메뉴 건너뛰기




Volumn 52, Issue 2, 2017, Pages 200-215

Accommodating Small Sample Sizes in Three-Level Models When the Third Level is Incidental

Author keywords

HLM; mixed effects model; multilevel model; small sample; Three level

Indexed keywords

HUMAN; MODEL; PSYCHOLOGY; SAMPLE SIZE; ADOLESCENT; ADOLESCENT BEHAVIOR; ALGORITHM; CHILD; CLUSTER ANALYSIS; COMPUTER SIMULATION; EDUCATIONAL STATUS; MONTE CARLO METHOD; MOTIVATION; MULTIVARIATE ANALYSIS; REGRESSION ANALYSIS; SCHOOL TEACHER; SOCIAL SUPPORT; STATISTICAL ANALYSIS; STUDENT; UNITED STATES;

EID: 85007258930     PISSN: 00273171     EISSN: None     Source Type: Journal    
DOI: 10.1080/00273171.2016.1262236     Document Type: Article
Times cited : (45)

References (69)
  • 3
    • 77952026461 scopus 로고    scopus 로고
    • Estimating multilevel logistic regression models when the number of clusters is low: a comparison of different statistical software procedures
    • Article 16
    • Austin, P. C., (2010). Estimating multilevel logistic regression models when the number of clusters is low:a comparison of different statistical software procedures. The International Journal of Biostatistics, 6, Article 16. doi:10.2202/1557-4679.1195
    • (2010) The International Journal of Biostatistics , vol.6
    • Austin, P.C.1
  • 4
    • 66349091570 scopus 로고    scopus 로고
    • Psychometric approaches for developing commensurate measures across independent studies: traditional and new models
    • Bauer, D. J., & Hussong, A. M., (2009). Psychometric approaches for developing commensurate measures across independent studies:traditional and new models. Psychological Methods, 14, 101–125. doi:10.1037/a0017642
    • (2009) Psychological Methods , vol.14 , pp. 101-125
    • Bauer, D.J.1    Hussong, A.M.2
  • 5
    • 83755185645 scopus 로고    scopus 로고
    • Fitting multilevel models with ordinal outcomes: Performance of alternative specifications and methods of estimation
    • Bauer, D. J., & Sterba, S. K., (2011). Fitting multilevel models with ordinal outcomes:Performance of alternative specifications and methods of estimation. Psychological Methods, 16, 373–390. doi:10.1037/a0025813
    • (2011) Psychological Methods , vol.16 , pp. 373-390
    • Bauer, D.J.1    Sterba, S.K.2
  • 6
    • 84922259964 scopus 로고    scopus 로고
    • Explaining fixed effects: Random effects modeling of time-series cross-sectional and panel data
    • Bell, A., & Jones, K., (2015). Explaining fixed effects:Random effects modeling of time-series cross-sectional and panel data. Political Science Research and Methods, 3, 133–153. doi:10.1017/psrm.2014.7
    • (2015) Political Science Research and Methods , vol.3 , pp. 133-153
    • Bell, A.1    Jones, K.2
  • 7
    • 84894161242 scopus 로고    scopus 로고
    • How low can you go? An investigation of the influence of sample size and model complexity on point and interval estimates in two-level linear models
    • Bell, B. A., Morgan, G. B., Schoeneberger, J. A., Kromrey, J. D., & Ferron, J. M., (2014). How low can you go? An investigation of the influence of sample size and model complexity on point and interval estimates in two-level linear models. Methodology, 10, 1–11. doi:10.1027/1614-2241/a000062
    • (2014) Methodology , vol.10 , pp. 1-11
    • Bell, B.A.1    Morgan, G.B.2    Schoeneberger, J.A.3    Kromrey, J.D.4    Ferron, J.M.5
  • 8
    • 85032330186 scopus 로고    scopus 로고
    • Understanding individual-level change through the basis functions of a latent curve model
