Survival Times of 33 Leukemia Patients

Description

This data set is taken from Ibrahim, Joseph G. (1990). Incomplete Data in Generalized Linear Models. Journal of the American Statistical Association, Vol.85, No. 411, pp. 765 - 769. The original source is Feigl, P., and Zelen, M. (1965), Estimation of Exponential Survival Probabilities With Concomitant Information, Biometrics, 21, pp. 826-838.

Usage

data(Leukemia.data)

Format

A data frame with 33 observations on the following 3 variables.

x1

a numeric vector (covariate)

x2

a numeric vector (covariate)

y

a numeric vector (the dependent variable)

Source

Feigl, P., and Zelen, M. (1965), Estimation of Exponential Survival Probabilities With Concomitant Information, Biometrics, 21, pp. 826-838. Ibrahim, Joseph G. (1990). Incomplete Data in Generalized Linear Models. Journal of the American Statistical Association, Vol.85, No. 411, pp. 765 - 769.

TLI Study of 82 Patients

Description

This data set is taken from Ibrahim, Joseph G. (1990). Incomplete Data in Generalized Linear Models. Journal of the American Statistical Association, Vol.85, No. 411, pp. 765 - 769. The original source is Colice, G. L., Stukel, T. A., and Dain, B. (1989), Laryngeal Complications of Prolonged Intubation, Chest, No. 96, pp. 877-884.

Usage

data(TLI.data)

Format

A data frame with 82 observations on the following 4 variables (3 independent variables and 1 dependent variable).

x1

a numeric vector

x2

a numeric vector

x3

a numeric vector

y

a numeric vector (the dependent variable)

Source

Colice, G. L., Stukel, T. A., and Dain, B. (1989), Laryngeal Complications of Prolonged Intubation, Chest, No. 96, pp. 877-884. Ibrahim, Joseph G. (1990). Incomplete Data in Generalized Linear Models. Journal of the American Statistical Association, Vol.85,

Complete incomplete data

Description

This function fills all incomplete data with a set of possible values equally weighted. This is done in order to apply icdglm.

Usage

expand_data(data, y, missing.x, value.set, weights = rep.int(1, NROW(data)),
                   indicator = rep.int(0, NROW(data)))

Arguments

Value

expand_data returns a list with the following elements:

• dataa data frame of the expanded data with all possible observations (independent variables). The dependent variable is included in the last column.

• weightsthe weights for each possible observation.

• indicatora vector which indicates which observations belong to each other. Such observations have the same integer being the indicator.

Examples

data(TLI.data)
          expand_data(data = TLI.data[,1:3],
          y = TLI.data[,4],
          missing.x = 1:3,
          value.set = 0:1)

EM by the Method of Weights for Incomplete Data in GLMs

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

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)

EM by the Method of Weights for Incomplete Data in GLMs (Algorithm)

Description

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

Usage

icdglm.fit(x, y, weights = rep.int(1, NROW(x)), indicator = rep.int(0, NROW(x)),
       family = binomial(link = "logit"), control=list())

Arguments

Value

icdglm.fit 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 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)
          example1 <- icdglm.fit(x = complete.data$data[, 1:3],
                                 y = complete.data$data[, 4],
                                 weights = complete.data$weights,
                                 indicator = complete.data$indicator,
                                 family = binomial(link = "logit"),
                                 control = list(epsilon = 1e-10,
                                                maxit = 100, trace = TRUE))

Summarizing Output of an EM Algorithm by the Method of Weights Using GLMs

Description

This function gives a summary of the output of icdglm. summary.icdglm inherits from summary.glm.

Usage

## S3 method for class 'icdglm'
summary(object, dispersion = NULL, correlation = FALSE, symbolic.cor = FALSE, ...)

Arguments

Value

summary.icdglm returns an object of class "summary.icdglm", a list with components:

• callfunction call of object

• termsthe terms object used.

• familythe component from object

• deviancethe component from object

• aicthe component from object

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

• null.deviancethe component from object

• df.nullthe residual degrees of freedom for the null model.

• iterthe number of iterations in icdglm.fit, component from object

• deviance.residthe deviance residuals: see residuals.glm

• coefficientsthe matrix of coefficients, (corrected) standard errors, t-values and p-values.

• aliasednamed logical vector showing if the original coefficients are aliased.

• dispersioneither the supplied argument or the inferred/estimated dispersion if the latter is NULL.

• dfa 3-vector of the rank of the model and the number of residual degrees of freedom, plus number of coefficients (including aliased ones).

• cov.unscaledthe unscaled (dispersion = 1) estimated covariance matrix of the estimated coefficients.

• cov.scaledditto, scaled by dispersion

• correlation(only if correlation is TRUE) The estimated correlations of the estimated coefficients.

• symbolic.cor(only if correlation is TRUE) The value of the argument symbolic.cor.

Note

The description of this function is taken from summary.glm apart from a few differences.

See Also

icdglm, summary.glm, summary, glm