plot.hglm: Plot Hierarchical Generalized Linear Model Objects
In hglm: Hierarchical Generalized Linear Models
Description
Usage
Arguments
Details
Author(s)
Examples
Description
Plots residuals for the mean and dispersion models, individual deviances and hatvalues for hglm objects
Usage
1
2
3
Arguments
x
the hglm object to be plotted
pch
symbol used in the plots
pcol
color of points
lcol
color of lines
device
if NULL, plot on screen devices, if 'pdf', plot to PDF files in the current working directory.
name
a string gives the main name of the PDF file when device = 'pdf'.
...
graphical parameters
Details
A S3 generic plot method for hglm objects. It produces a set of diagnostic plots for a hierarchical model.
Author(s)
Xia Shen
Examples
1
2
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# --------------------- #
# semiconductor example #
# --------------------- #
data(semiconductor)
h.gamma.normal <- hglm(fixed = y ~ x1 + x3 + x5 + x6,
random = ~ 1|Device,
family = Gamma(link = log),
disp = ~ x2 + x3, data = semiconductor)
summary(h.gamma.normal)
plot(h.gamma.normal, cex = .6, pch = 1,
cex.axis = 1/.6, cex.lab = 1/.6,
cex.main = 1/.6, mar = c(3, 4.5, 0, 1.5))
# ------------------- #
# redo it using hglm2 #
# ------------------- #
m1 <- hglm2(y ~ x1 + x3 + x5 + x6 + (1|Device),
family = Gamma(link = log),
disp = ~ x2 + x3, data = semiconductor)
summary(m1)
plot(m1, cex = .6, pch = 1,
cex.axis = 1/.6, cex.lab = 1/.6,
cex.main = 1/.6, mar = c(3, 4.5, 0, 1.5))
# --------------------------------------------- #
# simulated example with 2 random effects terms #
# --------------------------------------------- #
## Not run:
set.seed(911)
x1 <- rnorm(100)
x2 <- rnorm(100)
x3 <- rnorm(100)
z1 <- factor(rep(LETTERS[1:10], rep(10, 10)))
z2 <- factor(rep(letters[1:5], rep(20, 5)))
Z1 <- model.matrix(~ 0 + z1)
Z2 <- model.matrix(~ 0 + z2)
u1 <- rnorm(10, 0, sqrt(2))
u2 <- rnorm(5, 0, sqrt(3))
y <- 1 + 2*x1 + 3*x2 + Z1%*%u1 + Z2%*%u2 + rnorm(100, 0, sqrt(exp(x3)))
dd <- data.frame(x1 = x1, x2 = x2, x3 = x3, z1 = z1, z2 = z2, y = y)
(m2.1 <- hglm(X = cbind(rep(1, 100), x1, x2), y = y, Z = cbind(Z1, Z2),
RandC = c(10, 5)))
summary(m2.1)
plot(m2.1)
(m2.2 <- hglm2(y ~ x1 + x2 + (1|z1) + (1|z2), data = dd, vcovmat = TRUE))
image(m2.2$vcov)
summary(m2.2)
plot(m2.2)
m3 <- hglm2(y ~ x1 + x2 + (1|z1) + (1|z2), disp = ~ x3, data = dd)
print (m3)
summary(m3)
plot(m3)
## End(Not run)
Example output
Loading required package: Matrix
Loading required package: MASS
Loading required package: hglm.data
Loading required package: sp
hglm: Hierarchical Generalized Linear Models
Version 2.2-1 (2019-04-04) installed
Authors: Moudud Alam, Lars Ronnegard, Xia Shen
Maintainer: Xia Shen <xia.shen@ki.se>
Use citation("hglm") to know how to cite our work.