    • Blozis, S. A., & Harring, J. R., (2016). Understanding individual-level change through the basis functions of a latent curve model. Sociological Methods & Research. Advance online publication. doi:10.1177/0049124115605341
    • (2016) Sociological Methods & Research
    • Blozis, S.A.1    Harring, J.R.2
  • 10
    • 33847083094 scopus 로고    scopus 로고
    • A comparison of Bayesian and likelihood-based methods for fitting multilevel models
    • Browne, W. J., & Draper, D., (2006). A comparison of Bayesian and likelihood-based methods for fitting multilevel models. Bayesian Analysis, 1, 473–514. doi:10.1214/06-ba117
    • (2006) Bayesian Analysis , vol.1 , pp. 473-514
    • Browne, W.J.1    Draper, D.2
  • 11
    • 0002761705 scopus 로고
    • Toward a more appropriate conceptualization of research on school effects: A three-level hierarchical linear model
    • Bryk, A. S., & Raudenbush, S. W., (1988). Toward a more appropriate conceptualization of research on school effects:A three-level hierarchical linear model. American Journal of Education, 97, 65–108. doi:10.1086/443913
    • (1988) American Journal of Education , vol.97 , pp. 65-108
    • Bryk, A.S.1    Raudenbush, S.W.2
  • 12
    • 49749101681 scopus 로고    scopus 로고
    • Bootstrap-based improvements for inference with clustered errors
    • Cameron, A. C., Gelbach, J. B., & Miller, D. L., (2008). Bootstrap-based improvements for inference with clustered errors. The Review of Economics and Statistics, 90, 414–427. doi:10.1162/rest.90.3.414
    • (2008) The Review of Economics and Statistics , vol.90 , pp. 414-427
    • Cameron, A.C.1    Gelbach, J.B.2    Miller, D.L.3
  • 13
    • 47949122241 scopus 로고    scopus 로고
    • When can group level clustering be ignored? Multilevel models versus single-level models with sparse data
    • Clarke, P., (2008). When can group level clustering be ignored? Multilevel models versus single-level models with sparse data. Journal of Epidemiology and Community Health, 62, 752–758. doi:10.1136/jech.2007.060798
    • (2008) Journal of Epidemiology and Community Health , vol.62 , pp. 752-758
    • Clarke, P.1
  • 15
    • 66349089005 scopus 로고    scopus 로고
    • Integrative data analysis: the simultaneous analysis of multiple data sets
    • Curran, P. J., & Hussong, A. M., (2009). Integrative data analysis:the simultaneous analysis of multiple data sets. Psychological Methods, 14, 81–100. doi:10.1037/a0015914
    • (2009) Psychological Methods , vol.14 , pp. 81-100
    • Curran, P.J.1    Hussong, A.M.2
  • 16
    • 77951747413 scopus 로고    scopus 로고
    • Twelve frequently asked questions about growth curve modeling
    • Curran, P. J., Obeidat, K., & Losardo, D., (2010). Twelve frequently asked questions about growth curve modeling. Journal of Cognition and Development, 11, 121–136. doi:10.1080/15248371003699969
    • (2010) Journal of Cognition and Development , vol.11 , pp. 121-136
    • Curran, P.J.1    Obeidat, K.2    Losardo, D.3
  • 17
    • 0035184396 scopus 로고    scopus 로고
    • Small‐sample adjustments for Wald‐type tests using sandwich estimators
    • Fay, M. P., & Graubard, B. I., (2001). Small‐sample adjustments for Wald‐type tests using sandwich estimators. Biometrics, 57, 1198–1206. doi:10.1111/j.0006-341x.2001.01198.x
    • (2001) Biometrics , vol.57 , pp. 1198-1206
    • Fay, M.P.1    Graubard, B.I.2
  • 18
    • 66149144783 scopus 로고    scopus 로고
    • Making treatment effect inferences from multiple-baseline data: The utility of multilevel modeling approaches
