Function to solve a Generalized Estimation Equation Model

Produces an object of class "gee" which is a Generalized Estimation Equation fit of the data.

gee(formula, id,
    data, subset, na.action,
    R = NULL, b = NULL,
    tol = 0.001, maxiter = 25,
    family = gaussian, corstr = "independence",
    Mv = 1, silent = TRUE, contrasts = NULL,
    scale.fix = FALSE, scale.value = 1, v4.4compat = FALSE)

Arguments

formula

a formula expression as for other regression models, of the form response ~ predictors. See the documentation of lm and formula for details.

id

a vector which identifies the clusters. The length of id should be the same as the number of observations. Data are assumed to be sorted so that observations on a cluster are contiguous rows for all entities in the formula.

data

an optional data frame in which to interpret the variables occurring in the formula, along with the id and n variables.

subset

expression saying which subset of the rows of the data should be used in the fit. This can be a logical vector (which is replicated to have length equal to the number of observations), or a numeric vector indicating which observation numbers are to be included, or a character vector of the row names to be included. All observations are included by default.

na.action

a function to filter missing data. For gee only na.omit should be used here.

R

a square matrix of dimension maximum cluster size containing the user specified correlation. This is only appropriate if corstr = "fixed".

b

an initial estimate for the parameters.

tol

the tolerance used in the fitting algorithm.

maxiter

the maximum number of iterations.

family

a family object: a list of functions and expressions for defining link and variance functions. Families supported in gee are gaussian, binomial, poisson, Gamma, and quasi; see the glm and family documentation. Some links are not currently available: 1/mu^2 and sqrt have not been hard-coded in the cgee engine at present. The inverse gaussian variance function is not available. All combinations of remaining functions can be obtained either by family selection or by the use of quasi.

corstr

a character string specifying the correlation structure. The following are permitted: "independence", "fixed", "stat_M_dep", "non_stat_M_dep", "exchangeable", "AR-M" and "unstructured"

Mv

When corstr is "stat_M_dep", "non_stat_M_dep", or "AR-M" then Mv must be specified.

silent

a logical variable controlling whether parameter estimates at each iteration are printed.

contrasts

a list giving contrasts for some or all of the factors appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels.

scale.fix

a logical variable; if true, the scale parameter is fixed at the value of scale.value.

scale.value

numeric variable giving the value to which the scale parameter should be fixed; used only if scale.fix == TRUE.

v4.4compat

logical variable requesting compatibility of correlation parameter estimates with previous versions; the current version revises to be more faithful to the Liang and Zeger (1986) proposals (compatible with the Groemping SAS macro, version 2.03)

Value

An object of class "gee" representing the fit.

Side Effects

Offsets must be specified in the model formula, as in glm.

Details

Though input data need not be sorted by the variable named "id", the program will interpret physically contiguous records possessing the same value of id as members of the same cluster. Thus it is possible to use the following vector as an id vector to discriminate 4 clusters of size 4: c(0,0,0,0,1,1,1,1,0,0,0,0,1,1,1,1).

Note

This is version 4.8 of this user documentation file, revised 98/01/27. The assistance of Dr B Ripley is gratefully acknowledged.

References

Liang, K.Y. and Zeger, S.L. (1986) Longitudinal data analysis using generalized linear models. Biometrika, 73 13–22.

Zeger, S.L. and Liang, K.Y. (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42 121–130.

See also

glm, lm, formula.

