icdglm.fit: 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
Usage
Arguments
Value
References
See Also
Examples
Description
This function applies the EM algorithm by the method of weights to incomplete data in a general linearized model.
Usage
1
2
Arguments
x
a vector, matrix, list or data frame containing the independent variables
y
a vector of integers or numerics. This is the dependent variable.
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.
family
family for glm.fit. See glm or family for more details. Default is binomial(link = "logit").
control
a list of control characteristics. See glm.control for further information. Default settings are: epsilon = 1e-10, maxit = 100, trace = FALSE.
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
1
2
3
4
5
6
7
8
9
10
11
12
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))
Example output
Deviance deviation = 0.9991132 Iterations = 1
Deviance deviation = 0.001017535 Iterations = 2
Deviance deviation = 6.3549e-05 Iterations = 3
Deviance deviation = 1.173515e-06 Iterations = 4
Deviance deviation = 1.195021e-05 Iterations = 5
Deviance deviation = 1.530168e-05 Iterations = 6
Deviance deviation = 1.617554e-05 Iterations = 7
Deviance deviation = 1.578342e-05 Iterations = 8
Deviance deviation = 1.471047e-05 Iterations = 9
Deviance deviation = 1.330836e-05 Iterations = 10
Deviance deviation = 1.179385e-05 Iterations = 11
Deviance deviation = 1.029671e-05 Iterations = 12
Deviance deviation = 8.890071e-06 Iterations = 13
Deviance deviation = 7.610768e-06 Iterations = 14
Deviance deviation = 6.472902e-06 Iterations = 15
Deviance deviation = 5.476863e-06 Iterations = 16
Deviance deviation = 4.615211e-06 Iterations = 17
Deviance deviation = 3.876454e-06 Iterations = 18
Deviance deviation = 3.247422e-06 Iterations = 19
Deviance deviation = 2.714703e-06 Iterations = 20
Deviance deviation = 2.265471e-06 Iterations = 21
Deviance deviation = 1.88793e-06 Iterations = 22
Deviance deviation = 1.571506e-06 Iterations = 23
Deviance deviation = 1.30689e-06 Iterations = 24
Deviance deviation = 1.085995e-06 Iterations = 25
Deviance deviation = 9.018657e-07 Iterations = 26
Deviance deviation = 7.485662e-07 Iterations = 27
Deviance deviation = 6.210584e-07 Iterations = 28
Deviance deviation = 5.150877e-07 Iterations = 29
Deviance deviation = 4.270743e-07 Iterations = 30
Deviance deviation = 3.540146e-07 Iterations = 31
Deviance deviation = 2.933949e-07 Iterations = 32
Deviance deviation = 2.431155e-07 Iterations = 33
Deviance deviation = 2.014252e-07 Iterations = 34
Deviance deviation = 1.668653e-07 Iterations = 35
Deviance deviation = 1.382223e-07 Iterations = 36
Deviance deviation = 1.144872e-07 Iterations = 37
Deviance deviation = 9.482177e-08 Iterations = 38
Deviance deviation = 7.853013e-08 Iterations = 39
Deviance deviation = 6.503479e-08 Iterations = 40
Deviance deviation = 5.385667e-08 Iterations = 41
Deviance deviation = 4.459851e-08 Iterations = 42
Deviance deviation = 3.693095e-08 Iterations = 43
Deviance deviation = 3.0581e-08 Iterations = 44
Deviance deviation = 2.532244e-08 Iterations = 45
Deviance deviation = 2.096783e-08 Iterations = 46
Deviance deviation = 1.736186e-08 Iterations = 47
Deviance deviation = 1.437589e-08 Iterations = 48
Deviance deviation = 1.190337e-08 Iterations = 49
Deviance deviation = 9.856037e-09 Iterations = 50
Deviance deviation = 8.160791e-09 Iterations = 51
Deviance deviation = 6.757099e-09 Iterations = 52
Deviance deviation = 5.594827e-09 Iterations = 53
Deviance deviation = 4.63246e-09 Iterations = 54
Deviance deviation = 3.835621e-09 Iterations = 55
Deviance deviation = 3.17584e-09 Iterations = 56
Deviance deviation = 2.629547e-09 Iterations = 57
Deviance deviation = 2.177221e-09 Iterations = 58
Deviance deviation = 1.802701e-09 Iterations = 59
Deviance deviation = 1.492603e-09 Iterations = 60
Deviance deviation = 1.235847e-09 Iterations = 61
Deviance deviation = 1.023257e-09 Iterations = 62
Deviance deviation = 8.47236e-10 Iterations = 63
Deviance deviation = 7.014939e-10 Iterations = 64
Deviance deviation = 5.808224e-10 Iterations = 65
Deviance deviation = 4.809087e-10 Iterations = 66
Deviance deviation = 3.981822e-10 Iterations = 67
Deviance deviation = 3.296862e-10 Iterations = 68
Deviance deviation = 2.729731e-10 Iterations = 69
Deviance deviation = 2.260158e-10 Iterations = 70
Deviance deviation = 1.87136e-10 Iterations = 71
