EM Algorithm for Mixtures of Poisson Regressions — poisregmixEM • mixtools

Returns EM algorithm output for mixtures of Poisson regressions with arbitrarily many components.

Usage

poisregmixEM(y, x, lambda = NULL, beta = NULL, k = 2,
             addintercept = TRUE, epsilon = 1e-08, 
             maxit = 10000, verb = FALSE)

Arguments

y: An n-vector of response values.
x: An nxp matrix of predictors. See addintercept below.
lambda: Initial value of mixing proportions. Entries should sum to 1. This determines number of components. If NULL, then lambda is random from uniform Dirichlet and number of components is determined by beta.
beta: Initial value of beta parameters. Should be a pxk matrix, where p is the number of columns of x and k is number of components. If NULL, then beta is generated by binning the data into k bins and using glm on the values in each of the bins. If both lambda and beta are NULL, then number of components is determined by k.
k: Number of components. Ignored unless lambda and beta are both NULL.
addintercept: If TRUE, a column of ones is appended to the x matrix before the value of p is calculated.
epsilon: The convergence criterion.
maxit: The maximum number of iterations.
verb: If TRUE, then various updates are printed during each iteration of the algorithm.

Value

poisregmixEM returns a list of class mixEM with items:

x: The predictor values.
y: The response values.
lambda: The final mixing proportions.
beta: The final Poisson regression coefficients.
loglik: The final log-likelihood.
posterior: An nxk matrix of posterior probabilities for observations.
all.loglik: A vector of each iteration's log-likelihood.
restarts: The number of times the algorithm restarted due to unacceptable choice of initial values.
ft: A character vector giving the name of the function.

See also

logisregmixEM

References

McLachlan, G. J. and Peel, D. (2000) Finite Mixture Models, John Wiley and Sons, Inc.

Wang, P., Puterman, M. L., Cockburn, I. and Le, N. (1996) Mixed Poisson Regression Models with Covariate Dependent Rates, Biometrics, 52(2), 381–400.

