64 Application of HLM 6 ㈠㈡㈢㈣ covariance component models Dempster et al., 1981 multilevel linear models Hox, 1994 mixedeffects models Laird & Ware,

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1 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, a 1997a HLM individual level organizational level nested 2006 nested 1997a 1997a Dempster, Rubin, & Tsutakawa, 1981 HLM disaggregated aggregated 2006 Iα 1997a *

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

2 64 Application of HLM 6 ㈠㈡㈢㈣ 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

coefficient regression models Rosenber, 1973 HLM 1997 ㈠ I 1997a, 1997b ㈡ 1997a 1997a 1997

3 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, Bryk Raudebush 1992 n Crosignani 1997 α.05 power ( σ1 + σ 2 )( z1 α + z1 β ) n = Singer Willett SD = 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

Raudebush, 1992 2006 Bryk Raudebush 1992 n Crosignani 1997 α.05 power.

4 66 Application of HLM n = 64 n = 68 n % n % t / χ 2 M ± SD ± ± 8.08 t =.006 χ 2 = 11.87* χ 2 = a χ 2 = 7.83* χ 2 = χ 2 = 6.40* χ 2 = 4.38* a *p <.05. Symptom Distress Numeric Rating Scale, NRS Paice & Cohen, 1997 Conbach s α SPSS12.0 HLM 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 X it β 0i β 1i β 2i β 3i ε it 0 ㈠㈡ HLM

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.

5 67 10 β0i = γ 00 + γ 01wi + γ 0i+ 1zi + u0i i= 1 β = γ + γ w 1i i β = γ + γ w + u 2i 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 ㈢㈣ u 0i u 2i HLM γ M ± SD M ± SD ± ± ± ± ± ± ± ± ± ± ± ± U mean = mean = U null model Intraclass Correlation Coefficient, ICC

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.

6 68 Application of HLM ICC.53 ICC 3 43% 53% 3 timevarying HLM z i HLM HLM 46 γ γ 02 γ 011 τ 00 1 τ χ HLM t t γ ** * γ γ γ γ γ a γ a γ b γ b γ c γ c γ γ γ * γ γ * γ *** γ *** a b c 2* p <.05. **p <.01. ***p <.001.

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.

7 69 HLM χ 2 χ 2 ε u *** *** 407 u 2 < < ***p <.001. γ 20 γ 10 γ 21 = γ 11 =.410 U γ 20 γ 10 γ 11 = -.491p =.067 U τ 22 γ 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-

067 U τ 22 γ 31.343.715.001 HLM U Byles, Mishra, & Schofield, 2000; Kjerulff et al.

8 70 Application of HLM ulff et al., 2000 HLM HLM HLM HLM HLM HLM a b a b 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), 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),

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).

9 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), Dempster, A. P., Rubin, D. B., & Tsutakawa, R. K. (1981). Estimation in covariance component models. Journal of the American Statistical Association, 76, 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, 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), 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), 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), Laird, N. M., & Ware, H. (1982). Random-effects models for longitudinal data. Biometrics, 38, 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, Rosenber, B. (1973). Linear regression with randomly dispersed parameters. Biometrics, 60, 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),

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).

10 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) ext. 3006; wenft@scu.edu.tw

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.

11第十一章階層線性模式.DOC

11第十一章階層線性模式.DOC 11.1 11.1.1 (student-level) (personal-level) ( ) (school-level) (organization-level) ( ) 1. (disaggregation) (estimated standard errors) (type one error). (aggregation) (within-group) (1997) (hierarchical

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,

64 Application of HLM 6 ㈠㈡㈢㈣ covariance component models Dempster et al., 1981 multilevel linear models Hox, 1994 mixedeffects models Laird & Ware,