Improvement of confidence Interval for linear varying coefficients and its application to SEM

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Varying coefficients can be used for visualizations or interpretations of the covariate effects which might be varying on time axis. Satoh and Yanagihara (2010) proposed linear varying coefficients and constructed a simultaneous confidence interval as a function of time. Linear curve is useful to understand the scatter plot, but it might be not enough to approximate a non-linear curve especially when there are many observed time points. In this paper we consider a semiparametric varying coefficients with splines and estimate them on linear mixed effect model which proposed by Brumback et al. (1999), then we construct a simultaneous confidence interval.