Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T14:34:16.838Z Has data issue: false hasContentIssue false

Parceling in Structural Equation Modeling

A Comprehensive Introduction for Developmental Scientists

Published online by Cambridge University Press:  07 July 2022

Todd D. Little
Affiliation:
Texas Tech University and North-West University, South Africa
Charlie Rioux
Affiliation:
University of Oklahoma
Omolola A. Odejimi
Affiliation:
Children's Hospital Los Angeles
Zachary L. Stickley
Affiliation:
Texas Tech University

Summary

Parceling is pre-modeling strategy to create fewer and more reliable indicators of constructs for use with latent variable models. Parceling is particularly useful for developmental scientists because longitudinal models can become quite complex and even intractable when measurement models of items are fit. In this Element the authors provide a detailed account of the advantages of using parcels, their potential pitfalls, as well as the techniques for creating them for conducting latent variable structural equation modeling (SEM) in the context of the developmental sciences. They finish with a review of the recent use of parcels in developmental journals. Although they focus on developmental applications of parceling, parceling is also highly applicable to any discipline that uses latent variable SEM.
Get access
Type
Element
Information
Online ISBN: 9781009211659
Publisher: Cambridge University Press
Print publication: 28 July 2022

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Achenbach, T. M. (1991). Manual for the youth self-report form and 1991 profile. Burlington, VT: Department of Psychaiatry, University of Vermont.Google Scholar
Anderson, J. C., & Gerbing, D. W. (1984). The effect of sampling error on convergence, improper solutions, and goodness-of-fit indices for maximum likelihood confirmatory factor analysis. Psychometrika, 49(2), 155173. http://doi.org/10.1007/bf02294170CrossRefGoogle Scholar
Bagozzi, R. P., & Edwards, J. R. (1998). A general approach for representing constructs in organizational research. Organizational Research Methods, 1(1), 4587. http://doi.org/10.1177/109442819800100104Google Scholar
Bandalos, D. L. (2002). The effects of item parceling on goodness-of-fit and parameter estimate bias in structural equation modeling. Structural Equation Modeling, 9(1), 78102. http://doi.org/10.1207/s15328007sem0901_5Google Scholar
Bandalos, D. L., & Finney, S. J. (2001). Item parceling issues in structural equation modeling. In Marcoulides, G. A. & Schumacker, R. E. (Eds.), New developments and techniques in structural equation modeling (pp. 269296). Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
Barrett, P. T., & Kline, P. (1981). The observation to variable ratio in factor analysis. Personality Study and Group Behavior, 1(1), 2333.Google Scholar
Bentler, P. M. (1990). Comparative fit indexes in structural models. Psychological Bulletin, 107(2), 238.Google Scholar
Bodin, D., Pardini, D. A., Burns, T. G., & Stevens, A. B. (2009). Higher order factor structure of the WISC-IV in a clinical neuropsychological sample. Child Neuropsychology, 15(5), 417424. http://doi.org/10.1080/09297040802603661CrossRefGoogle Scholar
Bodner, T. E. (2006). Missing data: Prevalence and reporting practices. Psychological Reports, 99(3), 675680. http://doi.org/10.2466/pr0.99.3.675-680CrossRefGoogle ScholarPubMed
Bollen, K. A. (1989). Structural equations with latent variables (Vol. 210). John Wiley & Sons.Google Scholar
Bollen, K. A., & Noble, M. D. (2011). Structural equation models and the quantification of behavior. Proceedings of the National Academy of Sciences of the United States of America, 108, 1563915646. http://doi.org/10.1073/pnas.1010661108Google Scholar