Deviance deviation = 1.549446e-10 Iterations = 72
Deviance deviation = 1.282906e-10 Iterations = 73
Deviance deviation = 1.062218e-10 Iterations = 74
Deviance deviation = 8.794948e-11 Iterations = 75
[1] 75
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] 8.289316e-01 1.710684e-01 6.755730e-01 3.244270e-01 4.733534e-01
[6] 9.999996e-01 5.125468e-01 5.125468e-01 3.485040e-01 9.999996e-01
[11] 9.999996e-01 9.999996e-01 9.999996e-01 3.899821e-01 8.333737e-02
[16] 2.572849e-01 5.498059e-02 1.235546e-01 8.546019e-02 5.266466e-01
[21] 4.010612e-07 4.874532e-01 4.874532e-01 6.514960e-01 3.829282e-07
[26] 3.829282e-07 3.829282e-07 3.829282e-07 3.708890e-01 1.557915e-01
[31] 2.446885e-01 1.027812e-01 1.312500e-01 3.272513e-08 1.000000e+00
[36] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[41] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[46] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[51] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[56] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[61] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[66] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[71] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[76] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[81] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[86] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[91] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[96] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[101] 1.000000e+00 1.000000e+00 1.000000e+00
[1] 2.072329e-01 4.275410e-02 1.688933e-01 7.806193e-02 1.138958e-01
[6] 2.389248e-01 1.281367e-01 1.281367e-01 8.709951e-02 2.389248e-01
[11] 2.389248e-01 2.389248e-01 2.389248e-01 9.749552e-02 2.082801e-02
[16] 6.432122e-02 1.374097e-02 2.972907e-02 2.041856e-02 1.277940e-01
[21] 1.168046e-07 1.217981e-01 1.217981e-01 1.628687e-01 1.115235e-07
[26] 1.115235e-07 1.115235e-07 1.115235e-07 9.267265e-02 3.894662e-02
[31] 6.113941e-02 2.569446e-02 3.184862e-02 9.530824e-09 2.500000e-01
[36] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01
[41] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.498663e-01
[46] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01
[51] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.406148e-01
[56] 2.406148e-01 2.406148e-01 2.406148e-01 2.406148e-01 2.406148e-01
[61] 2.426561e-01 2.426561e-01 2.499919e-01 2.499919e-01 2.499919e-01
[66] 2.499919e-01 2.499919e-01 2.499919e-01 2.499919e-01 2.499240e-01
[71] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01
[76] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.498663e-01
[81] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01
[86] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.406148e-01
[91] 2.406148e-01 2.426561e-01 2.426561e-01 2.426561e-01 2.426561e-01
[96] 2.426561e-01 2.426561e-01 2.426561e-01 2.499240e-01 2.499240e-01
[101] 2.499240e-01 2.499919e-01 2.389249e-01
[1] 0.5000000 0.5087168 0.5000000 0.5968771 0.5968771 0.6052384 0.5000000
[8] 0.5000000 0.5087168 0.6052384 0.6052384 0.6052384 0.6052384 0.5000000
[15] 0.5087168 0.5000000 0.5087168 0.5968771 0.6052384 0.5856966 0.5941321
[22] 0.4884354 0.4884354 0.4971510 0.5941321 0.5941321 0.5941321 0.5941321
[29] 0.4884354 0.4971510 0.4884354 0.4971510 0.5856966 0.5941321 0.5000000
[36] 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000
[43] 0.5000000 0.5000000 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354
[50] 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354 0.5968771 0.5968771
[57] 0.5968771 0.5968771 0.5968771 0.5968771 0.5856966 0.5856966 0.4971510
[64] 0.4971510 0.4971510 0.4971510 0.4971510 0.4971510 0.4971510 0.5087168
[71] 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000
[78] 0.5000000 0.5000000 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354
[85] 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354 0.5968771 0.5968771
[92] 0.5856966 0.5856966 0.5856966 0.5856966 0.5856966 0.5856966 0.5856966
[99] 0.5087168 0.5087168 0.5087168 0.4971510 0.6052384
x1 x2 x3
x1 4.596889 1.441787 2.113460
x2 1.441787 5.684824 2.238459
x3 2.113460 2.238459 9.506458
icdGLM documentation built on May 2, 2019, 9:16 a.m.
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Description Usage Arguments Value References See Also Examples
Description
This function applies the EM algorithm by the method of weights to incomplete data in a general linearized model.
