63 階 層 線 性 模 式 於 追 蹤 研 究 之 應 用 -- 以 子 宮 切 除 婦 女 之 術 後 初 期 症 狀 困 擾 為 例 李 靜 芳 溫 福 星 * 階 層 線 性 模 式 為 目 前 處 理 多 層 次 資 料 時 最 佳 統 計 方 法 之 一, 而 追 蹤 研 究 資 料 則 屬 多 層 次 資 料 結 構, 欲 瞭 解 同 一 群 受 試 者 在 不 同 時 間 點 重 複 測 量 或 追 蹤 某 項 介 入 方 案 對 其 改 善 成 效 的 影 響, 則 可 以 採 用 此 一 統 計 分 析 模 式 本 研 究 欲 介 紹 階 層 線 性 模 式 於 追 蹤 研 究, 並 輔 以 子 宮 切 除 婦 女 在 術 後 期 間 之 症 狀 困 擾 實 例 來 說 明 此 方 法 之 應 用 本 研 究 採 類 實 驗 設 計 探 討 子 宮 切 除 婦 女 於 術 後 初 期 之 生 理 及 心 理 症 狀 困 擾 間 關 係, 觀 察 測 量 受 試 婦 女 三 次 的 症 狀 困 擾 數 字 量 表 問 卷, 並 透 過 階 層 線 性 模 式 的 成 長 模 型, 進 行 追 蹤 資 料 的 統 計 分 析 結 果 發 現, 階 層 線 性 模 式 可 以 捕 捉 受 試 婦 女 在 追 蹤 研 究 裡 的 變 化 軌 跡, 且 可 以 驗 證 受 試 婦 女 的 基 本 特 徵 對 其 變 化 軌 跡 的 影 響 ; 此 外, 實 驗 組 在 生 理 或 心 理 疾 病 困 擾 上 有 顯 著 差 異, 且 生 理 與 心 理 疾 病 困 擾 在 追 蹤 資 料 上 互 有 影 響 本 研 究 透 過 子 宮 切 除 婦 女 術 後 初 期 症 狀 困 擾 之 追 蹤 分 析 來 說 明 階 層 線 性 模 式 的 方 法 與 運 用 技 巧, 期 望 藉 由 此 篇 文 章 來 推 廣 階 層 線 性 模 式 在 追 蹤 研 究 上 的 應 用 階 層 線 性 模 式 追 蹤 研 究 子 宮 切 除 Hierarchical Linear Model, HLM multilevel data Holditch-Davis et al., 2001; Kelly, Stout, & Zywiak, 2006; White, Pieper, & Schmader, 1998 1997a 1997a 2004 1997 2003 2003 2005 2003 HLM individual level organizational level nested 2006 nested 1997a 1997a Dempster, Rubin, & Tsutakawa, 1981 HLM disaggregated aggregated 2006 Iα 1997a * 97 1 16 97 4 28 97 5 8 10048 56 02 23111531 3006
64 Application of HLM 6 ㈠ ㈡ ㈢ ㈣ covariance component models Dempster et al., 1981 multilevel linear models Hox, 1994 mixedeffects models Laird & Ware, 1982 random coefficient regression models Rosenber, 1973 HLM 1997 ㈠ I 1997a, 1997b ㈡ 1997a 1997a 1997 Dempster et al., 1981 atomistic fallacy ecological fallacy 2006 HLM 1997b Hox, 1994 growth model 2006 Little, Schnabel, & Baumert, 2000
65 2004 HLM time-varying variables 1997b HLM Gibbons et al., 1993 HLM HLM HLM HLM Bryk & Raudenbush, 1992 HLM Empirical Bayes borrowing strength Mean Square Error, MSE Bryk & Raudebush, 1992 2006 Bryk Raudebush 1992 n Crosignani 1997 α.05 power.8 2564 68 ( σ1 + σ 2 )( z1 α + z1 β ) n = Singer Willett 2003 3 3 2 6 2 6 2 94 8 1 12 31 64 68 45.88 SD = 5.44 45.87 SD = 8.08 χ 2 = 3.36, p >.05 χ 2 =.085, p >.05 χ 2 = 11.87, p <.05 χ 2 = 6.40, p <.05 χ 2 = 4.38, p <.05 5 χ 2 = 7.83, p <.05 2
66 Application of HLM n = 64 n = 68 n % n % t / χ 2 M ± SD 45.88 ± 5.44 45.87 ± 8.08 t =.006 χ 2 = 11.87* 26 40.6 17 25.0 22 34.4 14 20.6 16 25.0 37 54.4 χ 2 = 3.36 56 87.5 52 76.9 5 7.8 7 10.3 3 4.7 9 13.2 a χ 2 = 7.83* 21 33.3 21 30.9 31 49.2 21 30.9 11 17.5 26 38.2 45 70.3 47 69.1 χ 2 =.085 39 60.9 61 80.9 χ 2 = 6.40* 27 42.2 17 25.0 χ 2 = 4.38* a *p <.05. Symptom Distress Numeric Rating Scale, NRS 11 0 10 2003 Paice & Cohen, 1997 Conbach s α.83 88.3 SPSS12.0 HLM6.04 3 HLM HLM HLM HLM 2 Y = β + β Time + β Time + β X + ε it 0i 1i it 2i it 3 i it it Y it Time it 0 2 6 X it β 0i β 1i β 2i β 3i ε it 0 ㈠ ㈡ HLM