Discussion: https://r-forge.r-project.org/forum/?group_id=558
BugReports: https://r-forge.r-project.org/tracker/?group_id=558
VideoTutorials: http://www.youtube.com/playlist?list=PLn1OmZECD-n15vnYzvJDy5GxjNpVV5Jr8
Call:
hglm.formula(family = Gamma(link = log), fixed = y ~ x1 + x3 +
x5 + x6, random = ~1 | Device, disp = ~x2 + x3, data = semiconductor)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) -4.71168 0.06696 -70.368 < 2e-16 ***
x1 0.20979 0.06638 3.160 0.00263 **
x3 0.32893 0.06696 4.913 9.34e-06 ***
x5 -0.17314 0.06638 -2.608 0.01185 *
x6 -0.35690 0.06633 -5.380 1.80e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 52 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
as.factor(Device)1 0.2724 0.1787
as.factor(Device)2 0.0097 0.1787
as.factor(Device)3 -0.2697 0.1584
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
(Intercept) -2.5887 0.1972
x2 -0.6861 0.1971
x3 -0.5024 0.1971
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 0.0486
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
-3.0242 0.5172
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots1.pdf")
dev.new(): using pdf(file="Rplots2.pdf")
Call:
hglm2.formula(meanmodel = y ~ x1 + x3 + x5 + x6 + (1 | Device),
data = semiconductor, family = Gamma(link = log), disp = ~x2 +
x3)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) -4.71168 0.06696 -70.368 < 2e-16 ***
x1 0.20979 0.06638 3.160 0.00263 **
x3 0.32893 0.06696 4.913 9.34e-06 ***
x5 -0.17314 0.06638 -2.608 0.01185 *
x6 -0.35690 0.06633 -5.380 1.80e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 52 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| Device:1 0.2724 0.1787
(Intercept)| Device:2 0.0097 0.1787
(Intercept)| Device:3 -0.2697 0.1584
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
(Intercept) -2.5887 0.1972
x2 -0.6861 0.1971
x3 -0.5024 0.1971
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 0.0486
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
-3.0242 0.5172
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots3.pdf")
dev.new(): using pdf(file="Rplots4.pdf")
dev.new(): using pdf(file="Rplots5.pdf")
Call:
hglm.default(X = cbind(rep(1, 100), x1, x2), y = y, Z = cbind(Z1,
Z2), RandC = c(10, 5))
---------------------------
Estimates of the mean model
---------------------------
Fixed effects:
x1 x2
1.593223 2.163230 2.875127
Random effects:
z1A z1B z1C
0.5876582 0.7925926 -1.3893579
...
z1I z1J
-1.071900 1.615409
NOTE: to show all the random effects estimates, use print(hglm.object, print.ranef = TRUE).
Random effects:
z2a z2b z2c z2d z2e
1.0972865 -1.2008286 0.5139767 -0.8425195 0.4320849
Dispersion parameter for the mean model: 1.574819
Dispersion parameter for the random effects: 2.079812 1.597671
Estimation converged in 4 iterations
Call:
hglm.default(X = cbind(rep(1, 100), x1, x2), y = y, Z = cbind(Z1,
Z2), RandC = c(10, 5))
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
1.5932 0.7410 2.15 0.0343 *
x1 2.1632 0.1321 16.38 <2e-16 ***
x2 2.8751 0.1210 23.77 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 88 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
z1A 0.5877 0.8920
z1B 0.7926 0.8911
z1C -1.3894 0.8918
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
Summary of the random effects estimates:
Estimate Std. Error
z2a 1.0973 0.9263
z2b -1.2008 0.9254
z2c 0.5140 0.9254
z2d -0.8425 0.9255
z2e 0.4321 0.9252
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Dispersion parameter for the mean model:
[1] 1.574819
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
0.4541 0.1503
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 2.080 1.598
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
0.7323 0.5707
.|Random2
Estimate Std. Error
0.4685 0.9162
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots6.pdf")
dev.new(): using pdf(file="Rplots7.pdf")
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, vcovmat = TRUE)
---------------------------
Estimates of the mean model
---------------------------
Fixed effects:
(Intercept) x1 x2
1.593223 2.163230 2.875127
Random effects:
(Intercept)| z1:A (Intercept)| z1:B (Intercept)| z1:C
0.5876582 0.7925926 -1.3893579
...