Usage
1 2 |
Arguments
x |
a vector, matrix, list or data frame containing the independent variables |
y |
a vector of integers or numerics. This is the dependent variable. |
weights |
a vector which attaches a weight to each observation. For incomplete data, this is obtained from |
indicator |
a vector that indicates which observations belong to each other. This is obtained from |
family |
family for glm.fit. See |
control |
a list of control characteristics. See |
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.fitoutput for the last iteration. Seeglm.fitfor 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
1 2 3 4 5 6 7 8 9 10 11 12 | 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))
|
Example output
Deviance deviation = 0.9991132 Iterations = 1
Deviance deviation = 0.001017535 Iterations = 2
Deviance deviation = 6.3549e-05 Iterations = 3
Deviance deviation = 1.173515e-06 Iterations = 4
Deviance deviation = 1.195021e-05 Iterations = 5
Deviance deviation = 1.530168e-05 Iterations = 6
Deviance deviation = 1.617554e-05 Iterations = 7
Deviance deviation = 1.578342e-05 Iterations = 8
Deviance deviation = 1.471047e-05 Iterations = 9
Deviance deviation = 1.330836e-05 Iterations = 10
Deviance deviation = 1.179385e-05 Iterations = 11
Deviance deviation = 1.029671e-05 Iterations = 12
Deviance deviation = 8.890071e-06 Iterations = 13
Deviance deviation = 7.610768e-06 Iterations = 14
Deviance deviation = 6.472902e-06 Iterations = 15
Deviance deviation = 5.476863e-06 Iterations = 16
Deviance deviation = 4.615211e-06 Iterations = 17
Deviance deviation = 3.876454e-06 Iterations = 18
Deviance deviation = 3.247422e-06 Iterations = 19
Deviance deviation = 2.714703e-06 Iterations = 20
Deviance deviation = 2.265471e-06 Iterations = 21
Deviance deviation = 1.88793e-06 Iterations = 22
Deviance deviation = 1.571506e-06 Iterations = 23
Deviance deviation = 1.30689e-06 Iterations = 24
Deviance deviation = 1.085995e-06 Iterations = 25
Deviance deviation = 9.018657e-07 Iterations = 26
Deviance deviation = 7.485662e-07 Iterations = 27
Deviance deviation = 6.210584e-07 Iterations = 28
Deviance deviation = 5.150877e-07 Iterations = 29
Deviance deviation = 4.270743e-07 Iterations = 30
Deviance deviation = 3.540146e-07 Iterations = 31
Deviance deviation = 2.933949e-07 Iterations = 32
Deviance deviation = 2.431155e-07 Iterations = 33
Deviance deviation = 2.014252e-07 Iterations = 34
Deviance deviation = 1.668653e-07 Iterations = 35
Deviance deviation = 1.382223e-07 Iterations = 36
Deviance deviation = 1.144872e-07 Iterations = 37
Deviance deviation = 9.482177e-08 Iterations = 38
Deviance deviation = 7.853013e-08 Iterations = 39
Deviance deviation = 6.503479e-08 Iterations = 40
Deviance deviation = 5.385667e-08 Iterations = 41
Deviance deviation = 4.459851e-08 Iterations = 42
Deviance deviation = 3.693095e-08 Iterations = 43
Deviance deviation = 3.0581e-08 Iterations = 44
Deviance deviation = 2.532244e-08 Iterations = 45
Deviance deviation = 2.096783e-08 Iterations = 46
Deviance deviation = 1.736186e-08 Iterations = 47
Deviance deviation = 1.437589e-08 Iterations = 48
Deviance deviation = 1.190337e-08 Iterations = 49
Deviance deviation = 9.856037e-09 Iterations = 50
Deviance deviation = 8.160791e-09 Iterations = 51
Deviance deviation = 6.757099e-09 Iterations = 52
Deviance deviation = 5.594827e-09 Iterations = 53
Deviance deviation = 4.63246e-09 Iterations = 54
Deviance deviation = 3.835621e-09 Iterations = 55
Deviance deviation = 3.17584e-09 Iterations = 56
Deviance deviation = 2.629547e-09 Iterations = 57
Deviance deviation = 2.177221e-09 Iterations = 58
Deviance deviation = 1.802701e-09 Iterations = 59
Deviance deviation = 1.492603e-09 Iterations = 60
Deviance deviation = 1.235847e-09 Iterations = 61
Deviance deviation = 1.023257e-09 Iterations = 62
Deviance deviation = 8.47236e-10 Iterations = 63
Deviance deviation = 7.014939e-10 Iterations = 64
Deviance deviation = 5.808224e-10 Iterations = 65
Deviance deviation = 4.809087e-10 Iterations = 66
Deviance deviation = 3.981822e-10 Iterations = 67
Deviance deviation = 3.296862e-10 Iterations = 68
Deviance deviation = 2.729731e-10 Iterations = 69
Deviance deviation = 2.260158e-10 Iterations = 70
Deviance deviation = 1.87136e-10 Iterations = 71