Boyle, G. J. (1991). Does item homogeneity indicate internal consistency or item redundancy in psychometric scales? Personality and Individual Differences, 12(3), 291294. http://doi.org/10.1016/0191-8869(91)90115-rCrossRefGoogle Scholar
Browne, M. W., & Cudeck, R. (1993). Alternative ways of assessing model fit. In Bollen, K. A. & Long, J. S. (Eds.), Testing structural equation modeling (pp. 136162). Thousand Oaks, CA: Sage.Google Scholar
Byrne, B. M. (2005). Factor analytic models viewing the structure of an assessment instrument from three perspectives. Journal of Personality Assessment, 85(1), 1732. http://doi.org/10.1207/s15327752jpa8501_02CrossRefGoogle ScholarPubMed
Campbell, D. T., & Fiske, D. W. (1959). Convergent and discriminant validation by the multitrait-multimethod matrix. Psychological bulletin, 56(2), 81.Google Scholar
Carifio, J., & Perla, R. (2008). Resolving the 50-year debate around using and misusing Likert scales. Medical Education, 42(12), 11501152. http://doi.org/10.1111/j.1365-2923.2008.03172.xCrossRefGoogle ScholarPubMed
Castellanos-Ryan, N., & Conrod, P. (2011). Personality correlates of the common and unique variance across conduct disorder and substance misuse symptoms in adolescence. Journal of Abnormal Child Psychology, 39(4), 563576. http://doi.org/10.1007/s10802-010-9481-3Google Scholar
Castro, J., dePablo, J., Gomez, J., Arrindell, W. A., & Toro, J. (1997). Assessing rearing behaviour from the perspective of the parents: A new form of the EMBU. Social Psychiatry and Psychiatric Epidemiology, 32(4), 230235. http://doi.org/10.1007/bf00788243CrossRefGoogle ScholarPubMed
Cella, D., Yount, S., Rothrock, N. et al. (2010). The Patient-Reported Outcomes Measurement Information System (PROMIS) developed and tested its first wave of adult self-reported health outcome item banks: 2005–2008. Journal of Clinical Epidemiology, 63(11), 11791194. http://doi.org/10.1016/j.jclinepi.2010.04.011Google Scholar
Cheung, G. W., & Rensvold, R. B. (2001). The effects of model parsimony and sampling error on the fit of structural equation models. Organizational Research Methods, 4(3), 236264. http://doi.org/10.1177/109442810143004CrossRefGoogle Scholar
Coffman, D. L., & MacCallum, R. C. (2005). Using parcels to convert path analysis models into latent variable models. Multivariate Behavioral Research, 40, 235259. http://doi.org/10.1207/s15327906mbr4002_4Google Scholar
Collins, L. M., Schafer, J. L., & Kam, C. M. (2001). A comparison of inclusive and restrictive strategies in modern missing data procedures. Psychological Methods, 6(4), 330351. http://doi.org/10.1037//1082-989x.6.4.330Google Scholar
Comrey, A. L. (1961). Factored homogeneous item dimensions in personality research. Educational and Psychological Measurement, 21(2), 417431.Google Scholar
Cortes Hidalgo, A. P., Neumann, A., Bakermans-Kranenburg, M. J. et al. (2020). Prenatal maternal stress and child IQ. Child Development, 91(2), 347365. http://doi.org/10.1111/cdev.13177Google Scholar
Costa, P. T. Jr., & McCrae, R. R. (2008). The Revised NEO Personality Inventory (NEO-PI-R). In G. J. Boyle, G. Matthews, & D. H. Saklofske (Eds.), The SAGE handbook of personality theory and assessment, Vol. 2. Personality measurement and testing (pp. 179–198). Sage Publications, Inc. https://doi.org/10.4135/9781849200479.n9Google Scholar
Crede, M., & Harms, P. (2019). Questionable research practices when using confirmatory factor analysis. Journal of Managerial Psychology, 34(1), 1830. http://doi.org/10.1108/JMP-06-2018-0272Google Scholar
DeYoung, C. G. (2006). Higher-order factors of the Big Five in a multi-informant sample. Journal of Personality and Social Psychology, 91(6), 11381151. http://doi.org/10.1037/0022-3514.91.6.1138Google Scholar
