Non-Continuity and Heterogeneity: Application of Piecewise Growth Mixture Model in Language Development Study
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摘要: 多阶段混合增长模型（Piecewise Growth Mixture Modeling，PGMM）是近几年新兴的同时关注群体的发展阶段非连续性和潜在异质性的统计模型。它将多阶段增长模型和潜类别增长模型进行整合，可以描述同时存在发展转折点和不同发展类别的描述群体增长趋势的数据。文章以早期儿童的追踪研究（幼儿园版）为例，运用PGMM模型探索其增长趋势，得出：（1）两阶段混合增长模型能最有效地描述学生阅读能力的发展，转折点在一年级，随着年龄的增加，发展速度变慢；（2）发展趋势分为三类，大部分个体起点低、发展快，小部分个体起点高、发展慢，到三年级以后两个类别差距越来越小，另一部分整体发展都比较缓慢；（3）教师对学生行为的评价比父母的评价更能有效预测学生阅读成绩的类别和趋势。
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关键词:
- 多阶段混合增长模型(PGMM) /
- 非连续性 /
- 潜在异质性 /
- 模型拟合
Abstract: In recent researches, the piecewise growth mixture model (PGMM) has been used in longitudinal studies to detect the non-continued growing trend and heterogeneous population simultaneously. The present study used the data from Early Childhood Longitudinal Study-Kindergarten cohort (ECLS-K) as an example to illustrate the use of PGMM. An ideal model of PGMN is a two-piece growing model, with the turning point at Grade One, linear trajectory in the first period and quadratic trajectory in the second. The result showed that there should be a crucial turning point in the development of reading ability, with a rapid growing rate from kindergarten to Grade One and then a sharp-decline rate after entering the primary school. Furthermore, a three-class model was selected where the heterogeneous sample-based population was essential in describing the growing pattern. Finally, the result indicated the teachers' assessment of children's behavior was more likely to predict the latent class than that of the parents' with the control of the background effects. -
表 1 六次阅读成绩以及协变量的相关矩阵与均值、标准差
阅读1 阅读2 阅读4 阅读5 阅读6 阅读7 SES 父母评价 教师评价 阅读2 .793** 阅读4 .669** .777** 阅读5 .603** .657** .762** 阅读6 .584** .639** .721** .852** 阅读7 .542** .559** .604** .746** .795** SES .147** .132** .129** .157** .162** .178** 父母评价 -.019** -.014** -.028** -.012** -.027** -.024** .540** 教师评价 .269** .264** .244** .240** .233** .204** .092** .050** M -1.277 -0.715 0.128 0.798 1.046 1.293 0.014 3.492 3.086 SD 0.506 0.491 0.453 0.315 0.299 0.383 0.789 1.505 0.960 ** p＜.01 
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表 2 四个备选模型与数据的整体拟合
模型 χ2 df CFI RMSEA AIC BIC ABIC 模型1 52797.438 16 0.000 0.612 56593.443 56670.016 56635.060 模型2 18906.476 15 0.433 0.449 26187.379 26291.796 26244.129 模型3 11728.063 12 0.648 0.354 17145.410 17249.827 17202.160 模型4 4415.809 7 0.868 0.284 8426.164 8565.386 8501.830
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表 3 零模型(模型4)参数估计结果
