请教kenny, 关于HLM中控制变量-看了JBP加油的帖子的想法

helen526

kenny,
+ L' @: M5 X* s" R- O      看了JBP加油的关于HLM做跨层次调节的帖子，恰好最近也在学习这方面，我尝试写了一个检验三重交互作用的流程（其中，包括个体和组织层面的控制变量），不知是否合适，请您确认一下。如果不正确，请在附件的WORD文档中修改。 等您修改后，这个帖子估计就可以解决不少同学使用HLM做调节的问题。
8 ?: z* d( u2 f5 M4 K9 u$ J   1、我的主要疑惑也是如何在HLM模型中，体现控制变量
   2、D是个体层面的变量，分析时在level 2,用mean D代替可以吗？
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helen526

呼叫kenny, 请您确认我写的是否正确哦：）
也请大家多多提出有异议的地方

Kenneth

回复 1楼 helen526 的帖子

Helen 526,

* c6 D" z6 h$ d! [7 U: D5 k) Q你的模型是：
4 `/ S  ?9 U$ v* z; J; O

* i& E. U' x9 C4 C1 A

模型假设1：个体层面，A对B有显著的正向影响

假设2：C对A和B之间的关系，具有跨层次的调节作用

假设3：D、C对A和B之间的关系，具有三重调节作用

另，团队层面的控制变量包括，organiztion1, organiztion2; 个体层面的控制变量包括age，sex。A和B和D为个体层面变量，C为团队层面变量。

Model 1:只包含控制变量

Level 1
B ij=β0j+β1j(age)+ β2j(sex)+ β3j(C) + β4j(D) +file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gifij

Level 2
9 t1 N4 ]) o0 xβ0j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif01(organiztion1)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif02(organiztion2)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif

β1j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif10+U1j

β2j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif20+U2j

β3j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30+U3j

β4j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif40+U4j

(将调解变量C和D首先引入方程，是为了保证“在分析预测变量A的效果之前，首先控制C和D的作用”。请问，这样做可以吗？)

Model 2: 加入预测变量A

Level 1
B ij=β0j+β1j(age)+ β2j(sex)+ β3j(C) + β4j(D) + β5j(A) +file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gifij

Level 2
& O5 a5 j* e+ |& K0 O  @β0j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif01(organiztion1)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif02(organiztion2)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif

β1j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif10+U1j

β2j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif20+U2j

β3j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30+U3j

β4j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif40+U4j

β5j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif50+U5j（file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif50表示A对B的效应，验证假设1，对吗？）

Model 3: 加入所有的二维交互项A*C、A*D、C*D（验证假设2）

Level 1
  K: j5 _7 |6 A! P6 L- ?8 [( o5 VB ij=β0j+β1j(age)+ β2j(sex)+ β3j(C) + β4j(D) + β5j(A) + β6j(A*C) +β7j(A*D) + β8j(C*D) +file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gifij

Level 2
β0j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif01(organiztion1)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif02(organiztion2)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif

β1j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif10+U1j

β2j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif20+U2j

β3j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif31(C) +U3j

β4j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif40+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif41(mean D)+U4j（由于，D本来属于个体层面的变量，所以涉及到level2的分析，一律用mean D的值代替, 这样合适吗？或者您认为在D是低层面变量时，应当怎样处理？）
" A) K  o6 u" O( P  X( A' n

β5j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif50+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif51(A) +U5j

β6j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif60+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif61(A*C) +U6j

β7j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif70+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif71(A* mean D) +U7j

β8j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif80+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif81(C* mean D) +U8j

（看到JBP加油提供的文献中，file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30(C)表示C对A和B关系的调节作用，但是我认为是file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif31表示C对A和B关系的调节作用？）

Model 4: 三重交互作用（验证假设3）

Level 1
B ij=β0j+β1j(age)+ β2j(sex)+ β3j(C) + β4j(D) + β5j(A) + β6j(A*C) +β7j(A*D) + β8j(C*D) + β9j(A*C*D)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gifij

Level 2
' [% y- p* L* v: [/ N' A7 Uβ0j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif01(organiztion1)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif02(organiztion2)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif

β1j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif10+U1j

β2j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif20+U2j

β3j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif31(C) +U3j

β4j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif40+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif41(mean D)+U4j

β5j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif50+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif51(A) +U5j

β6j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif60+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif61(A*C) +U6j

β7j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif70+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif71(A* mean D) +U7j

β8j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif80+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif81(C* mean D) +U8j

β9j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif90+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif91(A*C* mean D) +U9j

（其中，file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif91(A*C*D)表示D对C\A\B关系的三重调节作用，对吗？）