    • Ferron, J. M., Bell, B. A., Hess, M. R., Rendina-Gobioff, G., & Hibbard, S. T., (2009). Making treatment effect inferences from multiple-baseline data:The utility of multilevel modeling approaches. Behavior Research Methods, 41, 372–384. doi:10.3758/brm.41.2.372
    • (2009) Behavior Research Methods , vol.41 , pp. 372-384
    • Ferron, J.M.1    Bell, B.A.2    Hess, M.R.3    Rendina-Gobioff, G.4    Hibbard, S.T.5
  • 20
    • 10844245499 scopus 로고    scopus 로고
    • An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data
    • Flora, D. B., & Curran, P. J., (2004). An empirical evaluation of alternative methods of estimation for confirmatory factor analysis with ordinal data. Psychological Methods, 9, 466–491. doi:10.1037/1082-989x.9.4.466
    • (2004) Psychological Methods , vol.9 , pp. 466-491
    • Flora, D.B.1    Curran, P.J.2
  • 21
    • 77956201379 scopus 로고    scopus 로고
    • A study of clustered data and approaches to its analysis
    • Galbraith, S., Daniel, J. A., & Vissel, B., (2010). A study of clustered data and approaches to its analysis. The Journal of Neuroscience, 30, 10601–10608. doi:10.1523/jneurosci.0362-10.2010
    • (2010) The Journal of Neuroscience , vol.30 , pp. 10601-10608
    • Galbraith, S.1    Daniel, J.A.2    Vissel, B.3
  • 22
    • 61749087965 scopus 로고    scopus 로고
    • Fixed effects, random effects and GEE: What are the differences?
    • Gardiner, J. C., Luo, Z., & Roman, L. A., (2009). Fixed effects, random effects and GEE:What are the differences?. Statistics in Medicine, 28, 221–239. doi:10.1002/sim.3478
    • (2009) Statistics in Medicine , vol.28 , pp. 221-239
    • Gardiner, J.C.1    Luo, Z.2    Roman, L.A.3
  • 24
    • 0004296209 scopus 로고    scopus 로고
    • Englewood Cliffs, NJ: Prentice-Hall
    • Greene, W., (2002). Econometric analysis. Englewood Cliffs, NJ:Prentice-Hall.
    • (2002) Econometric analysis
    • Greene, W.1
  • 25
    • 79959695262 scopus 로고    scopus 로고
    • Fixed effects vector decomposition: a magical solution to the problem of time-invariant variables in fixed effects models?
    • Greene, W., (2011). Fixed effects vector decomposition:a magical solution to the problem of time-invariant variables in fixed effects models?. Political Analysis, 19, 135–146. doi:10.1093/pan/mpq034
    • (2011) Political Analysis , vol.19 , pp. 135-146
    • Greene, W.1
  • 26
    • 84890913931 scopus 로고
    • Maximum likelihood approaches to variance component estimation and to related problems
    • Harville, D. A., (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association, 72, 320–338. doi:10.2307/2286796
    • (1977) Journal of the American Statistical Association , vol.72 , pp. 320-338
    • Harville, D.A.1
  • 27
    • 34247269174 scopus 로고    scopus 로고
    • Intraclass correlation values for planning group randomized trials in education
    • Hedges, L. V., & Hedberg, E. C., (2007). Intraclass correlation values for planning group randomized trials in education. Educational Evaluation and Policy Analysis, 29, 60–87. doi:10.3102/0162373707299706
    • (2007) Educational Evaluation and Policy Analysis , vol.29 , pp. 60-87
    • Hedges, L.V.1    Hedberg, E.C.2
  • 29
    • 84947036889 scopus 로고    scopus 로고
    • Alternatives to multilevel modeling for the analysis of clustered data
    • Huang, F. L., (2016). Alternatives to multilevel modeling for the analysis of clustered data. The Journal of Experimental Education, 84, 175–196. doi:10.1080/00220973.2014.952397
    • (2016) The Journal of Experimental Education , vol.84 , pp. 175-196
    • Huang, F.L.1
  • 30
    • 84875889078 scopus 로고    scopus 로고