Examples

data(warpbreaks)
## marginal analysis of random effects model for wool
summary(gee(breaks ~ tension, id=wool, data=warpbreaks, corstr="exchangeable"))
#> Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
#> running glm to get initial regression estimate
#> (Intercept)    tensionM    tensionH 
#>    36.38889   -10.00000   -14.72222 
#> 
#>  GEE:  GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
#>  gee S-function, version 4.13 modified 98/01/27 (1998) 
#> 
#> Model:
#>  Link:                      Identity 
#>  Variance to Mean Relation: Gaussian 
#>  Correlation Structure:     Exchangeable 
#> 
#> Call:
#> gee(formula = breaks ~ tension, id = wool, data = warpbreaks, 
#>     corstr = "exchangeable")
#> 
#> Summary of Residuals:
#>        Min         1Q     Median         3Q        Max 
#> -22.388889  -8.138889  -2.666667   6.333333  33.611111 
#> 
#> 
#> Coefficients:
#>              Estimate Naive S.E.   Naive z Robust S.E.  Robust z
#> (Intercept)  36.38889   3.069434 11.855246    5.774705  6.301428
#> tensionM    -10.00000   3.910008 -2.557539    7.463905 -1.339781
#> tensionH    -14.72222   3.910008 -3.765266    3.731952 -3.944912
#> 
#> Estimated Scale Parameter:  141.1481
#> Number of Iterations:  1
#> 
#> Working Correlation
#>             [,1]       [,2]       [,3]       [,4]       [,5]       [,6]
#>  [1,] 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [2,] 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404
#>  [3,] 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404
#>  [4,] 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404
#>  [5,] 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404
#>  [6,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000
#>  [7,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [8,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [9,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [10,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [11,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [12,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [13,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [14,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [15,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [16,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [17,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [18,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [19,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [20,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [21,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [22,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [23,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [24,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [25,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [26,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [27,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>             [,7]       [,8]       [,9]      [,10]      [,11]      [,12]
#>  [1,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [2,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [3,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [4,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [5,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [6,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [7,] 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [8,] 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404
#>  [9,] 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404
#> [10,] 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404
#> [11,] 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404
#> [12,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000
#> [13,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [14,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [15,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [16,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [17,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [18,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [19,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [20,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [21,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [22,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [23,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [24,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [25,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [26,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [27,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>            [,13]      [,14]      [,15]      [,16]      [,17]      [,18]
#>  [1,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [2,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [3,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [4,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [5,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [6,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [7,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [8,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [9,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [10,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [11,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [12,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [13,] 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [14,] 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404
