icdglm: EM by the Method of Weights for Incomplete Data in GLMs

In icdGLM: EM by the Method of Weights for Incomplete Categorical Data in Generlized Linear Models

Description

This function applies the EM algorithm by the method of weights to incomplete data in a general linearized model.

Usage

icdglm(formula, family = binomial(link = "logit"), data, weights = rep.int(1, NROW(data)),
              indicator = rep.int(0, NROW(data)), control = list(), model = TRUE)

Arguments

formula	an object of class "formula" (or one that can be coerced to that class): a symbolic description of the model to be fitted.
family	a description of the error distribution and link function to be used in the model. This can be a character string naming a family function, a family function or the result of a call to a family function. (See family for details of family functions.)
data	an optional data frame, list or environment (or object coercible by as.data.frame to a data frame) containing the variables in the model. If not found in data, the variables are taken from environment(formula)
weights	a vector which attaches a weight to each observation. For incomplete data, this is obtained from expand_data.
indicator	a vector that indicates which observations belong to each other. This is obtained from expand_data.
control	a list of control characteristics used for the iteration process in icdglm.fit. See glm.control for further information how this works. Default settings are: epsilon = 1e-10, maxit = 100, trace = FALSE.
model	a logical value indicating whether model frame should be included as a component of the returned value.

Value

icdglm returns an object of class inheriting from "icdglm.fit", "glm" and "lm". The function summary.icdglm can be used to obtain a summary of the results. icdglm returns a list with the following elements:

• xa matrix of numerics containing all independent variables

• ya vector of numerics containing the dependent variable

• new.weightsthe new weights obtained in the final iteration of icdglm.fit

• indicatora vector of integers indicating which observations belong to each other

• glm.fit.datatypical glm.fit output for the last iteration. See glm.fit for further information.

• coefficientsa named vector of coefficients

• qrQR Decomposition of the information matrix

• residualsthe residuals of the final iteration

• fitted.valuesthe fitted mean values, obtained by transforming the linear predictors by the inverse of the link function.

• rankthe numeric rank of the fitted linear model

• familythe family object used.

• linear.predictorsthe linear fit on link scale

• devianceup to a constant, minus twice the maximized log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero.

• aicsee glm

• null.devianceThe deviance for the null model, comparable with deviance. The null model will include the offset, and an intercept if there is one in the model. Note that this will be incorrect if the link function depends on the data other than through the fitted mean: specify a zero offset to force a correct calculation.

• iteran integer containing the number of iterations in icdglm.fit before convergence

• weightsthe working weights, that is the weights in the final iteration of the IWLS fit.

• prior.weightsthe weights initially supplied, a vector of 1s if none were.

• df.residualthe residual degrees of freedom from the initial data set

• df.nullthe residual degrees of freedom from initial data set for the null model

• modelmodel frame

• convergedTRUE if icdglm converged.

• callthe match call

• formulathe formula supplied

• termsthe terms object used

• datathe data argument

• controlthe value of the control argument used

References

Ibrahim, Joseph G. (1990). Incomplete Data in Generalized Linear Models. Journal of the American Statistical Association, Vol.85, No. 411, pp. 765 - 769.

See Also

expand_data, icdglm.fit, glm, glm.fit, glm.control, summary.glm

Examples

data(TLI.data)
          complete.data <- expand_data(data = TLI.data[,1:3],
                                       y = TLI.data[,4],
                                       missing.x = 1:3,
                                       value.set = 0:1)
          example <- icdglm(y ~ x1 + x2 + x3, family = binomial(link = "logit"),
                            data = complete.data$data, weights = complete.data$weights,
                            indicator = complete.data$indicator)
          summary(example)