Diamantopoulos, A., Sarstedt, M., Fuchs, C., Wilczynski, P., & Kaiser, S. (2012). Guidelines for choosing between multi-item and single-item scales for construct measurement: A predictive validity perspective. Journal of the Academy of Marketing Science, 40(3), 434449. http://doi.org/10.1007/s11747-011-0300-3CrossRefGoogle Scholar
Eekhout, I., de Vet, H. C. W., de Boer, M. R., Twisk, J. W. R., & Heymans, M. W. (2018). Passive imputation and parcel summaries are both valid to handle missing items in studies with many multi-item scales. Statistical Methods in Medical Research, 27(4), 11281140. http://doi.org/10.1177/0962280216654511Google Scholar
Enders, C. K. (2001). A primer on maximum likelihood algorithms available for use with missing data. Structural Equation Modeling: A Multidisciplinary Journal, 8(1), 128141. http://doi.org/10.1207/S15328007SEM0801_7CrossRefGoogle Scholar
Enders, C. K. (2008). A note on the use of missing auxiliary variables in full information maximum likelihood-based structural equation models. Structural Equation Modeling: A Multidisciplinary Journal, 15(3), 434448. http://doi.org/10.1080/10705510802154307Google Scholar
Enders, C. K. (2010). Applied missing data analysis. New York: Guilford Press.Google Scholar
Enders, C. K. (2017). Multiple imputation as a flexible tool for missing data handling in clinical research. Behaviour Research and Therapy, 98, 418. http://doi.org/10.1016/j.brat.2016.11.008Google Scholar
Field, A. (2016). An adventure in statistics: The reality enigma. Thousand Oaks, CA: Sage.Google Scholar
Galambos, J., & Kotz, S. (1978). Characterizations of probability distributions: A unified approach with an emphasis on exponential and related models. New York: Springer.CrossRefGoogle Scholar
Gorsuch, R. L. (1988). Exploratory factor analysis. In Nesselroade, J. R. & Cattell, R. B. (Eds.), Handbook of multivariate experimental psychology (pp. 231258). Boston, MA: Springer.Google Scholar
Gottschall, A. C., West, S. G., & Enders, C. K. (2012). A comparison of item-level and scale-level multiple imputation for questionnaire batteries. Multivariate Behavioral Research, 47(1), 125. http://doi.org/10.1080/00273171.2012.640589Google Scholar
Graham, J. W. (2003). Adding missing-data-relevant variables to FIML-based structural equation models. Structural Equation Modeling, 10(1), 80100. http://doi.org/10.1207/s15328007sem1001_4Google Scholar
Graham, J. W., Tatterson, J. W., & Widaman, K. F. (2000). Creating parcels for multi-dimensional constructs in structural equation modeling. In annual meeting of the Society of Multivariate Experimental Psychology, Saratoga Springs, NY.Google Scholar
Gruner, K., Muris, P., & Merckelbach, H. (1999). The relationship between anxious rearing behaviours and anxiety disorders symptomatology in normal children. Journal of Behavior Therapy and Experimental Psychiatry, 30(1), 2735. http://doi.org/10.1016/s0005-7916(99)00004-xGoogle Scholar
Hall, R. J., Snell, A. F., & Foust, M. S. (1999). Item parceling strategies in SEM: Investigating the subtle effects of unmodeled secondary constructs. Organizational Research Methods, 2, 233256. http://doi.org/10.1177/109442819923002Google Scholar
Hau, K. T., & Marsh, H. W. (2004). The use of item parcels in structural equation modelling: Non-normal data and small sample sizes. British Journal of Mathematical & Statistical Psychology, 57, 327351. http://doi.org/10.1111/j.2044-8317.2004.tb00142.xGoogle Scholar
Herman, K. C., Hodgson, C. G., Eddy, C. L. et al. (2020). Does child likeability mediate the link between academic competence and depressive symptoms in early elementary school? Child Development, 91(2), e331e344. http://doi.org/10.1111/cdev.13214Google Scholar