#> [15,] 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404
#> [16,] 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404
#> [17,] 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404
#> [18,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000
#> [19,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [20,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [21,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [22,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [23,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [24,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [25,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [26,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [27,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>            [,19]      [,20]      [,21]      [,22]      [,23]      [,24]
#>  [1,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [2,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [3,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [4,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [5,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [6,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [7,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [8,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>  [9,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [10,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [11,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [12,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [13,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [14,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [15,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [16,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [17,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [18,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [19,] 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [20,] 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404 0.02518404
#> [21,] 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404 0.02518404
#> [22,] 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404 0.02518404
#> [23,] 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000 0.02518404
#> [24,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 1.00000000
#> [25,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [26,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#> [27,] 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404 0.02518404
#>            [,25]      [,26]      [,27]
#>  [1,] 0.02518404 0.02518404 0.02518404
#>  [2,] 0.02518404 0.02518404 0.02518404
#>  [3,] 0.02518404 0.02518404 0.02518404
#>  [4,] 0.02518404 0.02518404 0.02518404
#>  [5,] 0.02518404 0.02518404 0.02518404
#>  [6,] 0.02518404 0.02518404 0.02518404
#>  [7,] 0.02518404 0.02518404 0.02518404
#>  [8,] 0.02518404 0.02518404 0.02518404
#>  [9,] 0.02518404 0.02518404 0.02518404
#> [10,] 0.02518404 0.02518404 0.02518404
#> [11,] 0.02518404 0.02518404 0.02518404
#> [12,] 0.02518404 0.02518404 0.02518404
#> [13,] 0.02518404 0.02518404 0.02518404
#> [14,] 0.02518404 0.02518404 0.02518404
#> [15,] 0.02518404 0.02518404 0.02518404
#> [16,] 0.02518404 0.02518404 0.02518404
#> [17,] 0.02518404 0.02518404 0.02518404
#> [18,] 0.02518404 0.02518404 0.02518404
#> [19,] 0.02518404 0.02518404 0.02518404
#> [20,] 0.02518404 0.02518404 0.02518404
#> [21,] 0.02518404 0.02518404 0.02518404
#> [22,] 0.02518404 0.02518404 0.02518404
#> [23,] 0.02518404 0.02518404 0.02518404
#> [24,] 0.02518404 0.02518404 0.02518404
#> [25,] 1.00000000 0.02518404 0.02518404
#> [26,] 0.02518404 1.00000000 0.02518404
#> [27,] 0.02518404 0.02518404 1.00000000
## test for serial correlation in blocks
summary(gee(breaks ~ tension, id=wool, data=warpbreaks, corstr="AR-M", Mv=1))
#> Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
#> running glm to get initial regression estimate
#> (Intercept)    tensionM    tensionH 
#>    36.38889   -10.00000   -14.72222 
#> 
#>  GEE:  GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
#>  gee S-function, version 4.13 modified 98/01/27 (1998) 
#> 
#> Model:
#>  Link:                      Identity 
#>  Variance to Mean Relation: Gaussian 
#>  Correlation Structure:     AR-M , M = 1 
#> 
#> Call:
#> gee(formula = breaks ~ tension, id = wool, data = warpbreaks, 
#>     corstr = "AR-M", Mv = 1)
#> 
#> Summary of Residuals:
#>        Min         1Q     Median         3Q        Max 
#> -22.413608  -8.095783  -2.688893   6.311107  33.586392 
#> 
#> 
#> Coefficients:
#>              Estimate Naive S.E.   Naive z Robust S.E.  Robust z
#> (Intercept)  36.41361   2.889306 12.602890    5.788146  6.291065
#> tensionM    -10.09043   4.077388 -2.474730    7.513413 -1.342989
#> tensionH    -14.72471   4.086060 -3.603646    3.758972 -3.917218
#> 
#> Estimated Scale Parameter:  141.1501
#> Number of Iterations:  2
#> 
#> Working Correlation
#>               [,1]         [,2]         [,3]         [,4]         [,5]
#>  [1,] 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06
#>  [2,] 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05
#>  [3,] 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03
