mlePoissonTweedie: Maximum likelihood estimation of the Poisson-Tweedie...
In tweeDEseq: RNA-seq data analysis using the Poisson-Tweedie family of distributions

Description Usage Arguments Details Value References See Also Examples

Maximum likelihood estimation of the Poisson-Tweedie parameters using L-BFGS-B quasi-Newton method.

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mlePoissonTweedie(x, a, D.ini, a.ini, maxit = 100, loglik=TRUE,
maxCount=20000, w = NULL, ...)
getParam(object)

`x`	numeric vector containing the read counts.
`a`	numeric scalar smaller than 1, if specified the PT shape parameter will be fixed.
`D.ini`	numeric positive scalar giving the initial value for the dispersion.
`a.ini`	numeric scalar smaller than 1 giving the initial value for the shape parameter (ignored if 'a' is specified).
`maxit`	numeric scalar providing the maximum number of 'L-BFGS-B' iterations to be performed (default is '100').
`loglik`	is log-likelihood computed? The default is TRUE
`object`	an object of class 'mlePT'.
`maxCount`	if max(x) > maxCount, then moment method is used to estimate model parameters to reduce computation time. The default is 20000.
`w`	vector of weights with length equal to the lenght of 'x'.
`...`	additional arguments to be passed to the 'optim' 'control' options.

The L-BFGS-B quasi-Newton method is used to calculate iteratively the maximum likelihood estimates of the three Poisson-Tweedie parameters. If 'a' argument is specified, this parameter will be fixed and the method will only estimate the other two.

An object of class 'mlePT' containing the following information:

par: numeric vector giving the estimated mean ('mu'), dispersion ('D') and shape parameter 'a'.

se: numeric vector containing the standard errors of the estimated parameters 'mu', 'D' and 'a'.

loglik: numeric scalar providing the value of the loglikelihod for the estimated parameters.

iter: numeric scalar giving the number of performed iterations.

paramZhu: numeric vector giving the values of the estimated parameters in the Zhu parameterization 'a', 'b' and 'c'.

paramHou: numeric vector giving the values of the estimated parameters in the Hougaard parameterization 'alpha', 'delta' and 'theta'.

skewness: numeric scalar providing the estimate of the skewness given the estimated parameters.

x: numeric vector containing the count data introduced as the 'x' argument by the user.

convergence: A character string giving any additional information returned by the optimizer, or 'NULL'.

Esnaola M, Puig P, Gonzalez D, Castelo R and Gonzalez JR (2013). A flexible count data model to fit the wide diversity of expression profiles arising from extensively replicated RNA-seq experiments. BMC Bioinformatics 14: 254

A.H. El-Shaarawi, R. Zhu, H. Joe (2010). Modelling species abundance using the Poisson-Tweedie family. Environmetrics 22, pages 152-164.

P. Hougaard, M.L. Ting Lee, and G.A. Whitmore (1997). Analysis of overdispersed count data by mixtures of poisson variables and poisson processes. Biometrics 53, pages 1225-1238.

testShapePT print.mlePT

# Generate 500 random counts following a Poisson Inverse Gaussian
# distribution with mean = 20 and dispersion = 5
randomCounts <- rPT(n = 500, mu = 20, D = 5, a = 0.5)

# Estimate all three parameters
res1 <- mlePoissonTweedie(x = randomCounts, a.ini = 0, D.ini
= 10)
res1
getParam(res1)

#Fix 'a = 0.5' and estimate the other two parameters
res2 <- mlePoissonTweedie(x = randomCounts, a = 0.5, D.ini
= 10)
res2
getParam(res2)

Poisson-Tweedie parameter estimates (MLE)

   estimate  s.e.
mu    19.91 0.456
D      5.23 0.412
a      0.54 0.091
Skewness: 1.32

 Zhu parameterization 
    a     b     c 
0.538 7.572 0.902 

 Hougaard parameterization 
alpha delta theta 
0.538 7.162 0.109 

 log-likelihood: -1807.421
 number of iterations: 9
        mu          D          a 
19.9120000  5.2306312  0.5384602 

Poisson-Tweedie parameter estimates (MLE)

   estimate s.e.
mu     19.9 0.45
D       5.2 0.36
a       0.5   NA
Skewness: 1.25

 Zhu parameterization 
    a     b     c 
0.500 7.303 0.893 

 Hougaard parameterization 
alpha delta theta 
0.500 6.901 0.120 

 log-likelihood: -1807.501
 number of iterations: 6
       mu         D         a 
19.912000  5.163067  0.500000