Holzinger, K. J., & Swineford, F. (1939). A study in factor analysis: The stability of a bi-factor solution. Supplementary Educational MonographsGoogle Scholar
Hopkins, J., Gouze, K. R., Lavigne, J. V., & Bryant, F. B. (2020). Multidomain risk factors in early childhood and depression symptoms in 6-year-olds: A longitudinal pathway model. Development and Psychopathology, 32(1), 5771. http://doi.org/10.1017/S0954579418001426Google Scholar
Howard, W. J., Rhemtulla, M., & Little, T. D. (2015). Using principal components as auxiliary variables in missing data estimation. Multivariate Behavioral Research, 50(3), 285299. http://doi.org/10.1080/00273171.2014.999267Google Scholar
Hoyle, R. H. (2012). Handbook of structural equation modeling. New York: Guilford Press.Google Scholar
Iliceto, P., & Fino, E. (2017). The Italian version of the Wong-Law Emotional Intelligence Scale (WLEIS-I): A second-order factor analysis. Personality and Individual Differences, 116, 274280. http://doi.org/10.1016/j.paid.2017.05.006Google Scholar
Jambon, M., & Smetana, J. G. (2020). Self-reported moral emotions and physical and relational aggression in early childhood: A social domain approach. Child Development, 91(1), e92e107. http://doi.org/10.1111/cdev.13174Google Scholar
Joo, H., Aguinis, H., & Bradley, K. J. (2017). Not all nonnormal distributions are created equal: Improved theoretical and measurement precision. Journal of Applied Psychology, 102(7), 10221053. http://doi.org/10.1037/apl0000214Google Scholar
Keith, T. Z., Fine, J. G., Taub, G. E., Reynolds, M. R., & Kranzler, J. H. (2006). Higher order, multisample, confirmatory factor analysis of the Wechsler intelligence scale for children-fourth edition: What does it measure? School Psychology Review, 35(1), 108127. ://WOS: 000202998000008.Google Scholar
Kishton, J. M., & Widaman, K. F. (1994). Unidimensional versus domain representative parceling of questionnaire items: An empirical example. Educational and Psychological Measurement, 54(3), 757765.Google Scholar
Landis, R. S., Beal, D. J., & Tesluk, P. E. (2000). A comparison of approaches to forming composite measures in structural equation models. Organizational Research Methods, 3(2), 186207. http://doi.org/10.1177/109442810032003Google Scholar
Lang, K. M., & Little, T. D. (2018). Principled missing data treatments. Prevention Science, 19(3), 284294. http://doi.org/10.1007/s11121-016-0644-5CrossRefGoogle ScholarPubMed
Lee, M. R., Bartholow, B. D., McCarthy, D. M., Pedersen, S. L., & Sher, K. J. (2015). Two alternative approaches to conventional person-mean imputation scoring of the Self-Rating of the Effects of Alcohol Scale (SRE). Psychology of Addictive Behaviors, 29(1), 231236. http://doi.org/10.1037/adb0000015Google Scholar
Lei, P. W., & Shiverdecker, L. K. (2020). Performance of estimators for confirmatory factor analysis of ordinal variables with missing data. Structural Equation Modeling: A Multidisciplinary Journal, 27(4), 584601. http://doi.org/10.1080/10705511.2019.1680292Google Scholar
Lei, P. W., & Wu, Q. (2007). Introduction to structural equation modeling: Issues and practical considerations. Educational Measurement: Issues and Practice, 26(3), 3343. http://doi.org/10.1111/j.1745-3992.2007.00099.xCrossRefGoogle Scholar
Li, C. H. (2016). Confirmatory factor analysis with ordinal data: Comparing robust maximum likelihood and diagonally weighted least squares. Behavior Research Methods, 48(3), 936949. http://doi.org/10.3758/s13428-015-0619-7CrossRefGoogle ScholarPubMed
Likert, R. (1932). A technique for the measurement of attitudes. Archives of Psychology, 22(140), 155.Google Scholar
Little, T. D. (2013). Longitudinal structural equation modeling. New York: Guildford Press.Google Scholar