    • Integrative data analysis in clinical psychology research
    • Hussong, A. M., Curran, P. J., & Bauer, D. J., (2013). Integrative data analysis in clinical psychology research. Annual Review of Clinical Psychology, 9, 61–89. doi:10.1146/annurev-clinpsy-050212-185522
    • (2013) Annual Review of Clinical Psychology , vol.9 , pp. 61-89
    • Hussong, A.M.1    Curran, P.J.2    Bauer, D.J.3
  • 32
    • 84953073092 scopus 로고
    • The effect of prolonged implementation of cooperative learning on social support within the classroom
    • Johnson, D. W., Johnson, R. T., Buckman, L. A., & Richards, P. S., (1985). The effect of prolonged implementation of cooperative learning on social support within the classroom. The Journal of Psychology, 119, 405–411. doi:10.1080/00223980.1985.10542911
    • (1985) The Journal of Psychology , vol.119 , pp. 405-411
    • Johnson, D.W.1    Johnson, R.T.2    Buckman, L.A.3    Richards, P.S.4
  • 33
    • 1542784440 scopus 로고    scopus 로고
    • A note on the efficiency of sandwich covariance matrix estimation
    • Kauermann, G., & Carroll, R. J., (2001). A note on the efficiency of sandwich covariance matrix estimation. Journal of the American Statistical Association, 96, 1387–1396. doi:10.1198/016214501753382309
    • (2001) Journal of the American Statistical Association , vol.96 , pp. 1387-1396
    • Kauermann, G.1    Carroll, R.J.2
  • 34
    • 0030880605 scopus 로고    scopus 로고
    • Small sample inference for fixed effects from restricted maximum likelihood
    • Kenward, M. G., & Roger, J. H., (1997). Small sample inference for fixed effects from restricted maximum likelihood. Biometrics, 53, 983–997. doi:10.2307/2533558
    • (1997) Biometrics , vol.53 , pp. 983-997
    • Kenward, M.G.1    Roger, J.H.2
  • 35
    • 61849100484 scopus 로고    scopus 로고
    • An improved approximation to the precision of fixed effects from restricted maximum likelihood
    • Kenward, M. G., & Roger, J. H., (2009). An improved approximation to the precision of fixed effects from restricted maximum likelihood. Computational Statistics & Data Analysis, 53, 2583–2595. doi:10.1016/j.csda.2008.12.013
    • (2009) Computational Statistics & Data Analysis , vol.53 , pp. 2583-2595
    • Kenward, M.G.1    Roger, J.H.2
  • 36
    • 84929045689 scopus 로고    scopus 로고
    • Examining the rule of thumb of not using multilevel modeling: The “design effect smaller than two” rule
    • Lai, M. H., & Kwok, O. M., (2015). Examining the rule of thumb of not using multilevel modeling:The “design effect smaller than two” rule. The Journal of Experimental Education, 83, 423–438. doi:10.1080/00220973.2014.907229
    • (2015) The Journal of Experimental Education , vol.83 , pp. 423-438
    • Lai, M.H.1    Kwok, O.M.2
  • 37
    • 0020333131 scopus 로고
    • Random-effects models for longitudinal data
    • Laird, N. M., & Ware, J. H., (1982). Random-effects models for longitudinal data. Biometrics, 38, 963–974. doi:10.2307/2529876
    • (1982) Biometrics , vol.38 , pp. 963-974
    • Laird, N.M.1    Ware, J.H.2
  • 38
    • 34547882049 scopus 로고    scopus 로고
    • A comparison of two bias-corrected covariance estimators for generalized estimating equations
    • Lu, B., Preisser, J. S., Qaqish, B. F., Suchindran, C., Bangdiwala, S. I., & Wolfson, M., (2007). A comparison of two bias-corrected covariance estimators for generalized estimating equations. Biometrics, 63, 935–941. doi:10.1111/j.1541-0420.2007.00764.x
    • (2007) Biometrics , vol.63 , pp. 935-941
