Analysis of Longitudinal Data (2nd Edition) by Peter Diggle, Patrick Heagerty, Kung-Yee Liang, Scott Zeger

By Peter Diggle, Patrick Heagerty, Kung-Yee Liang, Scott Zeger

The recent variation of this significant textual content has been thoroughly revised and accelerated to develop into the main up to date and thorough specialist reference textual content during this fast-moving and significant quarter of biostatistics. new chapters were extra on absolutely parametric types for discrete repeated measures info and on statistical types for time-dependent predictors the place there's suggestions among the predictor and reaction variables. It additionally includes the numerous priceless gains of the former variation corresponding to, layout concerns, exploratory equipment of study, linear types for non-stop facts, and versions and strategies for dealing with information and lacking values.


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Extra info for Analysis of Longitudinal Data (2nd Edition)

Example text

The smoothing spline which minimizes the criterion above is a twicedifferentiable piecewise cubic polynomial. It can be calculated from the observations (t„, y,), i = 1, ... ,m by solving relatively simple linear equations. 25 where g(t) is the density of points in the vicinity of time t. 25 indicates that the effective bandwidths do not change very quickly with the density of observations. The final method, lowess (Cleveland, 1979), is a natural extension of kernel methods made 'robust', that is less sensitive, to outlying Y values.

In subsequent chapters, the autocorrelation function will be one tool for identifying sensible models for the correlation in a longitudinal data set. The empirical function described above will be contrasted with the theoretical correlations for a candidate model. Hence, the EDA displays are later useful for model criticism as well. The autocorrelation function is most effective for studying equally spaced data that are roughly stationary. Autocorrelations are more difficult to estimate with irregularly spaced data unless we round observation times as was done above for the CD4+ data.

1 is an adequate display for exploring these growth data, although it is hard to pick out individual response profiles. We can do slightly better by adding a second display obtained from the first by standardizing each observation. This is achieved by subtracting the mean, 9 j , and dividing by the standard deviation, s 3 , of the 48 observations at time j, and replacing each yid by the standardized quantity y,*) = (y, i — M/s . The resulting plot is shown in Fig. 2. Its effect is as if we were running a magnifying glass along the overall mean response profile, adjusting the magnification as we go so as to maintain a roughly constant amount of variation.

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