(Intercept)| z1:I (Intercept)| z1:J
-1.071900 1.615409
NOTE: to show all the random effects estimates, use print(hglm.object, print.ranef = TRUE).
Random effects:
(Intercept)| z2:a (Intercept)| z2:b (Intercept)| z2:c (Intercept)| z2:d
1.0972865 -1.2008286 0.5139767 -0.8425195
(Intercept)| z2:e
0.4320849
Dispersion parameter for the mean model: 1.574819
Dispersion parameter for the random effects: 2.079812 1.597671
Estimation converged in 4 iterations
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, vcovmat = TRUE)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 1.5932 0.7410 2.15 0.0343 *
x1 2.1632 0.1321 16.38 <2e-16 ***
x2 2.8751 0.1210 23.77 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 88 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z1:A 0.5877 0.8920
(Intercept)| z1:B 0.7926 0.8911
(Intercept)| z1:C -1.3894 0.8918
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z2:a 1.0973 0.9263
(Intercept)| z2:b -1.2008 0.9254
(Intercept)| z2:c 0.5140 0.9254
(Intercept)| z2:d -0.8425 0.9255
(Intercept)| z2:e 0.4321 0.9252
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Dispersion parameter for the mean model:
[1] 1.574819
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
0.4541 0.1503
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 2.080 1.598
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
0.7323 0.5707
.|Random2
Estimate Std. Error
0.4685 0.9162
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots8.pdf")
dev.new(): using pdf(file="Rplots9.pdf")
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, disp = ~x3)
---------------------------
Estimates of the mean model
---------------------------
Fixed effects:
(Intercept) x1 x2
1.676184 2.148076 2.989964
Random effects:
(Intercept)| z1:A (Intercept)| z1:B (Intercept)| z1:C
0.1914595 1.3496934 -1.2882400
...
(Intercept)| z1:I (Intercept)| z1:J
-1.327242 1.596106
NOTE: to show all the random effects estimates, use print(hglm.object, print.ranef = TRUE).
Random effects:
(Intercept)| z2:a (Intercept)| z2:b (Intercept)| z2:c (Intercept)| z2:d
0.8394165 -0.9463058 0.5146495 -0.5542017
(Intercept)| z2:e
0.1464415
------------------------------------------
Estimates of the residual dispersion model
------------------------------------------
Link = log
Effects:
(Intercept) x3
-0.1065797 0.9969769
Dispersion parameter for the random effects: 2.041197 1.067874
Estimation converged in 6 iterations
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, disp = ~x3)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 1.67618 0.65467 2.56 0.0122 *
x1 2.14808 0.08218 26.14 <2e-16 ***
x2 2.98996 0.07374 40.55 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 88 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z1:A 0.1915 0.8087
(Intercept)| z1:B 1.3497 0.8047
(Intercept)| z1:C -1.2882 0.8179
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z2:a 0.8394 0.8051
(Intercept)| z2:b -0.9463 0.8055
(Intercept)| z2:c 0.5146 0.8051
(Intercept)| z2:d -0.5542 0.8049
(Intercept)| z2:e 0.1464 0.8070
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
(Intercept) -0.1066 0.1516
x3 0.9970 0.1485
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 2.041 1.068
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
0.7135 0.5449
.|Random2
Estimate Std. Error
0.0657 0.9867
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 6 iterations.
dev.new(): using pdf(file="Rplots10.pdf")
dev.new(): using pdf(file="Rplots11.pdf")
dev.new(): using pdf(file="Rplots12.pdf")
hglm documentation built on May 2, 2019, 6:11 p.m.
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Description Usage Arguments Details Author(s) Examples
Description
Plots residuals for the mean and dispersion models, individual deviances and hatvalues for hglm objects
Usage
1 2 3 |
Arguments
x |
the |
pch |
symbol used in the plots |
pcol |
color of points |
lcol |
color of lines |
device |
if |
name |
a string gives the main name of the PDF file when |
... |
graphical parameters |
Details
A S3 generic plot method for hglm objects. It produces a set of diagnostic plots for a hierarchical model.