Deviance deviation = 1.549446e-10 Iterations = 72
Deviance deviation = 1.282906e-10 Iterations = 73
Deviance deviation = 1.062218e-10 Iterations = 74
Deviance deviation = 8.794948e-11 Iterations = 75
[1] 75
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] 8.289316e-01 1.710684e-01 6.755730e-01 3.244270e-01 4.733534e-01
[6] 9.999996e-01 5.125468e-01 5.125468e-01 3.485040e-01 9.999996e-01
[11] 9.999996e-01 9.999996e-01 9.999996e-01 3.899821e-01 8.333737e-02
[16] 2.572849e-01 5.498059e-02 1.235546e-01 8.546019e-02 5.266466e-01
[21] 4.010612e-07 4.874532e-01 4.874532e-01 6.514960e-01 3.829282e-07
[26] 3.829282e-07 3.829282e-07 3.829282e-07 3.708890e-01 1.557915e-01
[31] 2.446885e-01 1.027812e-01 1.312500e-01 3.272513e-08 1.000000e+00
[36] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[41] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[46] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[51] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[56] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[61] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[66] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[71] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[76] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[81] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[86] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[91] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[96] 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00 1.000000e+00
[101] 1.000000e+00 1.000000e+00 1.000000e+00
[1] 2.072329e-01 4.275410e-02 1.688933e-01 7.806193e-02 1.138958e-01
[6] 2.389248e-01 1.281367e-01 1.281367e-01 8.709951e-02 2.389248e-01
[11] 2.389248e-01 2.389248e-01 2.389248e-01 9.749552e-02 2.082801e-02
[16] 6.432122e-02 1.374097e-02 2.972907e-02 2.041856e-02 1.277940e-01
[21] 1.168046e-07 1.217981e-01 1.217981e-01 1.628687e-01 1.115235e-07
[26] 1.115235e-07 1.115235e-07 1.115235e-07 9.267265e-02 3.894662e-02
[31] 6.113941e-02 2.569446e-02 3.184862e-02 9.530824e-09 2.500000e-01
[36] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01
[41] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.498663e-01
[46] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01
[51] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.406148e-01
[56] 2.406148e-01 2.406148e-01 2.406148e-01 2.406148e-01 2.406148e-01
[61] 2.426561e-01 2.426561e-01 2.499919e-01 2.499919e-01 2.499919e-01
[66] 2.499919e-01 2.499919e-01 2.499919e-01 2.499919e-01 2.499240e-01
[71] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01
[76] 2.500000e-01 2.500000e-01 2.500000e-01 2.500000e-01 2.498663e-01
[81] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01
[86] 2.498663e-01 2.498663e-01 2.498663e-01 2.498663e-01 2.406148e-01
[91] 2.406148e-01 2.426561e-01 2.426561e-01 2.426561e-01 2.426561e-01
[96] 2.426561e-01 2.426561e-01 2.426561e-01 2.499240e-01 2.499240e-01
[101] 2.499240e-01 2.499919e-01 2.389249e-01
[1] 0.5000000 0.5087168 0.5000000 0.5968771 0.5968771 0.6052384 0.5000000
[8] 0.5000000 0.5087168 0.6052384 0.6052384 0.6052384 0.6052384 0.5000000
[15] 0.5087168 0.5000000 0.5087168 0.5968771 0.6052384 0.5856966 0.5941321
[22] 0.4884354 0.4884354 0.4971510 0.5941321 0.5941321 0.5941321 0.5941321
[29] 0.4884354 0.4971510 0.4884354 0.4971510 0.5856966 0.5941321 0.5000000
[36] 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000
[43] 0.5000000 0.5000000 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354
[50] 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354 0.5968771 0.5968771
[57] 0.5968771 0.5968771 0.5968771 0.5968771 0.5856966 0.5856966 0.4971510
[64] 0.4971510 0.4971510 0.4971510 0.4971510 0.4971510 0.4971510 0.5087168
[71] 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000 0.5000000
[78] 0.5000000 0.5000000 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354
[85] 0.4884354 0.4884354 0.4884354 0.4884354 0.4884354 0.5968771 0.5968771
[92] 0.5856966 0.5856966 0.5856966 0.5856966 0.5856966 0.5856966 0.5856966
[99] 0.5087168 0.5087168 0.5087168 0.4971510 0.6052384
x1 x2 x3
x1 4.596889 1.441787 2.113460
x2 1.441787 5.684824 2.238459
x3 2.113460 2.238459 9.506458
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