    • Lu, B.1    Preisser, J.S.2    Qaqish, B.F.3    Suchindran, C.4    Bangdiwala, S.I.5    Wolfson, M.6
  • 39
    • 69949190053 scopus 로고    scopus 로고
    • Sufficient sample sizes for multilevel modeling
    • Maas, C. J., & Hox, J. J., (2005). Sufficient sample sizes for multilevel modeling. Methodology, 1, 86–92. doi:10.1027/1614-2241.1.3.85
    • (2005) Methodology , vol.1 , pp. 86-92
    • Maas, C.J.1    Hox, J.J.2
  • 40
    • 0035099161 scopus 로고    scopus 로고
    • A covariance estimator for GEE with improved small sample properties
    • Mancl, L. A., & DeRouen, T. A., (2001). A covariance estimator for GEE with improved small sample properties. Biometrics, 57, 126–134. doi:10.1111/j.0006-341x.2001.00126.x
    • (2001) Biometrics , vol.57 , pp. 126-134
    • Mancl, L.A.1    DeRouen, T.A.2
  • 41
    • 84925614904 scopus 로고    scopus 로고
    • Modeling sparsely clustered data: Design-based, model-based, and single-level methods
    • McNeish, D., (2014). Modeling sparsely clustered data:Design-based, model-based, and single-level methods. Psychological Methods, 19, 552–563. doi:10.1037/met0000024
    • (2014) Psychological Methods , vol.19 , pp. 552-563
    • McNeish, D.1
  • 42
    • 84974808077 scopus 로고    scopus 로고
    • On using Bayesian methods to address small sample problems
    • McNeish, D., (2016). On using Bayesian methods to address small sample problems. Structural Equation Modeling, 23, 750–773. doi:10.1080/10705511.2016.1186549
    • (2016) Structural Equation Modeling , vol.23 , pp. 750-773
    • McNeish, D.1
  • 43
    • 84992437384 scopus 로고    scopus 로고
    • Clustered data with small sample sizes: Comparing the performance of model-based and design-based approaches
    • McNeish, D. M., & Harring, J. R., (2015). Clustered data with small sample sizes:Comparing the performance of model-based and design-based approaches. Communications in Statistics-Simulation and Computation. Advance online publication. doi:10.1080/03610918.2014.983648
    • (2015) Communications in Statistics-Simulation and Computation
    • McNeish, D.M.1    Harring, J.R.2
  • 44
    • 84908298355 scopus 로고    scopus 로고
    • The effect of small sample size on two level model estimates: A review and illustration
    • McNeish, D., & Stapleton, L. M., (2016a). The effect of small sample size on two level model estimates:A review and illustration. Educational Psychology Review, 28, 295–314. doi:10.1007/s10648-014-9287-x
    • (2016) Educational Psychology Review , vol.28 , pp. 295-314
    • McNeish, D.1    Stapleton, L.M.2
  • 45
    • 84973596359 scopus 로고    scopus 로고
    • Modeling clustered data with very few clusters
    • McNeish, D., & Stapleton, L.M., (2016b). Modeling clustered data with very few clusters. Multivariate Behavioral Research, 51, 495–518. doi:10.1080/00273171.2016.1167008
    • (2016) Multivariate Behavioral Research , vol.51 , pp. 495-518
    • McNeish, D.1    Stapleton, L.M.2
  • 46
    • 85000936579 scopus 로고    scopus 로고
    • On the unnecessary ubiquity of hierarchical linear modeling
    • McNeish, D., Stapleton, L. M., & Silverman, R. D., (2016). On the unnecessary ubiquity of hierarchical linear modeling. Psychological Methods. Advance online publication. doi:10.1037/met0000078
    • (2016) Psychological Methods
    • McNeish, D.1    Stapleton, L.M.2    Silverman, R.D.3
  • 47
    • 3042811866 scopus 로고    scopus 로고
    • The consequence of ignoring a level of nesting in multilevel analysis