#>  [4,] 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02
#>  [5,] 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00
#>  [6,] 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02
#>  [7,] 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03
#>  [8,] 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05
#>  [9,] 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06
#> [10,] 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08
#> [11,] 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09
#> [12,] 1.094906e-16 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11
#> [13,] 3.876244e-18 1.094906e-16 3.092734e-15 8.735914e-14 2.467596e-12
#> [14,] 1.372288e-19 3.876244e-18 1.094906e-16 3.092734e-15 8.735914e-14
#> [15,] 4.858248e-21 1.372288e-19 3.876244e-18 1.094906e-16 3.092734e-15
#> [16,] 1.719942e-22 4.858248e-21 1.372288e-19 3.876244e-18 1.094906e-16
#> [17,] 6.089031e-24 1.719942e-22 4.858248e-21 1.372288e-19 3.876244e-18
#> [18,] 2.155671e-25 6.089031e-24 1.719942e-22 4.858248e-21 1.372288e-19
#> [19,] 7.631619e-27 2.155671e-25 6.089031e-24 1.719942e-22 4.858248e-21
#> [20,] 2.701786e-28 7.631619e-27 2.155671e-25 6.089031e-24 1.719942e-22
#> [21,] 9.565005e-30 2.701786e-28 7.631619e-27 2.155671e-25 6.089031e-24
#> [22,] 3.386253e-31 9.565005e-30 2.701786e-28 7.631619e-27 2.155671e-25
#> [23,] 1.198819e-32 3.386253e-31 9.565005e-30 2.701786e-28 7.631619e-27
#> [24,] 4.244123e-34 1.198819e-32 3.386253e-31 9.565005e-30 2.701786e-28
#> [25,] 1.502527e-35 4.244123e-34 1.198819e-32 3.386253e-31 9.565005e-30
#> [26,] 5.319325e-37 1.502527e-35 4.244123e-34 1.198819e-32 3.386253e-31
#> [27,] 1.883175e-38 5.319325e-37 1.502527e-35 4.244123e-34 1.198819e-32
#>               [,6]         [,7]         [,8]         [,9]        [,10]
#>  [1,] 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12 8.735914e-14
#>  [2,] 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12
#>  [3,] 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11
#>  [4,] 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09
#>  [5,] 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08
#>  [6,] 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06
#>  [7,] 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05
#>  [8,] 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03
#>  [9,] 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02
#> [10,] 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00
#> [11,] 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02
#> [12,] 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03
#> [13,] 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05
#> [14,] 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06
#> [15,] 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08
#> [16,] 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09
#> [17,] 1.094906e-16 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11
#> [18,] 3.876244e-18 1.094906e-16 3.092734e-15 8.735914e-14 2.467596e-12
#> [19,] 1.372288e-19 3.876244e-18 1.094906e-16 3.092734e-15 8.735914e-14
#> [20,] 4.858248e-21 1.372288e-19 3.876244e-18 1.094906e-16 3.092734e-15
#> [21,] 1.719942e-22 4.858248e-21 1.372288e-19 3.876244e-18 1.094906e-16
#> [22,] 6.089031e-24 1.719942e-22 4.858248e-21 1.372288e-19 3.876244e-18
#> [23,] 2.155671e-25 6.089031e-24 1.719942e-22 4.858248e-21 1.372288e-19
#> [24,] 7.631619e-27 2.155671e-25 6.089031e-24 1.719942e-22 4.858248e-21
#> [25,] 2.701786e-28 7.631619e-27 2.155671e-25 6.089031e-24 1.719942e-22
#> [26,] 9.565005e-30 2.701786e-28 7.631619e-27 2.155671e-25 6.089031e-24
#> [27,] 3.386253e-31 9.565005e-30 2.701786e-28 7.631619e-27 2.155671e-25
#>              [,11]        [,12]        [,13]        [,14]        [,15]
#>  [1,] 3.092734e-15 1.094906e-16 3.876244e-18 1.372288e-19 4.858248e-21
#>  [2,] 8.735914e-14 3.092734e-15 1.094906e-16 3.876244e-18 1.372288e-19
#>  [3,] 2.467596e-12 8.735914e-14 3.092734e-15 1.094906e-16 3.876244e-18
#>  [4,] 6.970113e-11 2.467596e-12 8.735914e-14 3.092734e-15 1.094906e-16
#>  [5,] 1.968818e-09 6.970113e-11 2.467596e-12 8.735914e-14 3.092734e-15
#>  [6,] 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12 8.735914e-14
#>  [7,] 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12
#>  [8,] 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11
#>  [9,] 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09
#> [10,] 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08
#> [11,] 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06
#> [12,] 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05
#> [13,] 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03
#> [14,] 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02
#> [15,] 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00
#> [16,] 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02
#> [17,] 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03
#> [18,] 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05
#> [19,] 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06
#> [20,] 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08
#> [21,] 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09
#> [22,] 1.094906e-16 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11
#> [23,] 3.876244e-18 1.094906e-16 3.092734e-15 8.735914e-14 2.467596e-12
#> [24,] 1.372288e-19 3.876244e-18 1.094906e-16 3.092734e-15 8.735914e-14