如果写论文，下面表格报告的格式可以吗？

	" Q9 s* ]5 l; a1 e# k: h Model 1	Model 2	Model 3	) Q. B1 V' |7 {# u+ N% K3 i Model 4 # a) b4 b2 F6 N3 W% x$ f8 H; N
Interceptfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif	; T4 Q  P. [% G0 @ 数值	数值	数值	- v( ^1 M: ?9 |% P4 E: D 数值   N( b- ~0 a' r
control variables	* f0 ?: h6 R8 W; r% M		, q" N% k  }. T( Y$ l5 y	- ^5 |1 J* U  H3 K; a
Organiztion1 (file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif01)	数值	- J: i: n" f/ z 数值	数值 6 s9 k7 U* O: s' B2 }! W0 C	+ w4 J+ s  N, u5 h% v2 `1 m 数值 ' t  g) Y( L  v* Z$ _. E+ ^$ X
Organiztion2 (file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif02)	/ m  E" p2 @2 N( }7 f# ^ 数值	数值 # d4 Z  `& v+ B	数值	. N/ h. z. C' w9 A' P4 h2 x 数值 " f+ o0 L7 H9 D) v* B
Age (file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif10) ' f9 K9 X1 {$ B. V	- l' _2 l& G, L 数值	) f; N- K0 k  j0 ~3 X, I3 \: k- H 数值	4 W- U' k" O: h# Y6 R 数值 , W: ^" Z0 ^7 }7 {7 Y6 D* P	数值
Sex (file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif20)	数值 / g0 Y/ h' _. y' P" ]& M	数值	4 V8 F0 m3 F( }+ F3 l9 K  p 数值 : I% @- m0 D$ b* M/ {4 a) g5 g	0 `  |) b0 g" e 数值
C(file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30)	数值 # v* s5 S& s8 O: \$ o	& g( I3 T6 n5 R- R1 j2 J/ v 数值	1 H% r$ t( {+ i2 [7 ~/ d 数值	& C" F8 |6 d' B% L 数值
D (file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif40)	数值	数值 ! }; W7 {% P. f  L  {: v6 u	数值 7 l7 G, Y/ h' d9 O3 m+ J3 o# v	: N1 L. A8 z; Q* K 数值
A (file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif50)		数值	数值	0 }) A8 n, P# y2 G! T* Q5 X 数值 2 U5 N9 ^- H; S3 E% N5 U' U2 ~
A*C(file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif60)	. d; |% g" z4 a% K5 I/ o. _		& X: u! H7 n. {2 m0 A7 a 数值 9 Y7 z3 B4 k, H* T! i% Z	5 @" V6 L" R% v 数值
A*D(file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif70)	+ n3 K2 S' R7 f- r, D3 m' p# H		& a5 W* ]. z% B) a. d2 k' [ 数值	数值 1 _4 y" R7 y5 H5 t2 h: t# W1 l6 u, X
C*D(file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif80)	6 l3 Q" s* v& d) ]9 {+ x# k& o	3 w/ {0 R8 D: R5 c) M1 a! s	6 @4 |6 P. K% ?" |$ y; J 数值	数值 4 I1 s8 i' r/ j6 z
A*C*D(file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif90)	# L) U  B$ y) h			: ^. f* y9 f' f5 M' e( j 数值
	, h. Y- G2 H3 m			9 V! T* r4 g6 P, D( ^$ t5 J; n0 |
X2	* f% Z9 c" Z& \) } 数值 ' L' D: P% [7 i" E6 @2 q	数值	- l! l9 R% _1 x' V: U9 O* B$ Z 数值 6 p2 Q4 |3 \. H( H* [	数值 / e# l( R6 U& C
Deviance	3 T8 @- ^5 m; h" z 数值	& [2 v% Q/ {- g5 N. R3 N$ y 数值 ( c: }% p" `. ~	数值 / z+ w) T' s: S3 l6 w  W	数值 " ?7 C% h  H/ v' |
Decrease in Deviance	2 u: r* e/ }$ c, W, `" T/ n  d m . G9 e/ u' ]1 s4 F	n	1 L7 d- d% \& q4 h( f; [ l	Z5 R. X. {9 D  R- ^2 b2 i3 T+ q k ! r. l0 l9 q. m. d3 z. o7 T
m代表 Decrease  in Deviance in comparison to the null model    n 代表Decrease  in Deviance in comparison to the model 1    l代表 Decrease  in Deviance in comparison to the model 2    k代表Decrease  in Deviance in comparison to the model 3

0 @$ L+ m4 t1 v$ D' A+ @( d1 {% CHelen，
; W$ |* W, {1 z4 r% y6 V* W& ^我怀疑你的模型根本就不可能，所以你的问题我不知道如何回答。
凡是一个高层阶的变量影响（或是调节）一个低层阶的变量，就表示这个高层阶的变量在低层阶中是不变的。所以在你的模型中，在每一个层阶中，C对A→B的影响是不变的。那么D何来再调节这个不变的影响呢？如果要有一个三阶的调节，而第一个是高层的话，另外一个一定也是高层的。你的问题只有当反过来说时，才会成立。就是D（低层）的变量调节A→B的影响，而这个调节再被C（高层变量）来调节。
在这个情形下，我会这样模拟：

Level 1
9 Y3 Y" X- H# Z1 n( w; y! MB ij=β0j+β1j(age)+ β2j(sex)+ β3j(Aij) + β4j(D) + β5j(D*A)+file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gifrij

Level 2
. q  t( z0 T8 n. }& vβ0j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif=gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif10 +U1j   （organization 是grouping variable，不用模拟的）
1 L0 ~  n. G/ X' M+ Wβ3j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif=gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30 +gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif31*C +u3j
1 P! |! f' W/ b$ l* ?

β4j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif=gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif40 +gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif41*C +u4j
- q7 j1 F# o% y: z4 D3 v

β5j=file:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image004.gif=gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif30 +gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif51*C +u5j

参数gfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image002.gif51就是你要的three-way interaction了。

Kenny
9 x+ h! d4 S4 F* i  F% O- R6 P

' }  ?  z2 Z; N- V' dfile:///C:/DOCUME%7E1/mnlaw/LOCALS%7E1/Temp/msohtmlclip1/01/clip_image006.gif

# D* o- u( e7 c* [# e* J0 }5 a- L& B