Author(s)
Xia Shen
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 | # --------------------- #
# semiconductor example #
# --------------------- #
data(semiconductor)
h.gamma.normal <- hglm(fixed = y ~ x1 + x3 + x5 + x6,
random = ~ 1|Device,
family = Gamma(link = log),
disp = ~ x2 + x3, data = semiconductor)
summary(h.gamma.normal)
plot(h.gamma.normal, cex = .6, pch = 1,
cex.axis = 1/.6, cex.lab = 1/.6,
cex.main = 1/.6, mar = c(3, 4.5, 0, 1.5))
# ------------------- #
# redo it using hglm2 #
# ------------------- #
m1 <- hglm2(y ~ x1 + x3 + x5 + x6 + (1|Device),
family = Gamma(link = log),
disp = ~ x2 + x3, data = semiconductor)
summary(m1)
plot(m1, cex = .6, pch = 1,
cex.axis = 1/.6, cex.lab = 1/.6,
cex.main = 1/.6, mar = c(3, 4.5, 0, 1.5))
# --------------------------------------------- #
# simulated example with 2 random effects terms #
# --------------------------------------------- #
## Not run:
set.seed(911)
x1 <- rnorm(100)
x2 <- rnorm(100)
x3 <- rnorm(100)
z1 <- factor(rep(LETTERS[1:10], rep(10, 10)))
z2 <- factor(rep(letters[1:5], rep(20, 5)))
Z1 <- model.matrix(~ 0 + z1)
Z2 <- model.matrix(~ 0 + z2)
u1 <- rnorm(10, 0, sqrt(2))
u2 <- rnorm(5, 0, sqrt(3))
y <- 1 + 2*x1 + 3*x2 + Z1%*%u1 + Z2%*%u2 + rnorm(100, 0, sqrt(exp(x3)))
dd <- data.frame(x1 = x1, x2 = x2, x3 = x3, z1 = z1, z2 = z2, y = y)
(m2.1 <- hglm(X = cbind(rep(1, 100), x1, x2), y = y, Z = cbind(Z1, Z2),
RandC = c(10, 5)))
summary(m2.1)
plot(m2.1)
(m2.2 <- hglm2(y ~ x1 + x2 + (1|z1) + (1|z2), data = dd, vcovmat = TRUE))
image(m2.2$vcov)
summary(m2.2)
plot(m2.2)
m3 <- hglm2(y ~ x1 + x2 + (1|z1) + (1|z2), disp = ~ x3, data = dd)
print (m3)
summary(m3)
plot(m3)
## End(Not run)
|
Example output
Loading required package: Matrix
Loading required package: MASS
Loading required package: hglm.data
Loading required package: sp
hglm: Hierarchical Generalized Linear Models
Version 2.2-1 (2019-04-04) installed
Authors: Moudud Alam, Lars Ronnegard, Xia Shen
Maintainer: Xia Shen <xia.shen@ki.se>
Use citation("hglm") to know how to cite our work.