    • Moerbeek, M., (2004). The consequence of ignoring a level of nesting in multilevel analysis. Multivariate Behavioral Research, 39, 129–149. doi:10.1207/s15327906mbr3901_5
    • (2004) Multivariate Behavioral Research , vol.39 , pp. 129-149
    • Moerbeek, M.1
  • 48
    • 34548301106 scopus 로고    scopus 로고
    • A simulation study of sample size for multilevel logistic regression models
    • Moineddin, R., Matheson, F. I., & Glazier, R. H., (2007). A simulation study of sample size for multilevel logistic regression models. BMC Medical Research Methodology, 7, 34. doi:10.1186/1471-2288-7-34
    • (2007) BMC Medical Research Methodology , vol.7 , pp. 34
    • Moineddin, R.1    Matheson, F.I.2    Glazier, R.H.3
  • 49
    • 0038684155 scopus 로고    scopus 로고
    • Small sample correction for the variance of GEE estimators
    • Morel, J. G., Bokossa, M. C., & Neerchal, N. K., (2003). Small sample correction for the variance of GEE estimators. Biometrical Journal, 45, 395–409. doi:10.1002/bimj.200390021
    • (2003) Biometrical Journal , vol.45 , pp. 395-409
    • Morel, J.G.1    Bokossa, M.C.2    Neerchal, N.K.3
  • 51
    • 0035873911 scopus 로고    scopus 로고
    • Statistical models appropriate for designs often used in group‐randomized trials
    • Murray, D. M., (2001). Statistical models appropriate for designs often used in group‐randomized trials. Statistics in Medicine, 20, 1373–1385. doi:10.1002/sim.675
    • (2001) Statistics in Medicine , vol.20 , pp. 1373-1385
    • Murray, D.M.1
  • 52
    • 1442305727 scopus 로고    scopus 로고
    • Design and analysis of group-randomized trials: a review of recent methodological developments
    • Murray, D. M., Varnell, S. P., & Blitstein, J. L., (2004). Design and analysis of group-randomized trials:a review of recent methodological developments. American Journal of Public Health, 94, 423–432. doi:10.2105/ajph.94.3.423
    • (2004) American Journal of Public Health , vol.94 , pp. 423-432
    • Murray, D.M.1    Varnell, S.P.2    Blitstein, J.L.3
  • 53
    • 84886337777 scopus 로고
    • Complex sample data in structural equation modeling
    • Muthén, B. O., & Satorra, A., (1995). Complex sample data in structural equation modeling. Sociological Methodology, 25, 267–316. doi:10.2307/271070
    • (1995) Sociological Methodology , vol.25 , pp. 267-316
    • Muthén, B.O.1    Satorra, A.2
  • 54
    • 0001860847 scopus 로고    scopus 로고
    • Effects of schools, teaching staff and classes on achievement and well-being in secondary education: Similarities and differences between school outcomes
    • Opdenakker, M. C., & Van Damme, J., (2000). Effects of schools, teaching staff and classes on achievement and well-being in secondary education:Similarities and differences between school outcomes. School Effectiveness and School Improvement, 11, 165–196. doi:10.1076/0924-3453(200006)11:2;1-q;ft165
    • (2000) School Effectiveness and School Improvement , vol.11 , pp. 165-196
    • Opdenakker, M.C.1    Van Damme, J.2
  • 55
    • 0037198575 scopus 로고    scopus 로고
    • Small‐sample adjustments in using the sandwich variance estimator in generalized estimating equations
    • Pan, W., & Wall, M. M., (2002). Small‐sample adjustments in using the sandwich variance estimator in generalized estimating equations. Statistics in Medicine, 21, 1429–1441. doi:10.1002/sim.1142
    • (2002) Statistics in Medicine , vol.21 , pp. 1429-1441
    • Pan, W.1    Wall, M.M.2
  • 56
    • 34047206285 scopus 로고    scopus 로고
    • Efficient estimation of time-invariant and rarely changing variables in finite sample panel analyses with unit fixed effects
