第20章 对数线性模型在高维列联表资料分析中的应用
思考与练习参考答案
一、最佳选择题
1. 对数线性模型优越性在于( E )。
A. 可有效地分析高维列联表资料
B. 可进行多个分类变量间关系的探索性分析
C. 既可分析反应变量与解释变量间的关系,也可分析解释变量间的关系 D. 可有效避免混杂因素的影响,提高分析效率 E. 以上答案都对
2. 对数线性模型中对主效应解释正确的是( D )。
A. 主效应大小反映了自变量对因变量的影响 B. 主效应反映了因变量对期望频数的贡献 C. 主效应反映了自变量对期望频数的贡献 D. 对主效应的分析无实际意义
E. 主效应无统计学意义时,不必再拟合其他谱系模型 3. 对数线性模型中对交互效应解释,描述不正确的是( B )。
A. 交互效应指某几个自变量对因变量的联合作用
B. 某两维交互效应为零,则包含该效应的三维交互效应必为零
C. 某三维交互效应不为零,并不表明该效应包含的所有两维交互效应也不为零 D. 高维列联表中,某单元格的频数越大,交互效应越大 E. 交互效应的大小受主效应大小的影响
4. 列联表资料中存在有序分类变量时,正确的处理方法是( C )。
A. 一律按无序分类变量引入模型 B. 一律按有序分类变量引入模型
C. 按有序还是无序变量引入,须视拟合效果和专业解释而定 D. 此种情形,不宜拟合对数线性模型 E. 以上答案都不对
5. 不能反映模型拟合效果的统计量或方法是( D )。
A. Pearson’s? B. 残差分析 C. 似然比统计量 D. 参数检验 E. AIC 二、思考题
2
1. 简述对数线性模型的分析思路。
答:① 判断适用条件,包括设计类型、样本含量。② 拟合饱和模型,通过参数初步了解可能有统计学意义的效应项。③ 采用逐步法,通常采用后退法筛选最优模型。④获得最优模型的参数估计结果。⑤ 结合专业解释结果。
2. 对于高维列联表,采用对数线性模型比分层分析有什么优点?
答: ① 提高分析效率。② 可同时考察更多的变量的关系。③ 可检验多个分类变量间是否存在高维交互效应。
3. 对比对数线性模型与Logistic模型的应用场合。
答:① 对数线性模型不属于因果关系模型,通常用于高维列联表资料的探索性分析。对数线性模型通常要求变量都为定性变量,如果为定量变量,需离散化。② Logistic模型描述一个分类变量与多个变量之间的关系,有明确的反应变量与解释变量,用于因果关系的描述,所以常用于验证性的分析。Logistic模型对自变量较宽容,可以是定量的,也可以是定性的,分布方面也没有特别的要求。 三、计算题
1. 引用第9章例9-5的数据,有研究表明不同国籍人的血型是不同的。现有2 500例不同国籍人的血型分布资料教材表20-21,请问国籍与血型是否有关?
教材表20-21 2 500例不同国籍人的血型分布
国籍
O
美国人 中国人 挪威人 合 计
450 300 190 940
血 型 A 410 250 250 910
B 100 350 40 490
AB 40 100 20 160
1 000 1 000 500 2 500 合 计
请用对数线性模型分别拟合主效应模型与饱和模型,并与第9章关联性分析结果对比,看看彼此之间有何联系?