67 10 β0i = γ 00 + γ 01wi + γ 0i+ 1zi + u0i i= 1 β = γ + γ w 1i 10 11 i β = γ + γ w + u 2i 20 21 i 2i β3i = γ 30 γ z i grand mean centering w i 1 0 γ 30 group mean centering u 0i u 2i 0 τ 00 τ 22 u 1i ㈢ ㈣ u 0i u 2i HLM γ 30 3 58 64 0 58 64 2 48 46 6 48 44 48 44 48 44 M ± SD M ± SD 0 1.96 ± 1.59 1.68 ± 1.17 2 2.46 ± 1.67 1.76 ± 1.39 6 1.36 ± 1.26 1.64 ± 1.28 0 2.30 ± 2.54 1.68 ± 2.00 2 1.95 ± 2.69 1.66 ± 2.11 6 1.44 ± 1.96 1.84 ± 1.80 3 U 2.46 1.70 2 6 mean = 2.30 1.95 1.44 mean = 1.68 1.66 1.84 3 U null model.85 1.16 Intraclass Correlation Coefficient, ICC
68 Application of HLM.43 2.55 2.29ICC.53 ICC 3 43% 53% 3 timevarying HLM z i HLM HLM 46 γ 00 1.625 2.094 0 γ 02 γ 011 τ 00 1 τ 00 1.076 3.268 χ 2.001 1 HLM t t γ 00 1.625** 0.512 3.177 2.094* 0.818 2.561 γ 01 0.079 0.265 0.297 0.283 0.426 0.664 γ 02-0.016 0.016-1.045-0.040 0.025-1.603 γ 03 0.064 0.234 0.275 0.180 0.374 0.481 γ 04-0.087 0.273-0.319-0.186 0.437-0.427 γ 05 0.102 0.254 0.402 0.348 0.407 0.855 a γ 06-0.085 0.381-0.223-0.418 0.610-0.685 a γ 07 0.521 0.549 0.949-0.111 0.877-0.127 b γ 08 0.296 0.311 0.953-0.032 0.496-0.065 b γ 09 0.219 0.325 0.673-0.692 0.512-1.336 2 5 c γ 010-0.044 0.283-0.153 0.210 0.450 0.466 5 c γ 011-0.127 0.337-0.378 0.490 0.539 0.910 γ 10 0.057 0.130 0.438 0.064 0.188 0.341 γ 11 0.410* 0.184 2.228-0.491 0.267-1.837 γ 20-0.013 0.021-0.604-0.004 0.030-0.127 γ 21-0.074* 0.029-2.545 0.064 0.042 1.523 γ 31 0.343*** 0.045 7.659 γ 31 0.715*** 0.094 7.609 a b c 2* p <.05. **p <.01. ***p <.001.
69 HLM χ 2 χ 2 ε 0.797 1.655 u 0 1.076*** 308 3.268*** 407 u 2 < 0.001 107 < 0.001 105 0 ***p <.001. γ 20 γ 10 γ 21 = -.074 γ 11 =.410 U γ 20 γ 10 γ 11 = -.491p =.067 U τ 22 γ 31.343.715.001 HLM U Byles, Mishra, & Schofield, 2000; Kjerulff et al., 2000 U Davies & Doyle, 2002 Byles et al., 2000; Kjerulff et al., 2000 Davies & Doyle, 2002; Kjer-
70 Application of HLM ulff et al., 2000 HLM HLM HLM HLM HLM HLM 2003 1997a 15 17 26 1997b 11 489 510 2005 22 4 503 524 1997a 15 1 10 1997b 15 11 16 2004 51 2 163 184 2003 10 2 159 191 2006 2004 27 2 399 419 1997 20 1 22 2003 109 86 100 2003 4 75 96 Bryk, A. S., & Raudenbush, S. W. (1992). Hierarchical linear models. Newbury Park, CA: Sage. Byles, J. E., Mishra, G., & Schofield, M. (2000). Factors associated with hysterectomy among women in Australia. Health & Place, 6(4), 301 308. Crosignani, P. G., Vercellini, P., Apolone, G., De Giorgi, O., Cortesi, I., & Meschia, M. (1997). Endometrial resection versus vaginal hysterectomy for menorrhagia: Long-term clinical and quality-of-life outcomes. American Journal of Obstetrics and Gynecology, 177(1), 95 101.
