Longitudinal Data Analysis by Ikuko Funatogawa & Takashi Funatogawa

Author:Ikuko Funatogawa & Takashi Funatogawa
Language: eng
Format: epub
ISBN: 9789811000775
Publisher: Springer Singapore

(3.2.5)

The models with the same variance covariance matrices across groups were better than the models with the different variance covariance matrices in all models based on the AICs, so we discuss the results of the former. The autoregressive linear mixed effects model with a random baseline and asymptote and AR(1) error showed the best fit with AIC = 19,892.3. Next to the two autoregressive linear mixed effects models, the discrete means with the UN showed good fit with AIC = 19,895.5. The discrete means with the ANTE(1) and a random intercept (AIC = 19,896.0) was slightly worse than the discrete means with the UN but showed a comparable fit. The discrete means with the AR(1), CS, or Toeplitz or the heterogeneous variance versions of these structures did not show good fit. Linear mixed effects models of linear or quadratic time trends did not show good fits.

Table 3.2 shows the estimates of marginal variances, covariances, and correlations for the autoregressive linear mixed effects model with a random baseline and asymptote and AR(1) error and the discrete means with the UN (Funatogawa et al. 2008b). The estimate of the marginal variance covariance matrix of the autoregressive linear mixed effects model is given by (2.​3.​17). The estimates of the UN with 21 parameters were similar to those of the autoregressive linear mixed effects model with 5 parameters. The variances increased with time but attenuated at the end. Let be the correlation. Considering the correlations, , with the fixed time intervals l, viewing diagonally, these were not constant. The correlation was larger for the later time j, and the correlation with the first time point, , was particularly lower than the other correlations . Considering the correlations, , with the fixed time j, viewing vertically, the correlation was smaller for the longer time interval l.Table 3.2Estimates of marginal variance, covariance, and correlation for PANSS data

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