Applied Functional Data Analysis: Methods and Case Studies by J.O. Ramsay

By J.O. Ramsay

"What do juggling, outdated bones, felony careers, and human development styles have in universal? all of them supply upward thrust to useful facts, which are available the shape of curves or capabilities instead of the numbers, or vectors of numbers, which are thought of in traditional facts. The authors' ebook sensible info research (1997) provided a thematic method of the statistical research of such info. in contrast, the current booklet introduces and explores the guidelines of practical facts research by means of the dignity of a few case stories, a lot of them provided for the 1st time. the 2 books are complementary, yet nor is a prerequisite for the opposite. The case stories are obtainable to investigate employees in quite a lot of disciplines. each reader, even if skilled researcher or graduate scholar, should still achieve not just a selected figuring out of the equipment of practical info research, yet, extra importantly, a basic perception into the underlying styles of inspiration. many of the reviews call for the advance of novel points of the technique of useful information research, yet technical info aimed toward the professional statistician are restricted to sections that the extra normal reader can accurately forget. there's an linked website with MATLAB and S-PLUS implementations of the tools mentioned, including the entire facts units that aren't proprietary.

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Example text

The R commands below fit models with and without the SOI and then calculates the difference in AIC. 7. 5. This small difference indicates that we should favour the simpler model without the SOI. Selecting the simpler of two models with a similar fit is an example of the principle of parsimony. 8 Non-linear Regression Using Splines The relationship between CVD death and temperature shown in Fig. 22 appears to be non-linear, as the scatter plot has a curved shape. To account for this we previously added a non-linear quadratic effect for temperature (Sect.

5 Generalized Linear Model For previous regression examples in this chapter we have assumed that the dependent variable had a Normal distribution. For dependent variables with a non-Normal distribution we can use much of the same theory by generalising the model [26]. The generalisation to non-Normal data is achieved using a link function. / is the link function. This regression model has p C 1 regression parameters (ˇ) including the intercept (ˇ0 ). 8). 6 shows the link functions that we will need, and gives an example of when the link function would be appropriate.

Denominator/: So we need to log-transform the denominator when we use it as an offset. We can fit an offset for the population size (and account for over-dispersion) using the R commands: > model<-gam(SczBroad˜SOI,data=schz,family= poisson(link=’log’),offset=log(NBirths),scale=-1) This command gives the parameter estimates Parametric coefficients: Estimate Std. 407 --Signif. 05 . 1 1 A 10 unit increase in the SOI changes the rate of schizophrenia by a factor of RR = exp. 407). The intercept is on a scale of “per birth”.

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