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Sample sizes for two-group second order latent growth curve models
Stockholm University, Faculty of Social Sciences, Department of Statistics.
2009 (English)In: Multivariate Behavioral Research, ISSN 0027-3171, E-ISSN 1532-7906, Vol. 44, no 5, 1532-7906 p.Article in journal (Refereed) Published
Abstract [en]

Second-order latent growth curve models (S. C. Duncan & Duncan, 1996; McArdle, 1988) can be used to study group differences in change in latent constructs. We give exact formulas for the covariance matrix of the parameter estimates and an algebraic expression for the estimation of slope differences. Formulas for calculations of the required sample size are presented, illustrated, and discussed. They are checked by Monte Carlo simulations in Mplus and also by Satorra and Saris's (1985) power approximation techniques for small and medium effect sizes (Cohen, 1988). Results are similar across methods. Not surprisingly, sample sizes decrease with effect sizes, indicator reliabilities, number of indicators, frequency of observation, and duration of study. The relative importance of these factors is also discussed, alone and in combination. The use of the sample size formula is illustrated using a modification of empirical results from Stoel, Peetsma, and Roeleveld (2003).

Place, publisher, year, edition, pages
Taylor & Francis , 2009. Vol. 44, no 5, 1532-7906 p.
National Category
Computer and Information Science
URN: urn:nbn:se:su:diva-24577DOI: 10.1080/00273170903202589ISI: 000274281300002OAI: diva2:197830
Part of urn:nbn:se:su:diva-7199Available from: 2007-11-27 Created: 2007-11-16 Last updated: 2010-12-01Bibliographically approved
In thesis
1. Intelligence and models for cognitive development
Open this publication in new window or tab >>Intelligence and models for cognitive development
2007 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This dissertation focuses on cognitive development. In papers I and II, I study a special model, the second order latent growth curve model, that can be used to study cognitive development. Algebraic expressions for the variance of the estimation of slope differences are given. They may be used to calculate the sample sizes needed to detect slope differences between groups. Illustrations of the formulas indicate that sample sizes decrease with effect size, number of indicators and their reliabilities, frequency of observation and duration of the study. In addition, observations near the beginning and end are more important than observations in the middle, and needed sample sizes increase with attrition. Smaller sample sizes are also needed in studies in which baseline levels between groups may be assumed equal, and correlations between factors can either increase or decrease needed sample size.

Papers III and IV address different aspects of cognitive development. The Flynn effect refers to the observed fact that IQ scores increase over time. In Paper III, we suggest outlining the boundaries within which this effect occurs prior to investigating possible causes. We observe an effect in a test in a large American dataset. This dataset contains information that can be used to outline these boundaries as well as to search for possible causes. Paper IV addresses the observed correlation between sibship size or birth order and cognitive ability. If sibship size negatively affects cognitive ability in children, this should be detected studying children’s cognitive development prior to, and after, the birth of a sibling. Using longitudinal multilevel analyses on a large sample of American children from ages five to fourteen, differences between children of different sibship sizes are noted. Their cognitive abilities do not change following the birth of a sibling however.

Place, publisher, year, edition, pages
Stockholm: Statistiska institutionen, 2007. 170 p.
intelligence, cognitive development, sample size, multilevel models, latent growth curve models
National Category
Probability Theory and Statistics
Research subject
urn:nbn:se:su:diva-7199 (URN)978-91-7155-545-8 (ISBN)
Public defence
2007-12-18, sal G, Arrheniuslaboratorierna, Svante Arrhenius väg 14-18, Stockholm, 10:00
Available from: 2007-11-27 Created: 2007-11-16Bibliographically approved

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