Fract.Poly {CorrMixed}  R Documentation 
Fits regression models with m terms of the form X^{p}, where the exponents p are selected from a small predefined set S of both integer and noninteger values.
Fract.Poly(Covariate, Outcome, S=c(2,1,0.5,0,0.5,1,2,3), Max.M=5, Dataset)
Covariate 
The covariate to be considered in the models. 
Outcome 
The outcome to be considered in the models. 
S 
The set S from which each power p^{m}
is selected. Default

Max.M 
The maximum order M to be considered for the fractional polynomial. This value can be 5 at most. When M=5, then fractional polynomials of order 1 to 5 are considered. Default 
Dataset 
A 
Results.M1 
The results (powers and AIC values) of the fractional polynomials of order 1. 
Results.M2 
The results (powers and AIC values) of the fractional polynomials of order 2. 
Results.M3 
The results (powers and AIC values) of the fractional polynomials of order 3. 
Results.M4 
The results (powers and AIC values) of the fractional polynomials of order 4. 
Results.M5 
The results (powers and AIC values) of the fractional polynomials of order 5. 
Wim Van der Elst, Geert Molenberghs, RalfDieter Hilgers, & Nicole Heussen
Van der Elst, W., Molenberghs, G., Hilgers, R., & Heussen, N. (2015). Estimating the reliability of repeatedly measured endpoints based on linear mixedeffects models. A tutorial. Submitted.
# Open data data(Example.Data) # Fit fractional polynomials, mox. order = 3 FP < Fract.Poly(Covariate = Time, Outcome = Outcome, Dataset = Example.Data, Max.M=3) # Explore results summary(FP) # best fitting model (based on AIC) for m=3, # powers: p_{1}=3, p_{2}=3, and p_{3}=2 # Fit model and compare with observed means # plot of mean Spaghetti.Plot(Dataset = Example.Data, Outcome = Outcome, Time = Time, Id=Id, Add.Profiles = FALSE, Lwd.Me=1, ylab="Mean Outcome") # Coding of predictors (note that when p_{1}=p_{2}, # beta_{1}*X ** {p_{1}} + beta_{2}*X ** {p_{1}} * log(X) # and when p=0, X ** {0}= log(X) ) term1 < Example.Data$Time**3 term2 < (Example.Data$Time**3) * log(Example.Data$Time) term3 < Example.Data$Time**2 # fit model Model < lm(Outcome~term1+term2+term3, data=Example.Data) Model$coef # regression weights (beta's) # make prediction for time 1 to 47 term1 < (1:47)**3 term2 < ((1:47)**3) * log(1:47) term3 < (1:47)**2 # compute predicted values pred < Model$coef[1] + (Model$coef[2] * term1) + (Model$coef[3] * term2) + (Model$coef[4] * term3) # Add predicted values to plot lines(x = 1:47, y=pred, lty=2) legend("topright", c("Observed", "Predicted"), lty=c(1, 2))