#> [25,] 4.858248e-21 1.372288e-19 3.876244e-18 1.094906e-16 3.092734e-15
#> [26,] 1.719942e-22 4.858248e-21 1.372288e-19 3.876244e-18 1.094906e-16
#> [27,] 6.089031e-24 1.719942e-22 4.858248e-21 1.372288e-19 3.876244e-18
#>              [,16]        [,17]        [,18]        [,19]        [,20]
#>  [1,] 1.719942e-22 6.089031e-24 2.155671e-25 7.631619e-27 2.701786e-28
#>  [2,] 4.858248e-21 1.719942e-22 6.089031e-24 2.155671e-25 7.631619e-27
#>  [3,] 1.372288e-19 4.858248e-21 1.719942e-22 6.089031e-24 2.155671e-25
#>  [4,] 3.876244e-18 1.372288e-19 4.858248e-21 1.719942e-22 6.089031e-24
#>  [5,] 1.094906e-16 3.876244e-18 1.372288e-19 4.858248e-21 1.719942e-22
#>  [6,] 3.092734e-15 1.094906e-16 3.876244e-18 1.372288e-19 4.858248e-21
#>  [7,] 8.735914e-14 3.092734e-15 1.094906e-16 3.876244e-18 1.372288e-19
#>  [8,] 2.467596e-12 8.735914e-14 3.092734e-15 1.094906e-16 3.876244e-18
#>  [9,] 6.970113e-11 2.467596e-12 8.735914e-14 3.092734e-15 1.094906e-16
#> [10,] 1.968818e-09 6.970113e-11 2.467596e-12 8.735914e-14 3.092734e-15
#> [11,] 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12 8.735914e-14
#> [12,] 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12
#> [13,] 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11
#> [14,] 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09
#> [15,] 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08
#> [16,] 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06
#> [17,] 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05
#> [18,] 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03
#> [19,] 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02
#> [20,] 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00
#> [21,] 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02
#> [22,] 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03
#> [23,] 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05
#> [24,] 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08 1.570858e-06
#> [25,] 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09 5.561236e-08
#> [26,] 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11 1.968818e-09
#> [27,] 1.094906e-16 3.092734e-15 8.735914e-14 2.467596e-12 6.970113e-11
#>              [,21]        [,22]        [,23]        [,24]        [,25]
#>  [1,] 9.565005e-30 3.386253e-31 1.198819e-32 4.244123e-34 1.502527e-35
#>  [2,] 2.701786e-28 9.565005e-30 3.386253e-31 1.198819e-32 4.244123e-34
#>  [3,] 7.631619e-27 2.701786e-28 9.565005e-30 3.386253e-31 1.198819e-32
#>  [4,] 2.155671e-25 7.631619e-27 2.701786e-28 9.565005e-30 3.386253e-31
#>  [5,] 6.089031e-24 2.155671e-25 7.631619e-27 2.701786e-28 9.565005e-30
#>  [6,] 1.719942e-22 6.089031e-24 2.155671e-25 7.631619e-27 2.701786e-28
#>  [7,] 4.858248e-21 1.719942e-22 6.089031e-24 2.155671e-25 7.631619e-27
#>  [8,] 1.372288e-19 4.858248e-21 1.719942e-22 6.089031e-24 2.155671e-25
#>  [9,] 3.876244e-18 1.372288e-19 4.858248e-21 1.719942e-22 6.089031e-24
#> [10,] 1.094906e-16 3.876244e-18 1.372288e-19 4.858248e-21 1.719942e-22
#> [11,] 3.092734e-15 1.094906e-16 3.876244e-18 1.372288e-19 4.858248e-21
#> [12,] 8.735914e-14 3.092734e-15 1.094906e-16 3.876244e-18 1.372288e-19
#> [13,] 2.467596e-12 8.735914e-14 3.092734e-15 1.094906e-16 3.876244e-18
#> [14,] 6.970113e-11 2.467596e-12 8.735914e-14 3.092734e-15 1.094906e-16
#> [15,] 1.968818e-09 6.970113e-11 2.467596e-12 8.735914e-14 3.092734e-15
#> [16,] 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12 8.735914e-14
#> [17,] 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11 2.467596e-12
#> [18,] 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09 6.970113e-11
#> [19,] 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08 1.968818e-09
#> [20,] 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06 5.561236e-08
#> [21,] 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05 1.570858e-06
#> [22,] 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03 4.437136e-05
#> [23,] 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02 1.253339e-03
#> [24,] 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00 3.540253e-02
#> [25,] 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02 1.000000e+00
#> [26,] 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03 3.540253e-02
#> [27,] 1.968818e-09 5.561236e-08 1.570858e-06 4.437136e-05 1.253339e-03
#>              [,26]        [,27]
#>  [1,] 5.319325e-37 1.883175e-38
#>  [2,] 1.502527e-35 5.319325e-37
#>  [3,] 4.244123e-34 1.502527e-35
#>  [4,] 1.198819e-32 4.244123e-34
#>  [5,] 3.386253e-31 1.198819e-32
#>  [6,] 9.565005e-30 3.386253e-31
#>  [7,] 2.701786e-28 9.565005e-30
#>  [8,] 7.631619e-27 2.701786e-28
#>  [9,] 2.155671e-25 7.631619e-27
#> [10,] 6.089031e-24 2.155671e-25
#> [11,] 1.719942e-22 6.089031e-24
#> [12,] 4.858248e-21 1.719942e-22
#> [13,] 1.372288e-19 4.858248e-21
#> [14,] 3.876244e-18 1.372288e-19
#> [15,] 1.094906e-16 3.876244e-18
#> [16,] 3.092734e-15 1.094906e-16
#> [17,] 8.735914e-14 3.092734e-15
#> [18,] 2.467596e-12 8.735914e-14
#> [19,] 6.970113e-11 2.467596e-12
#> [20,] 1.968818e-09 6.970113e-11
#> [21,] 5.561236e-08 1.968818e-09
#> [22,] 1.570858e-06 5.561236e-08
#> [23,] 4.437136e-05 1.570858e-06
#> [24,] 1.253339e-03 4.437136e-05
#> [25,] 3.540253e-02 1.253339e-03
#> [26,] 1.000000e+00 3.540253e-02
#> [27,] 3.540253e-02 1.000000e+00