Examples

## EM output for data generated from a 2-component model.

set.seed(100)
beta <- matrix(c(1, .5, .7, -.8), 2, 2)
x <- runif(50, 0, 10)
xbeta <- cbind(1, x)%*%beta
w <- rbinom(50, 1, .5)
y <- w*rpois(50, exp(xbeta[, 1]))+(1-w)*rpois(50, exp(xbeta[, 2]))
out <- poisregmixEM(y, x, verb = TRUE,  epsilon = 1e-03)
#> Need new starting values due to underflow... 
#> Need new starting values due to underflow... 
#> Need new starting values due to underflow... 
#> iteration= 1 diff= Inf log-likelihood -355.6115 
#> iteration= 2 diff= 234.2121 log-likelihood -121.3994 
#> Warning: glm.fit: algorithm did not converge
#> Warning: glm.fit: fitted rates numerically 0 occurred
#> iteration= 3 diff= 0.02347817 log-likelihood -121.3759 
#> Warning: glm.fit: algorithm did not converge
#> Need new starting values due to singularity... 
#> Warning: glm.fit: fitted rates numerically 0 occurred
#> iteration= 1 diff= 156.2348 log-likelihood -117.8764 
#> Warning: glm.fit: fitted rates numerically 0 occurred
#> iteration= 2 diff= 0.5641961 log-likelihood -117.3122 
#> Warning: glm.fit: fitted rates numerically 0 occurred
#> iteration= 3 diff= 0.006001777 log-likelihood -117.3062 
#> Warning: glm.fit: fitted rates numerically 0 occurred
#> iteration= 4 diff= 0.0004355172 log-likelihood -117.3058 
#> number of iterations= 4 
out
#> $x
#>                 x
#>  [1,] 1 3.0776611
#>  [2,] 1 2.5767250
#>  [3,] 1 5.5232243
#>  [4,] 1 0.5638315
#>  [5,] 1 4.6854928
#>  [6,] 1 4.8377074
#>  [7,] 1 8.1240262
#>  [8,] 1 3.7032054
#>  [9,] 1 5.4655860
#> [10,] 1 1.7026205
#> [11,] 1 6.2499648
#> [12,] 1 8.8216552
#> [13,] 1 2.8035384
#> [14,] 1 3.9848790
#> [15,] 1 7.6255108
#> [16,] 1 6.6902171
#> [17,] 1 2.0461216
#> [18,] 1 3.5752485
#> [19,] 1 3.5947511
#> [20,] 1 6.9029053
#> [21,] 1 5.3581115
#> [22,] 1 7.1080385
#> [23,] 1 5.3834870
#> [24,] 1 7.4897223
#> [25,] 1 4.2010145
#> [26,] 1 1.7142021
#> [27,] 1 7.7030161
#> [28,] 1 8.8195359
#> [29,] 1 5.4909671
#> [30,] 1 2.7772376
#> [31,] 1 4.8830599
#> [32,] 1 9.2850507
#> [33,] 1 3.4869198
#> [34,] 1 9.5415771
#> [35,] 1 6.9527414
#> [36,] 1 8.8945354
#> [37,] 1 1.8040725
#> [38,] 1 6.2939085
#> [39,] 1 9.8956414
#> [40,] 1 1.3028887
#> [41,] 1 3.3066053
#> [42,] 1 8.6512055
#> [43,] 1 7.7758444
#> [44,] 1 8.2730345
#> [45,] 1 6.0332436
#> [46,] 1 4.9123182
#> [47,] 1 7.8035851
#> [48,] 1 8.8422703
#> [49,] 1 2.0771390
#> [50,] 1 3.0708590
#> 
#> $y
#>  [1]   0   0   0   2  31   0   0   0  50   1   0 219   9  31   0   0   0   0   0
#> [20]  84   0   0  43  96  22   4 117 238  28   0   0 249  19 317   0 258   6   0
#> [39]   0   6  10   0   0   0  51   0 154   0   0  15
#> 
#> $lambda
#> [1] 0.5310379 0.4689621
#> 
#> $beta
#>           comp.1   comp.2
#> beta.0  8.981084 1.006641
#> beta.1 -5.473055 0.498414
#> 
#> $loglik
#> [1] -117.3058
#> 
#> $posterior
#>              comp.1       comp.2
#>  [1,]  9.999973e-01 2.738164e-06
#>  [2,]  9.999546e-01 4.539359e-05
#>  [3,]  1.000000e+00 0.000000e+00
#>  [4,] 3.297823e-158 1.000000e+00
#>  [5,] 6.360016e-260 1.000000e+00
#>  [6,]  1.000000e+00 5.018208e-14
#>  [7,]  1.000000e+00 0.000000e+00
#>  [8,]  1.000000e+00 2.640250e-08
#>  [9,]  0.000000e+00 1.000000e+00
#> [10,]  9.734848e-01 2.651516e-02
#> [11,]  1.000000e+00 0.000000e+00
#> [12,]  0.000000e+00 1.000000e+00
#> [13,]  2.018289e-30 1.000000e+00
#> [14,] 9.143009e-207 1.000000e+00
#> [15,]  1.000000e+00 0.000000e+00
#> [16,]  1.000000e+00 0.000000e+00
#> [17,]  9.995019e-01 4.980858e-04
#> [18,]  9.999999e-01 7.701756e-08
#> [19,]  9.999999e-01 6.570915e-08
#> [20,]  0.000000e+00 1.000000e+00
#> [21,]  1.000000e+00 0.000000e+00
#> [22,]  1.000000e+00 0.000000e+00
#> [23,]  0.000000e+00 1.000000e+00
#> [24,]  0.000000e+00 1.000000e+00
#> [25,] 7.295103e-156 1.000000e+00
#> [26,]  3.783680e-02 9.621632e-01
#> [27,]  0.000000e+00 1.000000e+00
#> [28,]  0.000000e+00 1.000000e+00
#> [29,] 1.544038e-286 1.000000e+00
#> [30,]  9.999840e-01 1.600539e-05
#> [31,]  1.000000e+00 2.498002e-14
#> [32,]  0.000000e+00 1.000000e+00
#> [33,] 8.326491e-101 1.000000e+00
#> [34,]  0.000000e+00 1.000000e+00
#> [35,]  1.000000e+00 0.000000e+00
#> [36,]  0.000000e+00 1.000000e+00
#> [37,]  2.761451e-05 9.999724e-01
#> [38,]  1.000000e+00 0.000000e+00
#> [39,]  1.000000e+00 0.000000e+00
#> [40,]  5.415414e-01 4.584586e-01
#> [41,]  4.841602e-46 1.000000e+00
#> [42,]  1.000000e+00 0.000000e+00
#> [43,]  1.000000e+00 0.000000e+00
#> [44,]  1.000000e+00 0.000000e+00
#> [45,]  0.000000e+00 1.000000e+00
#> [46,]  1.000000e+00 1.576517e-14
#> [47,]  0.000000e+00 1.000000e+00
#> [48,]  1.000000e+00 0.000000e+00
#> [49,]  9.995647e-01 4.353444e-04
#> [50,]  2.968915e-63 1.000000e+00
#> 
#> $all.loglik
#> [1] -274.1112 -117.8764 -117.3122 -117.3062 -117.3058
#> 
#> $restarts
#> [1] 4
#> 
#> $ft
#> [1] "poisregmixEM"
#> 
#> attr(,"class")
#> [1] "mixEM"