Example output

[1] 25

Family: binomial 
Link function: logit 

  [1] 0 0 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0
 [38] 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1
 [75] 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
  [1] 0.8294499084 0.1705500916 0.6742940260 0.3257059740 0.4754229237
  [6] 0.9944807715 0.5107607807 0.5107607807 0.3468240125 0.9946596911
 [11] 0.9946596911 0.9946596911 0.9946596911 0.3881737180 0.0832408019
 [16] 0.2557721190 0.0548483200 0.1235462631 0.0852078943 0.5245770763
 [21] 0.0055192285 0.4892392193 0.4892392193 0.6531759875 0.0053403089
 [26] 0.0053403089 0.0053403089 0.0053403089 0.3718175199 0.1567679602
 [31] 0.2449948323 0.1032962087 0.1318768832 0.0004574796 1.0000000000
 [36] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [41] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [46] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [51] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [56] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [61] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [66] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [71] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [76] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [81] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [86] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [91] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
 [96] 1.0000000000 1.0000000000 1.0000000000 1.0000000000 1.0000000000
[101] 1.0000000000 1.0000000000 1.0000000000
  [1] 0.2073504599 0.0426295106 0.1685603970 0.0784739771 0.1145533086
  [6] 0.2373164110 0.1276719906 0.1276719906 0.0866811769 0.2373673708
 [11] 0.2373673708 0.2373673708 0.2373673708 0.0970287079 0.0208048437
 [16] 0.0639332973 0.0137085435 0.0297644061 0.0203331450 0.1271397255
 [21] 0.0015985198 0.1222477336 0.1222477336 0.1633018425 0.0015472166
 [26] 0.0015472166 0.0015472166 0.0015472166 0.0929063577 0.0391950068
 [31] 0.0612170348 0.0258260269 0.0319676485 0.0001325362 0.2499848359
 [36] 0.2499848359 0.2499848359 0.2499848359 0.2499848359 0.2499848359
 [41] 0.2499848359 0.2499848359 0.2499848359 0.2499848359 0.2498517596
 [46] 0.2498517596 0.2498517596 0.2498517596 0.2498517596 0.2498517596
 [51] 0.2498517596 0.2498517596 0.2498517596 0.2498517596 0.2409264904
 [56] 0.2409264904 0.2409264904 0.2409264904 0.2409264904 0.2409264904
 [61] 0.2423878819 0.2423878819 0.2499972003 0.2499972003 0.2499972003
 [66] 0.2499972003 0.2499972003 0.2499972003 0.2499972003 0.2499563077
 [71] 0.2499848359 0.2499848359 0.2499848359 0.2499848359 0.2499848359
 [76] 0.2499848359 0.2499848359 0.2499848359 0.2499848359 0.2498517596
 [81] 0.2498517596 0.2498517596 0.2498517596 0.2498517596 0.2498517596
 [86] 0.2498517596 0.2498517596 0.2498517596 0.2498517596 0.2409264904
 [91] 0.2409264904 0.2423878819 0.2423878819 0.2423878819 0.2423878819
 [96] 0.2423878819 0.2423878819 0.2423878819 0.2499563077 0.2499563077
[101] 0.2499563077 0.2499972003 0.2389042285
  [1] 0.4961059 0.5066100 0.4961059 0.5952550 0.5952550 0.6053365 0.4961059
  [8] 0.4961059 0.5066100 0.6053365 0.6053365 0.6053365 0.6053365 0.4961059
 [15] 0.5066100 0.4961059 0.5066100 0.5952550 0.6053365 0.5872475 0.5973935
 [22] 0.4878246 0.4878246 0.4983268 0.5973935 0.5973935 0.5973935 0.5973935
 [29] 0.4878246 0.4983268 0.4878246 0.4983268 0.5872475 0.5973935 0.4961059
 [36] 0.4961059 0.4961059 0.4961059 0.4961059 0.4961059 0.4961059 0.4961059
 [43] 0.4961059 0.4961059 0.4878246 0.4878246 0.4878246 0.4878246 0.4878246
 [50] 0.4878246 0.4878246 0.4878246 0.4878246 0.4878246 0.5952550 0.5952550
 [57] 0.5952550 0.5952550 0.5952550 0.5952550 0.5872475 0.5872475 0.4983268
 [64] 0.4983268 0.4983268 0.4983268 0.4983268 0.4983268 0.4983268 0.5066100
 [71] 0.4961059 0.4961059 0.4961059 0.4961059 0.4961059 0.4961059 0.4961059
 [78] 0.4961059 0.4961059 0.4878246 0.4878246 0.4878246 0.4878246 0.4878246
 [85] 0.4878246 0.4878246 0.4878246 0.4878246 0.4878246 0.5952550 0.5952550
 [92] 0.5872475 0.5872475 0.5872475 0.5872475 0.5872475 0.5872475 0.5872475
 [99] 0.5066100 0.5066100 0.5066100 0.4983268 0.6053365
            (Intercept)       x1       x2       x3
(Intercept)   19.198062 4.584282 5.671776 9.504484
x1             4.584282 4.584282 1.428576 2.114663
x2             5.671776 1.428576 5.671776 2.235075
x3             9.504484 2.114663 2.235075 9.504484
Warning message:
icdglm.fit: algorithm did not converge 

Call:
icdglm(formula = y ~ x1 + x2 + x3, family = binomial(link = "logit"), 
    data = complete.data$data, weights = complete.data$weights, 
    indicator = complete.data$indicator)

Deviance Residuals: 
    Min       1Q   Median       3Q      Max  
-1.3591  -1.1708   0.3747   1.0318   1.1982  

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.01558    0.39124  -0.040    0.968
x1           0.04202    0.53576   0.078    0.937
x2           0.40131    0.50464   0.795    0.426
x3          -0.03313    0.46073  -0.072    0.943

(Dispersion parameter for binomial family taken to be 1)

    Null deviance: 113.48  on 81  degrees of freedom
Residual deviance: 112.77  on 78  degrees of freedom
AIC: 118.15

Number of Fisher Scoring iterations: 25

icdGLM documentation built on May 2, 2019, 9:16 a.m.