if(require(MASS)) {
data(OME)
## not fully appropriate link for these data.
(fm <- gee(cbind(Correct, Trials-Correct) ~ Loud + Age + OME, id = ID,
           data = OME, family = binomial, corstr = "exchangeable"))
summary(fm)
}
#> Loading required package: MASS
#> Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
#> running glm to get initial regression estimate
#> (Intercept)        Loud         Age     OMEhigh      OMElow 
#> -5.90984676  0.15516993  0.01876291 -0.07569691 -0.31660542 
#> 
#>  GEE:  GENERALIZED LINEAR MODELS FOR DEPENDENT DATA
#>  gee S-function, version 4.13 modified 98/01/27 (1998) 
#> 
#> Model:
#>  Link:                      Logit 
#>  Variance to Mean Relation: Binomial 
#>  Correlation Structure:     Exchangeable 
#> 
#> Call:
#> gee(formula = cbind(Correct, Trials - Correct) ~ Loud + Age + 
#>     OME, id = ID, data = OME, family = binomial, corstr = "exchangeable")
#> 
#> Summary of Residuals:
#>        Min         1Q     Median         3Q        Max 
#> -0.9585811  0.5507230  2.0414189  3.1210663 12.0241951 
#> 
#> 
#> Coefficients:
#>                Estimate  Naive S.E.     Naive z Robust S.E.    Robust z
#> (Intercept) -5.90100336 0.336455218 -17.5387482 0.231463368 -25.4943295
#> Loud         0.15507565 0.007513314  20.6401142 0.005321880  29.1392592
#> Age          0.01851319 0.003561640   5.1979385 0.003305525   5.6006793
#> OMEhigh     -0.04183516 0.160288285  -0.2609995 0.152182352  -0.2749015
#> OMElow      -0.28563252 0.131496124  -2.1721745 0.117510247  -2.4307031
#> 
#> Estimated Scale Parameter:  1.250466
#> Number of Iterations:  4
#> 
#> Working Correlation
#>              [,1]        [,2]        [,3]        [,4]        [,5]        [,6]
#>  [1,]  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [2,] -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [3,] -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803
#>  [4,] -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803
#>  [5,] -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803
#>  [6,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000
#>  [7,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [8,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [9,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [10,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [11,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [12,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [13,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [14,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [15,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [16,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [17,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [18,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [19,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [20,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [21,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [22,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [23,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [24,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [25,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [26,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [27,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [28,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [29,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [30,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>              [,7]        [,8]        [,9]       [,10]       [,11]       [,12]
#>  [1,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [2,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [3,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [4,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [5,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [6,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [7,]  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [8,] -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [9,] -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803
#> [10,] -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803
#> [11,] -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803
#> [12,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000
#> [13,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [14,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [15,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [16,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [17,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [18,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [19,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [20,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [21,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [22,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [23,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [24,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [25,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [26,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [27,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [28,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [29,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [30,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>             [,13]       [,14]       [,15]       [,16]       [,17]       [,18]
#>  [1,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [2,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [3,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [4,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [5,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [6,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [7,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [8,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [9,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [10,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [11,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [12,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [13,]  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [14,] -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [15,] -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803
#> [16,] -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803
#> [17,] -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803
#> [18,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000
#> [19,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [20,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [21,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [22,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [23,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [24,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [25,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [26,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [27,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [28,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [29,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [30,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>             [,19]       [,20]       [,21]       [,22]       [,23]       [,24]
#>  [1,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [2,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [3,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [4,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [5,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [6,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [7,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [8,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [9,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [10,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [11,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [12,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [13,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [14,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [15,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [16,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [17,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [18,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [19,]  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [20,] -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [21,] -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803
#> [22,] -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803
#> [23,] -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803
#> [24,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000
#> [25,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [26,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [27,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [28,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [29,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [30,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>             [,25]       [,26]       [,27]       [,28]       [,29]       [,30]
#>  [1,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [2,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [3,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [4,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [5,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [6,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [7,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [8,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#>  [9,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [10,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [11,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [12,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [13,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [14,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [15,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [16,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [17,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [18,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [19,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [20,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [21,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [22,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [23,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [24,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [25,]  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [26,] -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803 -0.02344803
#> [27,] -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803 -0.02344803
#> [28,] -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803 -0.02344803
#> [29,] -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000 -0.02344803
#> [30,] -0.02344803 -0.02344803 -0.02344803 -0.02344803 -0.02344803  1.00000000