71 Davies, J. E., & Doyle, P. M. (2002). Quality of life studies in unselected gynaecological outpatients and inpatients before and after hysterectomy. Journal of Obstetrics and Gynecology, 22(5), 523 526. Dempster, A. P., Rubin, D. B., & Tsutakawa, R. K. (1981). Estimation in covariance component models. Journal of the American Statistical Association, 76, 341 353. Gibbons, R. D., Hedeker, D., Elkin, I., Waternaux, C., Kraemer, H. C. Greenhouse, J. B., et al. (1993). Some conceptual and statistical issues in analysis of longitudinal psychiatric data. Archives of General Psychiatry, 50, 739 750. Holditch-Davis, D., Miles, M. S., Burchinal, M., O Donnell, K., Mckinney, R., & Lim, W. (2001). Parental caregiving and developmental outcomes of infants of mothers with HIV. Nursing Research, 50(1), 5 14. Hox, J. J. (1994). Applied multilevel analysis. Amsterdam: TT Publikaties. Kelly, J. F., Stout, R., & Zywiak, W. (2006). A 3-year study of addiction mutual group participation following intensive outpatient treatment. Alcoholism: Clinical & Experimental Research, 30(8), 1381 1390. Kjerulff, H., Langenberg, P. W., Rhodes, J. C., Harvey, L. A., Guzinski, G. M., & Stolley, P. D. (2000). Effectiveness of hysterectomy. Obstetrics & Gynecology, 95(3), 319 326. Laird, N. M., & Ware, H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 963 974. Little, T. D., Schnabel, K. U., & Baumert, J. (2000). Modeling longitudinal and multilevel data: Practical issues, applied approaches and specific examples. Mahwah, NJ: Lawrence Erlbaum Associates. Paice, J. A., & Cohen, F. L. (1997). Validity of verbally administered numeric rating scale to measure cancer pain intensity. Cancer Nursing, 20, 88 93. Rosenber, B. (1973). Linear regression with randomly dispersed parameters. Biometrics, 60, 61 75. Singer, J. D., & Willett, J. B. (2003). Applied Longitudinal Data Analysis. New York: Oxford University Press. White, H., Pieper, C., & Schmader, K. (1998). The association of weight change in Alzheimer s disease with severity of disease and mortality: A longitudinal analysis. Journal of the American Geriatrics Society, 46(10), 1223 1227.
72 Application of HLM Applying the Hierarchical Linear Model in Longitudinal Studies: An Example of Symptom Distress in Women Who Had Undergone a Hysterectomy Ching-Fang Lee Fur-Hsing Wen * Abstract: The purpose of this study was to introduce the Hierarchical Linear Model (HLM) and apply it to the topic of symptom distress in women who had undergone a hysterectomy. HLM was developed to analyze multilevel data and included a longitudinal study, which focused in particular on unbalanced design. A quasi-experimental design was conducted. Data on symptom distress in women who had undergone a hysterectomy (experimental group) and those who had not (control group) were collected over a six-week period and analyzed using HLM. Findings indicated that the experimental group had a quadratic trajectory in physical distress changes and a negative linear trend in psychological distress, both of which differed significantly from the control group. Additionally, physical and psychological distress influenced one another in three measurement variables, and physical distress in the experimental group actually improved over the six week period. Using HLM was able to estimate the different trajectories for each subject in the experimental group. This study shows that HLM can be applied effectively in longitudinal studies. Key Words: Hierarchical Linear Model, longitudinal study, hysterectomy. RN, MSN, Instructor, Department of Nursing, Oriental Institute of Technology College & Doctoral Student, Department of Health Education, National Taiwan Normal University; *PhD, Assistant Professor, Department of International Business, Soochow University. Received: January 16, 2008 Revised: April 28, 2008 Accepted: May 8, 2008 Address correspondence to: Fur-Hsing Wen, No. 56, Kueiyang St. Sec.1, Taipei 10048, Taiwan, ROC. Tel: +886 (2) 2311-1531 ext. 3006; E-mail: wenft@scu.edu.tw