Parameter estimate for each builtin model and model averaged estimate for final size and turning point of outbreak.
Description
This function gives the parameter estimate for each builtin model and model averaged estimate for final size and turning point of outbreak. Also this function, when all the builtin models are used, gives the AIC of each model, the model averaged weights and predicted incidence and cumulative cases. This function is used retrospectively, that is, when all the data are available.
Usage
1 2 
Arguments
inc,time 
Vector of equal length specifying incidence (number of reported cases per time unit) and time interval (from the start of outbreak). 
start 
A list with the starting values of the model to be used for fitting the data. If model= "all" the imput must be a list of a list with the starting values of Richards, 3P logistic, Sigmoid Emax, Gompertz, Weibull and 5P logistic model parameters. By default, the initial values are provided by selfstarting functions.

model 
The nonlinear model to be used for fitting the data. Builtin models are "Richards", "Logistic3P", "SigmEmax", "Gompertz", "Weibull" and "Logistic5P". If model = "all" the parameter estimate will be done taking into account all builtin models via model averaging.For all builtin model, C(t) represents the cumulative number of reported cases at time t and also the turning point (eta) and the final size of epidemic (alpha) are parameters in the models. The model expressions of each builtin model are given as follow:

Value
An object with the parameter estimate for each builtin model and model averaged estimate for final size and turning point of outbreak. It is a list:
Incidence 
All the available incidences 
Time 
All the available time points 
AIC 
The AIC for each builtin model and model averaged 
tTable 
A table with parameter estimates and t test. It is not available when all the model are used. 
Weights 
Model averaged weights. It is not availabe when is used only one builtin model 
FinalSize 
95% confidence interval and point estimate of the final size of outbreak for each builtin model and model averaged estimate 
TurningPoint 
95% confidence interval and point estimate of the turning point of outbreak for each builtin model and model averaged estimate 
Predict 
Predicted cumulative cases for each builtin model 
PredictMA 
Predicted cumulative cases for model averaged 
PredInc 
Predicted incidence for each builtin model 
PredMAInc 
Predicted incidence for model averaged 
function.type 
Name of the function 
model.type 
models used to estimate 
Generic functions such as plot and summary have methods to show the results of the fit
Author(s)
Carlos Sebrango, Lizet Sanchez, Ziv Shkedy
References
K. Burnham, D. R. Anderson, Model Selection and Multimodel Inference: A Practical Informationtheoretic Approach,
2nd Edition, SpringerVerlag, New York, 2002.
J. MacDougall, Analysis of dose responses Studies: Emax model, in: N. Ting (Ed.), Dose Finding in Drug Development, Statistics for Biology and Health, Springer New York, pp. 127, 2006.
G. Claeskens, N. L. Hjort, Model selection and model averaging, Cambridge University Press, 2008.
D. Ratkowsky, Handbook of nonlinear regression models, Marcel Dekker, New York, 1990.
F. Richards, A flexible growth function for empirical use, Journal of Experimental Botany 10 (29), pp 290301, 1959.
Y.H. Hsieh, Temporal trend and regional variability of 20012002 multiwave DENV3 epidemic in Havana City: did Hurricane Michelle contribute to its severity?, Tropical Medicine and International Health, Vol. 18, no. 7, pp 830838, 2013.
A. Tsoularis, J. Wallace, Analysis of logistic growth models, Mathematical Biosciences, Vol. 179, no. 1, pp 2155, 2002.
J. Liao, R. Liu, Reparameterization of fiveparameter logistic function, Journal of Chemometrics 23 (5), pp 248253, 2009.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45  ## (data example 1)
data("dengueoutbreak1")
## Not run:
## Parameter estimate for Richards model (for Incidence data example 1)
allmodels(dengueoutbreak1$Incidence,dengueoutbreak1$Time,
start=list(alpha=375,k=2.38,gamma=0.76,eta=16), model="Richards")
## End(Not run)
## or
p1<allmodels(dengueoutbreak1$Incidence,dengueoutbreak1$Time, model="Richards")
## summary function for a allmodels object
summary(p1)
## plot function for a allmodels object
plot(p1,which=c(1,2))
## Not run:
## Parameter estimate for each builtin model and model averaged
##estimate for final size and turning point of outbreak
allmodels(dengueoutbreak1$Incidence,dengueoutbreak1$Time,
start=list(list(alpha=375,k=2.38,gamma=0.76,eta=16),
list(alpha=375,gamma=1,eta=16),list(alpha=380,eta=13,beta=7,n=5),
list(alpha=380,eta=20,beta=0,gamma=1),list(alpha=410,eta=12,beta=11,k=3),
list(alpha=380,beta=4,g=1,eta=13,k=15)), model="all")
## or
allmodels(dengueoutbreak1$Incidence,dengueoutbreak1$Time,model="all")
## (data example 2)
data("dengueoutbreak2")
# Parameter estimate for 3P Logistic model
allmodels(dengueoutbreak2$Incidence,dengueoutbreak2$Time,
start=list(alpha=375,gamma=1,eta=16), model="logistic3P")
## or
allmodels(dengueoutbreak2$Incidence,dengueoutbreak2$Time,model="logistic3P")
## Parameter estimate for each builtin model and model averaged estimate
##for final size and turning point of outbreak
##for Incidence data example 2
allmodels(dengueoutbreak2$Incidence,dengueoutbreak2$Time,
start=list(list(alpha=355,k=1,gamma=1,eta=14),
list(alpha=355,gamma=1,eta=14), list(alpha=355,eta=13,beta=10,n=6),
list(alpha=355,eta=11,beta=20,gamma=1),list(alpha=355,eta=12,beta=22,k=3),
list(alpha=355,beta=15,g=1,eta=13,k=10)),model="all")
## or
allmodels(dengueoutbreak2$Incidence,dengueoutbreak2$Time,model="all")
## End(Not run)