Discussion: https://r-forge.r-project.org/forum/?group_id=558
BugReports: https://r-forge.r-project.org/tracker/?group_id=558
VideoTutorials: http://www.youtube.com/playlist?list=PLn1OmZECD-n15vnYzvJDy5GxjNpVV5Jr8
Call:
hglm.formula(family = Gamma(link = log), fixed = y ~ x1 + x3 +
x5 + x6, random = ~1 | Device, disp = ~x2 + x3, data = semiconductor)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) -4.71168 0.06696 -70.368 < 2e-16 ***
x1 0.20979 0.06638 3.160 0.00263 **
x3 0.32893 0.06696 4.913 9.34e-06 ***
x5 -0.17314 0.06638 -2.608 0.01185 *
x6 -0.35690 0.06633 -5.380 1.80e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 52 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
as.factor(Device)1 0.2724 0.1787
as.factor(Device)2 0.0097 0.1787
as.factor(Device)3 -0.2697 0.1584
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
(Intercept) -2.5887 0.1972
x2 -0.6861 0.1971
x3 -0.5024 0.1971
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 0.0486
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
-3.0242 0.5172
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots1.pdf")
dev.new(): using pdf(file="Rplots2.pdf")
Call:
hglm2.formula(meanmodel = y ~ x1 + x3 + x5 + x6 + (1 | Device),
data = semiconductor, family = Gamma(link = log), disp = ~x2 +
x3)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) -4.71168 0.06696 -70.368 < 2e-16 ***
x1 0.20979 0.06638 3.160 0.00263 **
x3 0.32893 0.06696 4.913 9.34e-06 ***
x5 -0.17314 0.06638 -2.608 0.01185 *
x6 -0.35690 0.06633 -5.380 1.80e-06 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 52 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| Device:1 0.2724 0.1787
(Intercept)| Device:2 0.0097 0.1787
(Intercept)| Device:3 -0.2697 0.1584
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
(Intercept) -2.5887 0.1972
x2 -0.6861 0.1971
x3 -0.5024 0.1971
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 0.0486
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
-3.0242 0.5172
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots3.pdf")
dev.new(): using pdf(file="Rplots4.pdf")
dev.new(): using pdf(file="Rplots5.pdf")
Call:
hglm.default(X = cbind(rep(1, 100), x1, x2), y = y, Z = cbind(Z1,
Z2), RandC = c(10, 5))
---------------------------
Estimates of the mean model
---------------------------
Fixed effects:
x1 x2
1.593223 2.163230 2.875127
Random effects:
z1A z1B z1C
0.5876582 0.7925926 -1.3893579
...
z1I z1J
-1.071900 1.615409
NOTE: to show all the random effects estimates, use print(hglm.object, print.ranef = TRUE).
Random effects:
z2a z2b z2c z2d z2e
1.0972865 -1.2008286 0.5139767 -0.8425195 0.4320849
Dispersion parameter for the mean model: 1.574819
Dispersion parameter for the random effects: 2.079812 1.597671
Estimation converged in 4 iterations
Call:
hglm.default(X = cbind(rep(1, 100), x1, x2), y = y, Z = cbind(Z1,
Z2), RandC = c(10, 5))
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
1.5932 0.7410 2.15 0.0343 *
x1 2.1632 0.1321 16.38 <2e-16 ***
x2 2.8751 0.1210 23.77 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 88 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
z1A 0.5877 0.8920
z1B 0.7926 0.8911
z1C -1.3894 0.8918
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
Summary of the random effects estimates:
Estimate Std. Error
z2a 1.0973 0.9263
z2b -1.2008 0.9254
z2c 0.5140 0.9254
z2d -0.8425 0.9255
z2e 0.4321 0.9252
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Dispersion parameter for the mean model:
[1] 1.574819
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
0.4541 0.1503
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 2.080 1.598
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
0.7323 0.5707
.|Random2
Estimate Std. Error
0.4685 0.9162
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots6.pdf")
dev.new(): using pdf(file="Rplots7.pdf")
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, vcovmat = TRUE)
---------------------------
Estimates of the mean model
---------------------------
Fixed effects:
(Intercept) x1 x2
1.593223 2.163230 2.875127
Random effects:
(Intercept)| z1:A (Intercept)| z1:B (Intercept)| z1:C
0.5876582 0.7925926 -1.3893579
...
(Intercept)| z1:I (Intercept)| z1:J
-1.071900 1.615409
NOTE: to show all the random effects estimates, use print(hglm.object, print.ranef = TRUE).
