mmm: an R function to fit the multivariate marginal models to...
In mmm: an R package for analyzing multivariate longitudinal data with multivariate marginal models
Description
Usage
Arguments
Value
Note
Author(s)
References
See Also
Examples
Description
fits multivariate marginal models to analyze multivariate longitudinal data, for both continuous and discrete responses
Usage
1
2
3
Arguments
formula
a formula expression, see the examples given below.
id
a vector for identification of the clusters.
data
an optional data frame.
correlation
a user specified square matrix for the working correlation matrix, appropriate when corstr="fixed".
initEstim
user specified initials for the parameter estimates.
tol
the tolerance which specifies the convergency of the algorithm.
maxiter
the maximum number of iterations to be consumed by the algorithm.
family
an object which defines the link and variance function. The possible choices are same with the ones in the "gee" package. For details see the gee documentation. Note that family=binomial handles multivariate longitudinal binary data, family=poisson handles multivariate longitudinal count data, family=gaussian handles multivariate longitudinal (normal type) continous data and family=gamma handles multivariate longitudinal (gamma type) continous data.
corStruct
a character string which defines the structure of the working correlation matrix. For details see the gee documentation.
Mv
specifies the lag value, e.g. specification of "corstr=AR-M" and "Mv=1" indicates AR(1).
silent
a logial variable which decides the print of the iterations.
scale.fix
a logical variable for fixing the scale parameter to a user specified value.
scale.value
a user specified scale parameter value, appropriate when scale.fix=TRUE.
Value
Returns an onject of the results. See the examples given below.
Note
Version 1.1.
Author(s)
Ozgur Asar, Ozlem Ilk
References
Asar, O. (2012). On multivariate longitudinal binary data models and their applications in forecasting. MS Thesis, Middle East Technical University.
Available online at http://www.lancaster.ac.uk/pg/asar/thesis-Ozgur-Asar
Asar, O., Ilk, O. (2013). mmm: an R package for analyzing multivariate longitudinal data with multivariate marginal models,
Computer Methods and Programs in Biomedicine, 112, 649-654.
Liang, K. L., Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
Shelton, B. J., Gilbert, G. H., Liu, B., Fisher, M. (2004). A SAS macro for the analysis of multivariate longitudinal binary outcomes. Computer Methods and Programs in Biomedicine, 76, 163-175.
Zeger, S. L., Liang, K. L (1986). Longitudinal data analysis for discrete and continous outcomes. Biometrics, 42, 121-130.
See Also
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
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
#########################
## Binary data example ##
#########################
data(motherStress)
fit1<-mmm(formula=cbind(stress,illness)~married+education+
employed+chlth+mhlth+race+csex+housize+bstress+billness+
week,id=motherStress$id,data=motherStress,family=binomial,corStruct="exchangeable")
summary(fit1)
########################
## Count data example ##
########################
## First we illustrate how the data set is simulated
## Then the R script to analyze the data set by mmm is given
## Note: no need to run the script to generate the data set, unless of interest
## Not run:
### Generating the data by the help of 'corcounts' package
# loading the package 'corcounts'
library("corcounts")
# setting the seed to 12
set.seed(12)
# number of subjects in the study
n1 <- 500
# defining the response and covariate families (Poi indicates Poisson distribution)
margins <- c("Poi","Poi","Poi","Poi","Poi","Poi","Poi","Poi","Poi")
# the means of the responses and covariate. while 5 and 8 are the means of the responses
# 20 is the mean of the time independent covariate
mu <- c(5, 8, 20, 5, 8, 5, 8, 5, 8)
# the correlation structure which 'corcounts' uses to generate correlated count data
# (unstr indicates unstructured correlation structure)
corstr <- "unstr"
# the correlation matrix corcounts assumes the correlated count data have
corpar<-matrix(c(1,0.4,0.6,0.9,0.37,0.8,0.34,0.7,0.31,
0.4,1,0.6,0.37,0.9,0.34,0.8,0.31,0.7,
0.6,0.6,1,0.6,0.6,0.6,0.6,0.6,0.6,
0.9,0.37,0.6,1,0.4,0.9,0.37,0.8,0.34,
0.37,0.9,0.6,0.4,1,0.37,0.9,0.34,0.8,
0.8,0.34,0.6,0.9,0.37,1,0.4,0.9,0.37,
0.34,0.8,0.6,0.37,0.9,0.4,1,0.37,0.9,
0.7,0.31,0.6,0.8,0.34,0.9,0.37,1,0.4,
0.31,0.7,0.6,0.34,0.8,0.37,0.9,0.4,1),ncol=9,byrow=T)
# generating the correlated count data by 'rcounts' function avaiable in 'corcounts'
data1 <- rcounts(N=n1,margins=margins,mu=mu,corstr=corstr,corpar=corpar)
