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Latent growth models and reliability estimation of longitudinal physical performances Park, Il Hyeok

Abstract

There are four purposes to this study. The first is to introduce Latent Growth Models (LGM) to Human Kinetics researchers. The second is to examine the merits and practical problems of LGM in the analysis of longitudinal physical performance data. The third purpose is to examine the developmental patterns of children's physical performances. The fourth purpose is to compare the capacity of the two most widely used longitudinal factor models, LGM and a quasi-simplex model, to accurately estimate reliability for longitudinal data under various conditions. In study 1, the first, second and third purposes of the study were accomplished, and in study 2, the fourth purpose was accomplished. In study 1, two longitudinal data sets were obtained, however, only one set was deemed appropriate for subsequent analyses. The data included seven physical performance variables, measured at five time points, from 210 children aged eight to twelve years, and five predictor variables of physical performances. The univariate LGM analyses revealed that the children's individual development over a 5-year period was adequately explained by either a Linear (jump-and-reach and sit-and-reach), Quadratic (flexed-arm hang), Cubic (standing long jump) or Unspecified Curve model (agility shuttle run, endurance shuttle run and 30-yard dash). The children improved in their physical performances between ages 8 and 12 except for flexibility, in which children's performance declined over time. Children showed considerable variations in the developmental rate and patterns of physical performances. Among the predictor variables, the test practice (the number of previous testing sessions) and age in months showed positive effects on the children's performance at the initial time point. A negative test practice effect on the development in physical performance was also found. The effect of other predictor variables varied for different performance variables. The multivariate analyses showed that the factor structure of three hypothesized factors, "Run", "Power" and "Motor Ability", holds at all five time points. However, only the change in the "Run" factor was adequately explained by the Unspecified Curve model. There were significant test practice, age, measured season and measured year effects on the performance at the initial time of testing, and significant test practice and measured year effects on the curve factor. The cross-validation procedure generally supported these findings. It was concluded that a LGM has several merits over traditional methods in the analysis of change in that a LGM provides an individual level of analysis, and thus allows one to test various research questions regarding the predictors of change, measurement error, and multivariate change. Additionally, it requires less strict statistical assumptions than traditional methods. Because of the merits of the LGM analysis used here, this study provided some interesting findings regarding children's development of physical performances— findings that were not detectable in previous studies because of the use of traditional statistical analyses. The difficulty in comparing non-nested models, and the unknown relationship between the change in indicator variables and the change in the factor in the analysis of multivariate "curve-of-factors" model were discussed as practical problems in the application of LGM. In study 2, several longimdinal developmental data sets with known parameters under various conditions were generated by computer. The conditions were varied by the magnitude of correlations between initial status and change, the magnitude of reliability, and the magnitude of correlated errors between time points. The data were analyzed using two models, a LGM and a simplex model, and the estimated reliability coefficients were compared. The simplex model overestimated the reliability in all conditions, while the LGM provided relatively accurate reliability estimates in almost all conditions. Neither the magnitude of correlation between the initial status and change nor the magnitude of reliability affected the reliability estimation, while the correlated errors leaded to an overestimation of reliability for both models. On the other hand, the magnitude of reliability showed a negative effect on the goodness-of-fit of the simplex model. It was concluded that a LGM, rather than the often used simplex model, be used for reliability analyses of longitudinal data.

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