### Abstract

Multilevel modeling has become the main methodology for analyzing longitudinal or repeated measures data recently. Moreover, determining the required sample size at different levels is the important issue for longitudinal studies. However, few simulation study discusses the required sample size to gain unbiased estimated parameters on growth curve modeling at different levels. This work designed Monte Carlo simulation to investigate the impacts of an unconditional growth model and those of a conditional growth model on the accuracies of estimated parameters (regression coefficients) and random effect variances, respectively. The manipulated factors were ‘the number of time points per person’ and ‘the number of people.’ All the analyses were conducted by using Mplus 5.21; simulated data were generated from the command of MONTECARLO, and then the data were estimated by ML estimation.The results indicated that the estimated regression coefficients were unbiased in both unconditional and conditional growth models when the second level contained more than 100 units, no matter the first level unit. In addition, when the second level has a small sample (i.e., small number of people), the estimations for random effect were seriously biased. However, a larger sample had its estimations more accurately. In sum, if the researchers only discuss fixed effects in the model, a small sample (e.g., 100) in the level 2 can gain the good estimations. If the researchers focus on the random effects as well, a large sample is needed to have accurately estimated parameters

Date of Award | 2012 |
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Original language | English |

Supervisor | 偉明 陸 (Supervisor) |

### Keywords

- multilevel modeling
- growth curve modeling
- determining sample sizes
- Monte Carlo simulation study