### The reconstruction of the generated correlated count data to
### the longitudinal data (long) format
# seperating the bivariate responses measured at the first time
# point and the time independent covariate
time11<-data1[,1:3]
# seperating the bivariate responses measured at the second time
# point and combining them with the time independent covariate
time12<-cbind(data1[,4:5],data1[,3])
# seperating the bivariate responses measured at the third time
# point and combining them with the time independent covariate
time13<-cbind(data1[,6:7],data1[,3])
# seperating the bivariate responses measured at the fourth time
# point and combining them with the time independent covariate
time14<-cbind(data1[,8:9],data1[,3])
# combining the data for all the time points
data12<-rbind(time11,time12,time13,time14)
# constructing the time variable
time1<-matrix(rep(seq(1:4),each=n1))
# constructing the id variable
id1<-matrix(rep(seq(1:n1),4))
# combining the id of the subjects, the simulated data and the time variable
data13<-cbind(id1,data12,time1)
# reconstructing the data subject by subject which 'mmm' expects it has
data14<-NULL
for (i in 1:n1) data14<-rbind(data14,data13[data13[,1]==i,])
### Data manipulations on the covariates
# taking natural logarithm of the time independent covariate
data14[,4]<-log(data14[,4])
# standardizing time variable
data14[,5]<-scale(data14[,5])
# adding the interaction of the time independent covariate
# and time as a new covariate
multiLongCount<-as.data.frame(cbind(data14,data14[,4]*data14[,5]))
names(multiLongCount)<-c("ID","resp1","resp2","X","time","X.time")
## End(Not run)
### R script to analyze the count data set
### It is already stored in mmm pacakge
data(multiLongCount)
fit2<-mmm(formula=cbind(resp1,resp2)~X+time+X.time,
id=multiLongCount$ID,data=multiLongCount,family=poisson,corStruct="unstructured")
summary(fit2)
#############################
## Continuous data example ##
#############################
## First we illustrate how the data set is simulated
## Then the R script to analyze the data set by mmm is given
## Note: no need to run the script to generate the data set, unless of interest
## Not run:
### Generating the data by the help of mvtnorm package
# loading package 'mvtnorm'
library("mvtnorm")
# number of subjects in the study
n2<-500
# setting the seed to 12
set.seed(12)
# specifying the correlation matrix which 'mvtnorm' assumes the correlated data have
cormat<-matrix(c(1,0.4,0.6,0.9,0.37,0.8,0.34,0.7,0.31,
0.4,1,0.6,0.37,0.9,0.34,0.8,0.31,0.7,
0.6,0.6,1,0.6,0.6,0.6,0.6,0.6,0.6,
0.9,0.37,0.6,1,0.4,0.9,0.37,0.8,0.34,
0.37,0.9,0.6,0.4,1,0.37,0.9,0.34,0.8,
0.8,0.34,0.6,0.9,0.37,1,0.4,0.9,0.37,
0.34,0.8,0.6,0.37,0.9,0.4,1,0.37,0.9,
0.7,0.31,0.6,0.8,0.34,0.9,0.37,1,0.4,
0.31,0.7,0.6,0.34,0.8,0.37,0.9,0.4,1),ncol=9,byrow=T)
# variances of the responses and time independent covariate
# while 0.97 and 1.1 correspond to the variances of the bivariate responses
# 4 corresponds to the variance of the time independent covariate
variance<-c(0.97,1.1,4,0.97,1.1,0.97,1.1,0.97,1.1)
# constructing the (diaonal) standard deviation matrix
std<-diag(sqrt(variance),9)
# constructing the variance covariance matrix, sigma
sigma<-std
# generating the correlated continuous data utilizing 'rmvnorm' function available
# in 'mvtnorm'; method="svd" indicates use of 'singular value decomposition method
data2<-rmvnorm(n2,mean = rep(0,nrow(sigma)),sigma=sigma,method="svd")
### The reconstruction of the generated correlated continuous data to the
### longitudinal data (long) format
# seperating the bivariate responses measured at first time point
# and the time independent covariate
time21<-data2[,1:3]
# seperating the bivariate responses measured at second time point
# and combining them with the time independent covariate
time22<-cbind(data2[,4:5],data2[,3])
# seperating the bivariate responses measured at third time point
# and combining them with the time independent covariate
time23<-cbind(data2[,6:7],data2[,3])
# seperating the bivariate responses measured at fourth time point
# and combining them with the time independent covariate
time24<-cbind(data2[,8:9],data2[,3])
# combining the data for all the time points
data22<-rbind(time21,time22,time23,time24)
# constructing the time variable
time2<-matrix(rep(seq(1:4),each=n2))
# constructing the id variable
id2<-matrix(rep(seq(1:n2),4))
# combining the id of the subjects, the generated data and the time variable
data23<-cbind(id2,data22,time2)
# reconstructing the data subject by subject which 'mmm' expects it has
data24<-NULL
for (i in 1:n2) data24<-rbind(data24,data23[data23[,1]==i,])
### Data manipulations on the covariates
# standardizing the time variable
data24[,5]<-scale(data24[,5])