Little, T. D. (in press). Longitudinal structural equation modeling (2nd ed.). New York: Guildford Press.Google Scholar
Little, T. D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling, 9(2), 151173. http://doi.org/10.1207/s15328007sem0902_1Google Scholar
Little, T. D., Lindenberger, U., & Nesselroade, J. R. (1999). On selecting indicators for multivariate measurement and modeling with latent variables: When “good” indicators are bad and “bad” indicators are good. Psychological Methods, 4(2), 192211. http://doi.org/10.1037/1082-989x.4.2.192Google Scholar
Little, T. D., Oettingen, G., & Baltes, P. B. (1995). The revised control, agency, and means-ends interview (CAMI): A multi-cultural validity assessment using mean and covariance structures (MACS) analyses. Berlin: Max Planck Institute.Google Scholar
Little, T. D., & Rhemtulla, M. (2013). Planned missing data designs for developmental researchers. Child Development Perspectives, 7(4), 199204. http://doi.org/10.1111/cdep.12043Google Scholar
Little, T. D., Rhemtulla, M., Gibson, K., & Schoemann, A. M. (2013). Why the items versus parcels controversy needn’t be one. Psychological Methods, 18(3), 285300. http://doi.org/10.1037/a0033266Google Scholar
MacCallum, R. C., & Austin, J. T. (2000). Applications of structural equation modeling in psychological research. Annual Review of Psychology, 51, 201226. http://doi.org/10.1146/annurev.psych.51.1.201CrossRefGoogle ScholarPubMed
Madley-Dowd, P., Hughes, R., Tilling, K., & Heron, J. (2019). The proportion of missing data should not be used to guide decisions on multiple imputation. Journal of Clinical Epidemiology, 110, 6373. http://doi.org/10.1016/j.jclinepi.2019.02.016Google Scholar
Marsh, H. W., Ludtke, O., Nagengast, B., Morin, A. J. S., & Von Davier, M. (2013). Why item parcels are (almost) never appropriate: Two wrongs do not make a right – camouflaging misspecification with item parcels in CFA models. Psychological Methods, 18(3), 257284. http://doi.org/10.1037/a0032773Google Scholar
Massé, R., Poulin, C., Dassa, C. et al. (1998). The structure of mental health: Higher-order confirmatory factor analyses of psychological distress and well-being measures. Social Indicators Research, 45(1–3), 475504. http://doi.org/10.1023/a:1006992032387Google Scholar
Mathieu, S. L., Conlon, E. G., Waters, A. M., & Farrell, L. J. (2020). Perceived parental rearing in paediatric obsessive-compulsive disorder: Examining the factor structure of the EMBU child and parent versions and associations with OCD symptoms. Child Psychiatry & Human Development, 51(6), 956968. http://doi.org/10.1007/s10578-020-00979-6CrossRefGoogle ScholarPubMed
Matsunaga, M. (2008). Item parceling in structural equation modeling: A primer. Communication Methods and Measures, 2(4), 260293. http://doi.org/10.1080/19312450802458935CrossRefGoogle Scholar
Matsunaga, M. (2010). How to factor-analyze your data right: Do’s, don’ts, and how-to’s. International Journal of Psychological Research, 3(1), 97110. http://doi.org/10.21500/20112084.854Google Scholar
Mazza, G. L., Enders, C. K., & Ruehlman, L. S. (2015). Addressing item-level missing data: A comparison of proration and full information maximum likelihood estimation. Multivariate Behavioral Research, 50(5), 504519. http://doi.org/10.1080/00273171.2015.1068157Google Scholar
McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: Lawrence Erlbaum Associates.Google Scholar
Montigny, C., Castellanos-Ryan, N., Whelan, R. et al. (2013). A phenotypic structure and neural correlates of compulsive behaviors in adolescents. Plos One, 8(11), 13. http://doi.org/10.1371/journal.pone.0080151Google Scholar