    • Plümper, T., & Troeger, V. E., (2007). Efficient estimation of time-invariant and rarely changing variables in finite sample panel analyses with unit fixed effects. Political Analysis, 15, 124–139. doi:10.1093/pan/mpm002
    • (2007) Political Analysis , vol.15 , pp. 124-139
    • Plümper, T.1    Troeger, V.E.2
  • 58
    • 84914152543 scopus 로고    scopus 로고
    • Ignoring clustering in confirmatory factor analysis: some consequences for model fit and standardized parameter estimates
    • Pornprasertmanit, S., Lee, J., & Preacher, K. J., (2014). Ignoring clustering in confirmatory factor analysis:some consequences for model fit and standardized parameter estimates. Multivariate Behavioral Research, 49, 518–543. doi:10.1080/00273171.2014.933762
    • (2014) Multivariate Behavioral Research , vol.49 , pp. 518-543
    • Pornprasertmanit, S.1    Lee, J.2    Preacher, K.J.3
  • 62
    • 84954028050 scopus 로고    scopus 로고
    • The impact of sample size and other factors when estimating multilevel logistic models
    • Schoeneberger, J. A., (2015). The impact of sample size and other factors when estimating multilevel logistic models. The Journal of Experimental Education, 84, 373–397. doi:10.1080/00220973.2015.1027805
    • (2015) The Journal of Experimental Education , vol.84 , pp. 373-397
    • Schoeneberger, J.A.1
  • 63
    • 84867138209 scopus 로고    scopus 로고
    • A practical guide to calculating Cohen's f2, a measure of local effect size, from PROC MIXED
    • Selya, A. S., Rose, J. S., Dierker, L. C., Hedeker, D., & Mermelstein, R. J., (2012). A practical guide to calculating Cohen's f2, a measure of local effect size, from PROC MIXED. Frontiers in Psychology, 3, 1–6. doi:10.3389/fpsyg.2012.00111
    • (2012) Frontiers in Psychology , vol.3 , pp. 1-6
    • Selya, A.S.1    Rose, J.S.2    Dierker, L.C.3    Hedeker, D.4    Mermelstein, R.J.5
  • 64
    • 0033560362 scopus 로고    scopus 로고
    • Tutorial in biostatistics. An introduction to hierarchical linear modelling
    • Sullivan, L. M., Dukes, K. A., & Losina, E., (1999). Tutorial in biostatistics. An introduction to hierarchical linear modelling. Statistics in Medicine, 18, 855–888. doi:10.1002/0470023724.ch1b(i)
    • (1999) Statistics in Medicine , vol.18 , pp. 855-888
    • Sullivan, L.M.1    Dukes, K.A.2    Losina, E.3
  • 66
    • 0031555662 scopus 로고    scopus 로고
    • The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data
    • Verbeke, G., & Lesaffre, E., (1997). The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data. Computational Statistics & Data Analysis, 23, 541–556. doi:10.1016/s0167-9473(96)00047-3
    • (1997) Computational Statistics & Data Analysis , vol.23 , pp. 541-556
    • Verbeke, G.1    Lesaffre, E.2
  • 67
    • 84879180863 scopus 로고    scopus 로고
    • A bias correction for covariance estimators to improve inference with generalized estimating equations that use an unstructured correlation matrix
    • Westgate, P. M., (2013). A bias correction for covariance estimators to improve inference with generalized estimating equations that use an unstructured correlation matrix. Statistics in Medicine, 32, 2850–2858. doi:10.1002/sim.5709
    • (2013) Statistics in Medicine , vol.32 , pp. 2850-2858
    • Westgate, P.M.1
  • 68
    • 0000095552 scopus 로고
    • A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity
    • White, H., (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48, 817–838.
    • (1980) Econometrica , pp. 817-838
    • White, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.