(1,1)/sd(1,4))  .
! j) d! H* f3 d$ }# w5 tcompute dfs =  nc(1,1)-3-1 .
4 \- a4 M& {+ Kcompute pslopes = (1 - tcdf(abs(tslopes),dfs)) * 2.
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* df & t values -- from Darlington p 516 & Howell 87 p 586 --  p = 05 two-tailed .
1 y9 N- S) G  C% k' }2 ycompute 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,
9 r- q3 d% `( _) r  s' |, N 30,32,34,36,38,40,43,46,49,52,56,60,65,70,75,80,85,90,95,100,110,120,130,
& h) q: Q4 t% K4 R$ j 150,175,200,250,300,400,500,600,700,800,900,1000,1000000000;
% ]& c& j5 o1 }/ 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,
  d- b! u# p& `2 K8 E; ` 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,
7 _# g* O8 n4 E$ \3 \# 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 }.
compute tabledT = 0.
loop #a = 1 to 59  .
$ D6 T3 c; g' {% P/ `/ Gdo if (dfs ge dft(1,#a) and dfs < dft(1,#a+1) ).
compute tabledT = dft(2,#a) .
end if.
end loop if (tabledT > 0).
compute confidLo = (zslopes - (tabledT &* zSE))   .
: K6 ~8 r) v' D+ t( l7 P1 Y) Pcompute confidHi = (zslopes + (tabledT &* zSE))  .

print { aslopes , slopes , tslopes , df , pslopes}  
; ~  G5 A; G. H3 t. `$ w  /title="Simple Slope Coefficients for the DV on the IDV at 3"
: j0 M+ J$ l5 G; T  n+ " levels of the Moderator:"
! u; ~% B- @0 i! S3 b9 j  /rlabels="Mod=low" "Mod=med" "Mod=high"
  /clabels="a" "raw b" "t-test" "df" "Sig. T".
print { zslopes , zSE , confidLO, confidHI }
% L! R2 f6 T6 O3 o3 l4 H /title="Standardized Simple Slopes & 95% Confidence Intervals: "
  /rlabels="Mod=low" "Mod=med" "Mod=high"
% v9 m. f5 }6 O  /clabels="std. beta" "SE" "95%  Low" "95%  Hi".
5 A$ j$ A, P  H- Y3 {8 ~; |print ((b(1,1)/b(1,3))*-1)/title="The simple slope for the DV on the IDV"
$ W" L4 F9 z4 }+ " is zero (flat) at Moderator =".
" J5 ^/ @- A7 H! Q0 v8 @4 x3 Dprint ((b(1,2)/b(1,3))*-1)/title="The simple regression lines at "
8 M: R8 w# o8 v8 j% {7 K. ?) }+ "Mod=high and Mod=low intersect at IDV =".
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* @2 t4 |1 V7 f* data for plot.
compute idvlo = mn(1,1) - (sd(1,1) * multiIDV).
compute idvhi = mn(1,1) + (sd(1,1) * multiIDV)  .
8 a" z/ g5 x) g. b- Icompute idv = { idvlo; idvhi; idvlo; idvhi; idvlo; idvhi } .
3 u/ r& l$ f2 Kdo if (dichotom = 1).
- e& a0 S3 K  ~5 q* `0 ]2 v. ecompute idv = { dichotLO;dichotHi; dichotLO;dichotHi; dichotLO;dichotHi }.
" v- H- v) j7 Pend if.
compute 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 }.
, r6 Z+ c: z3 [, _! ]
- I1 g! y  q4 Q! ?' y+ n  N3 s" p2 yprint data /title="Data for simple slope plots:" /clabels="IV" "Moderator" "DV" .
1 M! \4 V( ~0 }% f! V7 r& T
- I* c+ ^/ i6 E5 z0 K" E0 usave data /outfile=* / var=zb1 zb2 b3.

end matrix.
* n  Q8 T" j1 Q" M0 Q& n
+ P( ?3 Y- m& M" n' [9 C7 `7 cplot vsize=15 / hsize=50 / format=contour(3) / plot=b3 with zb1 by zb2.
+ P4 b. q5 j+ S; y& ^2 t+ X$ Igraph   / 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