Motti-Stefanidi, F., Pavlopoulos, V., Mastrotheodoros, S., & Asendorpf, J. B. (2020). Longitudinal interplay between peer likeability and youth’s adaptation and psychological well-being: A study of immigrant and nonimmigrant adolescents in the school context. International Journal of Behavioral Development, 44(5), 393403. http://doi.org/10.1177/0165025419894721Google Scholar
Murray, J. S. (2018). Multiple imputation: A review of practical and theoretical findings. Statistical Science, 33(2), 142159. http://doi.org/10.1214/18-sts644CrossRefGoogle Scholar
Nasser, F., & Wisenbaker, J. (2003). A Monte Carlo study investigating the impact of item parceling on measures of fit in confirmatory factor analysis. Educational and Psychological Measurement, 63(5), 729757. http://doi.org/10.1177/0013164403258228Google Scholar
Nunnally, J. C. (1978). Psychometric theory (2nd ed.). New York: McGraw-Hill.Google Scholar
Orçan, F., & Yanyun, Y. (2016). A note on the use of item parceling in structural equation modeling with missing data. Journal of Measurement and Evaluation in Education and Psychology, 7(1), 5972. http://doi.org/10.21031/epod.88204Google Scholar
Peugh, J. L., & Enders, C. K. (2004). Missing data in educational research: A review of reporting practices and suggestions for improvement. Review of Educational Research, 74(4), 525556. http://doi.org/10.3102/00346543074004525CrossRefGoogle Scholar
Pilkonis, P. A., Choi, S. W., Reise, S. P. et al. (2011). Item banks for measuring emotional distress from the Patient-Reported Outcomes Measurement Information System (PROMIS (R)): Depression, anxiety, and anger. Assessment, 18(3), 263283. http://doi.org/10.1177/1073191111411667CrossRefGoogle Scholar
R Core Team. (2020). R: A language and environment for statistical computing. Vienna: R Foundation for Statistical Computing.Google Scholar
Reddy, S. K. (1992). Effects of ignoring correlated measurement error in structural equation models. Educational and Psychological Measurement, 52(3), 549570. http://doi.org/10.1177/0013164492052003005Google Scholar
Rhemtulla, M. (2016). Population performance of SEM parceling srategies under measurement and structural model misspecification. Psychological Methods, 21(3), 348368. http://doi.org/10.1037/met0000072Google Scholar
Rhemtulla, M., & Hancock, G. R. (2016). Planned missing data designs in educational psychology research. Educational Psychologist, 51(3–4), 305316. http://doi.org/10.1080/00461520.2016.1208094Google Scholar
Rigdon, E. E., Becker, J.-M., & Sarstedt, M. (2019). Parceling cannot reduce factor indeterminacy in factor analysis: A research note. Psychometrika, 84, 772780. http://doi.org/10.1007/s11336-019-09677-2Google Scholar
Rioux, C., Lewin, A., Odejimi, O. A., & Little, T. D. (2020). Reflection on modern methods: Planned missing data designs for epidemiological research. International Journal of Epidemiology, 49(5), 17021711. http://doi.org/10.1093/ije/dyaa042Google Scholar
Rioux, C., & Little, T. D. (2020). Underused methods in developmental science to inform policy and practice. Child Development Perspectives, 14(2), 97103. http://doi.org/10.1111/cdep.12364Google Scholar
Rioux, C., & Little, T. D. (2021). Missing data treatments in intervention studies: What was, what is, and what should be. International Journal of Behavioral Development, 45(1), 5158. http://doi.org/10.1177/0165025419880609Google Scholar
Rioux, C., Stickley, Z., Odejimi, O. A., & Little, T. D. (2020). Item parcels as indicators: Why, when, and how to use them in small sample research. In Van De Schoot, R. & Miočević, M. (Eds.), Small sample size solutions: A guide for applied researchers and practitioners (pp. 203214). London: Routledge.Google Scholar