固定部分估计值 SE t 随机部分方差 SE χ2 截距 -1.715 0.008 -226.817*** 0.337 0.008 43.815*** 线性斜率1 0.960 0.004 257.225*** 0.017 0.002 10.318*** 线性斜率2 0.368 0.003 143.902*** 0.004 0.001 4.646*** 曲线斜率2 -0.022 ＜0.001 -94.611*** ＜0.001 ＜0.001 ＜0.001 *** p＜.001
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表 4 不同发展组的增长曲线参数估计结果
缓慢发展组 中等发展组 快速发展组 估计值 SE t 估计值 SE t 估计值 SE t 截距 -1.768 0.048 -36.914*** -2.416 0.054 -44.821*** -1.236 0.105 -11.783*** 线性斜率1 0.977 0.013 76.282*** 0.873 0.05 17.327*** 0.983 0.028 35.220*** 线性斜率2 0.378 0.014 26.955*** 0.530 0.02 25.883*** 0.256 0.024 10.575*** 曲线斜率2 -0.023 0.001 -20.330*** -0.034 0.002 -20.741*** -0.013 0.002 -5.540*** *** p＜.001
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表 5 三个不同类别上预测变量的描述统计结果
中等发展组 缓慢发展组 快速发展组 频次 百分比 频次 百分比 频次 百分比 性别(男) 2970 73.4% 613 15.2% 463 11.4% 性别(女) 3040 81.0% 282 7.5% 432 11.5% 家庭语言非英语 663 74.9% 167 18.9% 55 6.2% 家庭语言英语 5173 77.4% 686 10.3% 825 12.3% M SD M SD M SD 年龄(月) 68.446 4.136 67.700 4.649 69.378 4.076 社会经济地位 0.270 1.661 -0.042 2.063 0.593 1.357 父母评价 3.488 1.475 3.626 2.067 3.383 0.911 教师评价 3.034 0.639 2.489 0.627 3.299 0.580
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表 6 阅读能力发展类别预测的参数估计结果
标准化系数 SE Wald检验值 p 发生比 缓慢发展组 截距 2.942 0.665 19.591 ＜.001 社会经济地位 -0.704 0.057 150.117 ＜.001 0.495 年龄 -0.037 0.01 14.024 ＜.001 0.964 父母评价 0.020 0.028 0.535 .464 1.020 教师评价 -1.080 0.066 269.708 ＜.001 0.340 性别 0.532 0.086 38.741 ＜.001 1.703 家庭语言 0.305 0.109 7.805 .005 1.357 快速发展组 截距 -6.83 0.647 111.434 ＜.001 社会经济地位 0.633 0.049 167.602 ＜.001 1.884 年龄 0.043 0.009 22.539 ＜.001 1.044 父母评价 -0.059 0.043 1.89 .169 0.942 教师评价 0.616 0.066 86.118 ＜.001 1.852 性别 0.175 0.077 5.195 .023 1.192 家庭语言 -0.251 0.154 2.666 .102 0.778 注：对于阅读能力发展，参考组为中间组；对于分类预测变量，性别的参照组为女生，家庭交流所使用语言的参照组为使用英语组。
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表 7 阅读能力发展水平和速度影响因素分析结果
缓慢发展组 中等发展组 快速发展组 标准化系数 t 标准化系数 t 标准化系数 t 初始水平(截距) 性别 -.138 -4.184 -.014 -1.138 -.017 -.467 家庭语言 .052 1.599 .133 10.382 .012 .337 初始年龄 .243 7.322 .142 11.239 .139 3.847 社会经济地位 .340 10.424 .203 15.583 .192 5.156 父母评价 .010 .302 .006 .513 .177 4.944 教师评价 .133 4.025 .296 22.786 .146 4.096 第一阶段斜率 性别 .140 4.163 .044 3.170 -.080 -2.280 家庭语言 -.017 -.520 -.039 -2.767 -.060 -1.690 初始年龄 -.202 -5.980 -.139 -10.151 -.208 -5.973 社会经济地位 -.341 -10.273 -.108 -7.610 .303 8.495 父母评价 .019 .579 -.001 -.101 .068 1.977 教师评价 -.139 -4.149 -.100 -7.064 .119 3.462 第二阶段斜率 性别 .068 1.839 -.013 -.925 -.045 -1.189 家庭语言 -.104 -2.856 -.110 -7.793 -.037 -.987 初始年龄 -.193 -5.171 -.116 -8.370 -.121 -3.247 社会经济地位 -.016 -.447 .077 5.424 .003 .067 父母阶段评价 .011 .311 .005 .333 -.170 -4.623 教师阶段评价 -.008 -.219 -.102 -7.167 .009 .245
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