解:SPSS数据输入格式如下(练习图20-1):
练习图20-1 SPSS数据输入格式
主要分析结果如下:
(1)主效应分析结果
Goodness-of-Fit Tests(a,b) Likelihood Ratio Pearson Chi-Square a Model: Poisson
b Design: Constant + 国籍 + 血型
Value 331.147 332.967 df 6 6 Sig. .000 .000 (2)饱和模型分析结果
Parameter Estimates(b,c) Parameter Constant [血型 = 1] [血型 = 2] [血型 = 3] [国籍 = 1] [国籍 = 2]
[血型 = 1] * [国籍 = 1] [血型 = 1] * [国籍 = 2] [血型 = 2] * [国籍 = 1] [血型 = 2] * [国籍 = 2] [血型 = 3] * [国籍 = 1] [血型 = 3] * [国籍 = 2]
Estimate
3.020 2.229 2.503 .681 .681 1.590 .180 -1.134 -.187 -1.590 .228 .568
Std. Error
.221 .232 .230 .271 .271 .242 .284 .259 .283 .258 .329 .294
Z 13.676 9.591 10.896 2.512 2.512 6.560 .632 -4.371 -.661 -6.155 .693 1.935
Sig. .000 .000 .000 .012 .012 .000 .527 .000 .508 .000 .488 .053
a This parameter is set to zero because it is redundant. b Model: Poisson
c Design: Constant + 血型 + 国籍 + 血型 * 国籍
(3)结果分析
主效应分析结果提示,模型拟合效果不好,说明血型与国籍两个变量并不独立,拟合优度Pearson
?2=332.967,与第9章所求统计量完全相等,读者可自行考虑为什么。饱和模
型的参数估计结果提示,两维交互效应的参数估计值有统计学意义,表示两变量具有关联性。 2. Sewell与Shan对Wisconsin州的10 317名高中生是否计划上大学的一项调查,调查变量包括家庭的社会经济地位(socioeconomic status,低/中低/中高/高)、智力水平(intelligence,低/中下/中上/高)、是否计划入学(plan college,是/否)、性别(sex,男/女)和父母重视鼓励程度(parental encouragement,低/高)。5个变量分别以T、I、P、S、E表示,构成4×4×2×2×2的高维表,见教材表20-22。试分析与“是否计划入学”有关的因素。
教材表20-22 对Wisconsin州的10 317名高中生是否计划上大学的调查资料
计划入学 性 别 父母重视 地位(T) 低 中低 中高 高
(P) (S) (E) 智力(I) 低 中低 中高 高 低 中低 中高 高 低 中低 中高 高 低 中低 中高 高
高 4 9 12 10 2 7 12 17 8 4 17 6 4 5 9 8
男 低
是
高 5 15 8 13 11 19 12 15 7 13 12 20 16 5 13 13
女 低
高 349 207 126 67 232 201 115 79 164 120 92 42 48 47 41 17
男
低
否
高 455 312 216 96 285 236 164 113 163 193 174 81 50 70 47 49
女
低 44 47 35 24 61 88 85 50 72 90 100 77 58 76 81 98
13 33 38 89 27 64 93 119 47 74 148 198 39 123 224 414
9 14 20 28 29 47 62 72 36 75 91 142 36 110 230 360
64 72 54 43 84 95 92 59 91 110 100 73 57 90 65 54
解:主要分析结果:
用后退法获得最优模型[PETI,SET,STI,PSI],偏关联似然比检验如下:
If Deleted Simple Effect is DF L.R. Chisq Change Prob P*E*T*I 9 23.581 .0050 S*E*T 3 17.468 .0006 S*T*I 9 22.788 .0067 P*S*I 3 32.371 .0000
分析结果提示:各变量对入学态度都有不同的影响,其中智力、社会地位、性别与入学态度具有联合作用,父母鼓励重视程度对学生智力及是否入学具有较强的影响。
模型参数估计结果(剔除了冗余项)如下表:
Parameter Estimates
Parameter Constant [E = 1] [I = 1] [I = 2] [I = 3] [P = 1] [S = 1] [T = 1] [T = 2] [T = 3]
[E = 1] * [I = 1] [E = 1] * [I = 2] [E = 1] * [I = 3] [P = 1] * [E = 1]
Z Estimate Std. Error Sig.