Rodriguez, J. H., Gregus, S. J., Craig, J. T., Pastrana, F. A., & Cavell, T. A. (2020). Anxiety sensitivity and children’s risk for both internalizing problems and peer victimization experiences. Child Psychiatry & Human Development, 51(2), 174186. http://doi.org/10.1007/s10578-019-00919-zGoogle Scholar
Rosseel, Y. (2012). lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 136. http://doi.org/10.18637/jss.v048.i02CrossRefGoogle Scholar
RStudio Team. (2020). RStudio: Integrated development environment for R. Boston, MA: RStudio.Google Scholar
Rubin, D. B. (1976). Inference and missing data. Biometrika, 63(3), 581590. http://doi.org/10.1093/biomet/63.3.581Google Scholar
Rubin, D. B. (1987). Multiple imputation for nonresponse in surveys. New York: Wiley.Google Scholar
Rushton, J. P., Brainerd, C. J., & Pressley, M. (1983). Behavioral development and construct validity: The principle of aggregation. Psychological Bulletin, 94(1), 1838. http://doi.org/10.1037/0033-2909.94.1.18Google Scholar
Sass, D. A., & Smith, P. L. (2006). The effects of parceling unidimensional scales on structural parameter estimates in structural equation modeling. Structural Equation Modeling: A Multidisciplinary Journal, 13(4), 566586. http://doi.org/10.1207/s15328007sem1304_4Google Scholar
Schafer, J. L., & Graham, J. W. (2002). Missing data: Our view of the state of the art. Psychological Methods, 7(2), 147177. http://doi.org/10.1037/1082-989x.7.2.147Google Scholar
Schlomer, G. L., Bauman, S., & Card, N. A. (2010). Best practices for missing data management in counseling psychology. Journal of Counseling Psychology, 57(1), 110. http://doi.org/10.1037/a0018082Google Scholar
Seaman, S., Galati, J., Jackson, D., & Carlin, J. (2013). What is meant by “missing at random”? Statistical Science, 28(2), 257268. http://doi.org/10.1214/13-sts415Google Scholar
Stein, G. L., Mejia, Y., Gonzalez, L. M., Kiang, L., & Supple, A. J. (2020). Familism in action in an emerging immigrant community: An examination of indirect effects in early adolescence. Developmental Psychology, 56(8), 14751483. http://doi.org/10.1037/dev0000791Google Scholar
Sterba, S. K. (2019). Problems with rationales for parceling that fail to consider parcel-allocation variability. Multivariate Behavioral Research, 54(2), 264287. http://doi.org/10.1080/00273171.2018.1522497Google Scholar
Sterba, S. K., & MacCallum, R. C. (2010). Variability in parameter estimates and model fit across repeated allocations of items to parcels. Multivariate Behavioral Research, 45(2), 322358. http://doi.org/10.1080/00273171003680302CrossRefGoogle ScholarPubMed
Sterba, S. K., & Rights, J. D. (2017). Effects of parceling on model selection: Parcel-allocation variability in model ranking. Psychological Methods, 22(1), 4768. http://doi.org/10.1037/met0000067Google Scholar
Syed, M., Eriksson, P. L., Frisén, A., Hwang, C. P., & Lamb, M. E. (2020). Personality development from age 2 to 33: Stability and change in ego resiliency and ego control and associations with adult adaptation. Developmental Psychology, 56(4), 815832. http://doi.org/10.1037/dev0000895Google Scholar
Takacs, L., Smolik, F., Kazmierczak, M., & Putnam, S. P. (2020). Early infant temperament shapes the nature of mother-infant bonding in the first postpartum year. Infant Behavior & Development, 58. http://doi.org/10.1016/j.infbeh.2020.101428Google Scholar
Tarka, P. (2018). An over view of structural equation modeling: Its beginnings, historical development, usefulness and controversies in the social sciences. Quality & Quantity, 52(1), 313354. http://doi.org/10.1007/s11135-017-0469-8Google Scholar
Thompson, B., & Melancon, J. (1996). Using item “testlets/parcels” in confirmatory factor analysis: An example using the PPDP-78. Paper presented at the annual meeting of the Mid-South Educational Research Association, Tuscaloosa, AL. https://eric.ed.gov/?id=ED404349Google Scholar