Random effects:
(Intercept)| z2:a (Intercept)| z2:b (Intercept)| z2:c (Intercept)| z2:d
1.0972865 -1.2008286 0.5139767 -0.8425195
(Intercept)| z2:e
0.4320849
Dispersion parameter for the mean model: 1.574819
Dispersion parameter for the random effects: 2.079812 1.597671
Estimation converged in 4 iterations
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, vcovmat = TRUE)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 1.5932 0.7410 2.15 0.0343 *
x1 2.1632 0.1321 16.38 <2e-16 ***
x2 2.8751 0.1210 23.77 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 88 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z1:A 0.5877 0.8920
(Intercept)| z1:B 0.7926 0.8911
(Intercept)| z1:C -1.3894 0.8918
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z2:a 1.0973 0.9263
(Intercept)| z2:b -1.2008 0.9254
(Intercept)| z2:c 0.5140 0.9254
(Intercept)| z2:d -0.8425 0.9255
(Intercept)| z2:e 0.4321 0.9252
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Dispersion parameter for the mean model:
[1] 1.574819
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
0.4541 0.1503
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 2.080 1.598
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
0.7323 0.5707
.|Random2
Estimate Std. Error
0.4685 0.9162
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 4 iterations.
dev.new(): using pdf(file="Rplots8.pdf")
dev.new(): using pdf(file="Rplots9.pdf")
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, disp = ~x3)
---------------------------
Estimates of the mean model
---------------------------
Fixed effects:
(Intercept) x1 x2
1.676184 2.148076 2.989964
Random effects:
(Intercept)| z1:A (Intercept)| z1:B (Intercept)| z1:C
0.1914595 1.3496934 -1.2882400
...
(Intercept)| z1:I (Intercept)| z1:J
-1.327242 1.596106
NOTE: to show all the random effects estimates, use print(hglm.object, print.ranef = TRUE).
Random effects:
(Intercept)| z2:a (Intercept)| z2:b (Intercept)| z2:c (Intercept)| z2:d
0.8394165 -0.9463058 0.5146495 -0.5542017
(Intercept)| z2:e
0.1464415
------------------------------------------
Estimates of the residual dispersion model
------------------------------------------
Link = log
Effects:
(Intercept) x3
-0.1065797 0.9969769
Dispersion parameter for the random effects: 2.041197 1.067874
Estimation converged in 6 iterations
Call:
hglm2.formula(meanmodel = y ~ x1 + x2 + (1 | z1) + (1 | z2),
data = dd, disp = ~x3)
----------
MEAN MODEL
----------
Summary of the fixed effects estimates:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 1.67618 0.65467 2.56 0.0122 *
x1 2.14808 0.08218 26.14 <2e-16 ***
x2 2.98996 0.07374 40.55 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Note: P-values are based on 88 degrees of freedom
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z1:A 0.1915 0.8087
(Intercept)| z1:B 1.3497 0.8047
(Intercept)| z1:C -1.2882 0.8179
...
NOTE: to show all the random effects, use print(summary(hglm.object), print.ranef = TRUE).
Summary of the random effects estimates:
Estimate Std. Error
(Intercept)| z2:a 0.8394 0.8051
(Intercept)| z2:b -0.9463 0.8055
(Intercept)| z2:c 0.5146 0.8051
(Intercept)| z2:d -0.5542 0.8049
(Intercept)| z2:e 0.1464 0.8070
----------------
DISPERSION MODEL
----------------
NOTE: h-likelihood estimates through EQL can be biased.
Model estimates for the dispersion term:
Link = log
Effects:
Estimate Std. Error
(Intercept) -0.1066 0.1516
x3 0.9970 0.1485
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
Dispersion parameter for the random effects:
[1] 2.041 1.068
Dispersion model for the random effects:
Link = log
Effects:
.|Random1
Estimate Std. Error
0.7135 0.5449
.|Random2
Estimate Std. Error
0.0657 0.9867
Dispersion = 1 is used in Gamma model on deviances to calculate the standard error(s).
EQL estimation converged in 6 iterations.
dev.new(): using pdf(file="Rplots10.pdf")
dev.new(): using pdf(file="Rplots11.pdf")
dev.new(): using pdf(file="Rplots12.pdf")
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