4.523(a) -.716 .152 -4.700 .000 -.537 .145 -3.691 .000 -.160 .130 -1.231 .218 -.108 .129 -.839 .401 1.394 .097 14.392 .000 -.429 .097 -4.411 .000 -1.317 .168 -7.848 .000 -.556 .137 -4.044 .000 -.125 .124 -1.006 .314 .719 .203 3.548 .000 .528 .191 2.756 .006 .341 .200 1.702 .089 -2.732 .266 -10.262 .000
[S = 1] * [E = 1] [E = 1] * [T = 1] [E = 1] * [T = 2] [E = 1] * [T = 3] [P = 1] * [I = 1] [P = 1] * [I = 2] [P = 1] * [I = 3] [S = 1] * [I = 1] [S = 1] * [I = 2] [S = 1] * [I = 3] [T = 1] * [I = 1] [T = 1] * [I = 2] [T = 1] * [I = 3] [T = 2] * [I = 1] [T = 2] * [I = 2] [T = 2] * [I = 3] [T = 3] * [I = 1] [T = 3] * [I = 2] [T = 3] * [I = 3] [P = 1] * [S = 1] [P = 1] * [T = 1] [P = 1] * [T = 2] [P = 1] * [T = 3] [S = 1] * [T = 1] [S = 1] * [T = 2] [S = 1] * [T = 3]
[P = 1] * [E = 1] * [I = 1] [P = 1] * [E = 1] * [I = 2] [P = 1] * [E = 1] * [I = 3] [E = 1] * [T = 1] * [I = 1] [E = 1] * [T = 1] * [I = 2] [E = 1] * [T = 1] * [I = 3] [E = 1] * [T = 2] * [I = 1] [E = 1] * [T = 2] * [I = 2] [E = 1] * [T = 2] * [I = 3] [E = 1] * [T = 3] * [I = 1] [E = 1] * [T = 3] * [I = 2] [E = 1] * [T = 3] * [I = 3] [P = 1] * [E = 1] * [T = 1] [P = 1] * [E = 1] * [T = 2] [P = 1] * [E = 1] * [T = 3] [S = 1] * [E = 1] * [T = 1] [S = 1] * [E = 1] * [T = 2] [S = 1] * [E = 1] * [T = 3] [P = 1] * [S = 1] * [I = 1] [P = 1] * [S = 1] * [I = 2] [P = 1] * [S = 1] * [I = 3] [P = 1] * [T = 1] * [I = 1] [P = 1] * [T = 1] * [I = 2] [P = 1] * [T = 1] * [I = 3] [P = 1] * [T = 2] * [I = 1] [P = 1] * [T = 2] * [I = 2] [P = 1] * [T = 2] * [I = 3] [P = 1] * [T = 3] * [I = 1] [P = 1] * [T = 3] * [I = 2] [P = 1] * [T = 3] * [I = 3] [S = 1] * [T = 1] * [I = 1] [S = 1] * [T = 1] * [I = 2] [S = 1] * [T = 1] * [I = 3] [S = 1] * [T = 2] * [I = 1] [S = 1] * [T = 2] * [I = 2] [S = 1] * [T = 2] * [I = 3] [S = 1] * [T = 3] * [I = 1] [S = 1] * [T = 3] * [I = 2] [S = 1] * [T = 3] * [I = 3]
[P = 1] * [E = 1] * [T = 1] * [I = 1] [P = 1] * [E = 1] * [T = 1] * [I = 2]
-.333 2.068 1.481 .739 -1.693 -1.040 -.419 .558 .538 .164 .978 .765 .488 .736 .600 .586 .268 .319 .290 .512 -1.188 -1.129 -.843 .969 .492 .262 1.549 -.069 .238 .411 .045 .082 .003 -.208 -.450 .267 .155 .173 .324 .433 .431 -.552 -.098 -.236 -.768 -.540 -.177 .054 -.077 -.427 .611 .291 -.167 .618 .209 -.140 -.501 -.587 -.320 -.396 -.393 -.150 .095 -.277 .053 -2.098 .326
.114 .218 .197 .197 .188 .149 .142 .157 .138 .136 .227 .215 .223 .201 .185 .185 .193 .174 .173 .091 .180 .151 .133 .143 .120 .106 .392 .436 .370 .271 .262 .276 .254 .243 .253 .256 .245 .253 .380 .349 .357 .149 .138 .139 .158 .132 .126 .331 .269 .265 .264 .218 .210 .241 .199 .190 .196 .183 .185 .185 .166 .163 .182 .161 .153 .628 .580
-2.933 9.493 7.509 3.750 -8.988 -6.972 -2.952 3.555 3.907 1.206 4.305 3.549 2.192 3.662 3.244 3.172 1.386 1.827 1.681 5.633 -6.620 -7.491 -6.329 6.776 4.108 2.460 3.953 -.159 .644 1.518 .173 .298 .013 -.856 -1.783 1.041 .632 .683 .852 1.242 1.207 -3.701 -.709 -1.700 -4.867 -4.106 -1.403 .164 -.286 -1.613 2.316 1.333 -.795 2.561 1.049 -.737 -2.552 -3.217 -1.727 -2.142 -2.372 -.917 .523 -1.721 .349 -3.341 .562
.003 .000 .000 .000 .000 .000 .003 .000 .000 .228 .000 .000 .028 .000 .001 .002 .166 .068 .093 .000 .000 .000 .000 .000 .000 .014 .000 .874 .519 .129 .863 .765 .990 .392 .075 .298 .528 .494 .394 .214 .227 .000 .479 .089 .000 .000 .161 .870 .775 .107 .021 .182 .427 .010 .294 .461 .011 .001 .084 .032 .018 .359 .601 .085 .727 .001 .574
生物医学研究的统计学方法_课后习题解答
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