Tomarken, A. J., & Waller, N. G. (2005). Structural equation modeling: Strengths, limitations, and misconceptions. Annual Review of Clinical Psychology, 1, 3165. http://doi.org/10.1146/annurev.clinpsy.1.102803.144239Google Scholar
Tucker, L. R., & Lewis, C. (1973). A reliability coefficient for maximum likelihood factor analysis. Psychometrika, 38(1), 110. http://doi.org/10.1007/bf02291170Google Scholar
Van Buuren, S. (2018). Flexible imputation of missing data (2nd ed.). Boca Raton, FL: CRC Press.Google Scholar
Van De Schoot, R., Schmidt, P., De Beuckelaer, A., Lek, K., & Zondervan-Zwijnenburg, M. (2015). Editorial: Measurement invariance. Frontiers in Psychology, 6(1064). http://doi.org/10.3389/fpsyg.2015.01064Google Scholar
Velicer, W. F., & Fava, J. L. (1998). Effects of variable and subject sampling on factor pattern recovery. Psychological Methods, 3(2), 231251. http://doi.org/10.1037//1082-989x.3.2.231Google Scholar
Violato, C., & Hecker, K. G. (2007). How to use structural equation modeling in medical education research: A brief guide. Teaching and Learning in Medicine, 19(4), 362371. http://doi.org/10.1080/10401330701542685Google Scholar
Wei, J., Sze, I. N.-L., Ng, F. F.-Y., & Pomerantz, E. M. (2020). Parents’ responses to their children’s performance: A process examination in the United States and China. Developmental Psychology, 56(12), 23312344. http://doi.org/10.1037/dev0001125Google Scholar
Weijters, B., & Baumgartner, H. (2022). On the use of balanced item parceling to counter acquiescence bias in structural equation models. Organizational Research Methods, 25(1), 170180Google Scholar
Widaman, K. F., Ferrer, E., & Conger, R. D. (2010). Factorial invariance within longitudinal structural equation models: Measuring the same construct across time. Child Development Perspectives, 4(1), 1018. http://doi.org/10.1111/j.1750-8606.2009.00110.xGoogle Scholar
Widaman, K. F., & Thompson, J. S. (2003). On specifying the null model for incremental fit indices in structural equation modeling. Psychological Methods, 8(1), 1637. http://doi.org/10.1037/1082-989x.8.1.16Google Scholar
Williams, L. J., & O’Boyle, E. H. (2008). Measurement models for linking latent variables and indicators: A review of human resource management research using parcels. Human Resource Management Review, 18(4), 233242. http://doi.org/10.1016/j.hrmr.2008.07.002Google Scholar
Yang, C. M., Nay, S., & Hoyle, R. H. (2010). Three approaches to using lengthy ordinal scales in structural equation models parceling, latent scoring, and shortening scales. Applied Psychological Measurement, 34(2), 122142. http://doi.org/10.1177/0146621609338592Google Scholar
Yoo, J. E. (2009). The effect of auxiliary variables and multiple imputation on parameter estimation in confirmatory factor analysis. Educational and Psychological Measurement, 69(6), 929947. http://doi.org/10.1177/0013164409332225Google Scholar
Yu, Y., & Kushnir, T. (2020). The ontogeny of cumulative culture: Individual toddlers vary in faithful imitation and goal emulation. Developmental Science, 23(1). http://doi.org/10.1111/desc.12862Google Scholar
Yuan, K.-H., Bentler, P. M., & Kano, Y. (1997). On averaging variables in a confirmatory factor analysis model. Behaviormetrika, 24(1), 7183. http://doi.org/10.2333/bhmk.24.71Google Scholar

Save element to Kindle

To save this element to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Parceling in Structural Equation Modeling
Available formats
×

Save element to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Parceling in Structural Equation Modeling
Available formats
×

Save element to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Parceling in Structural Equation Modeling
Available formats
×