# adding the interaction of the time independent covariate
# and time as a new covariate
multiLongGaussian<-as.data.frame(cbind(data24,data24[,4]*data24[,5]))
names(multiLongGaussian)<-c("ID","resp1","resp2","X","time","X.time")
## End(Not run)
### R script to analyze the continuous data set
### It is already stored in mmm pacakge
data(multiLongGaussian)
fit3<-mmm(formula=cbind(resp1,resp2)~X+time+X.time,
id=multiLongGaussian$ID,data=multiLongGaussian,family=gaussian,corStruct="unstructured")
summary(fit3)
Example output
Loading required package: gee
Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
running glm to get initial regression estimate
stress.Intercept stress.married stress.education stress.employed
-2.180720871 0.019430701 0.378751056 -0.642639022
stress.chlth stress.mhlth stress.race stress.csex
-0.254767051 -0.185567901 0.061986473 -0.007871376
stress.housize stress.bstress stress.billness stress.week
0.033264472 3.882818003 0.766096223 -0.430352406
illness.Intercept illness.married illness.education illness.employed
-1.615583265 0.508179899 -0.035048178 -0.218950724
illness.chlth illness.mhlth illness.race illness.csex
-0.388314564 0.002553814 0.133293195 0.040354347
illness.housize illness.bstress illness.billness illness.week
-0.615464854 0.224095099 1.930771378 -0.194958339
Multivariate Marginal Models
Version 1.4 (01/2014)
Model:
Link: Logit
Variance to Mean Relation: Binomial
Correlation Structure: Exchangeable
Call:
gee(formula = formula2, id = id5, data = cov3, R = correlation,
b = initEstim, tol = tol, maxiter = maxiter, family = family,
corstr = corStruct, Mv = Mv, silent = silent, scale.fix = scale.fix,
scale.value = scale.value)
Summary of Residuals:
Min 1Q Median 3Q Max
-0.54684804 -0.11674926 -0.07385203 -0.04499435 0.97009440
Coefficients:
Estimate Naive S.E. Naive z Robust S.E. Robust z
stress.Intercept -2.138108065 0.3864089 -5.53327797 0.4152241 -5.14928699
stress.married -0.005031438 0.2173216 -0.02315204 0.2356163 -0.02135437
stress.education 0.364051429 0.2376232 1.53205358 0.2254810 1.61455489
stress.employed -0.646912681 0.2452896 -2.63734225 0.2499109 -2.58857330
stress.chlth -0.260979015 0.1327819 -1.96547162 0.1330329 -1.96176319
stress.mhlth -0.171999294 0.1291866 -1.33140241 0.1234630 -1.39312376
stress.race -0.014867099 0.2265020 -0.06563783 0.2416023 -0.06153541
stress.csex -0.043166175 0.2038832 -0.21172011 0.2199978 -0.19621185
stress.housize 0.061457566 0.2250456 0.27308935 0.2393628 0.25675489
stress.bstress 3.894148584 0.6901308 5.64262421 0.7109605 5.47730640
stress.billness 0.858467730 0.6690715 1.28307325 0.7082821 1.21204219
stress.week -0.429332576 0.1450881 -2.95911583 0.1621079 -2.64843753
illness.Intercept -1.576188192 0.3745326 -4.20841404 0.4780402 -3.29718757
illness.married 0.499098985 0.2203245 2.26529081 0.2660131 1.87621960
illness.education -0.055276625 0.2319788 -0.23828304 0.2871428 -0.19250570
illness.employed -0.218074096 0.2387195 -0.91351607 0.3287659 -0.66331115
illness.chlth -0.400065494 0.1310395 -3.05301349 0.1561921 -2.56136874
illness.mhlth 0.025130852 0.1263277 0.19893375 0.1657948 0.15157805
illness.race 0.019617144 0.2262809 0.08669376 0.2442925 0.08030186
illness.csex 0.018774821 0.1999519 0.09389666 0.2457134 0.07640943
illness.housize -0.564393489 0.2221188 -2.54095363 0.2585483 -2.18293280
illness.bstress 0.061179972 0.7384118 0.08285346 0.9805477 0.06239367
illness.billness 2.175750375 0.6618790 3.28723267 0.7521979 2.89252395
illness.week -0.194479469 0.1441036 -1.34958082 0.2158324 -0.90106704
Estimated Scale Parameter: 0.9907396
Number of Iterations: 5
Working Correlation
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
[7,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[13,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[19,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[7,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
[13,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[19,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[7,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[13,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
[19,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[7,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[13,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[19,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
running glm to get initial regression estimate
resp1.Intercept resp1.X resp1.time resp1.X.time resp2.Intercept
-1.975302855 1.199162395 -0.021954619 0.009498535 -0.687791871
resp2.X resp2.time resp2.X.time
0.926931138 -0.037415199 0.014558684
Multivariate Marginal Models
Version 1.4 (01/2014)
Model:
Link: Logarithm
Variance to Mean Relation: Poisson
Correlation Structure: Unstructured
Call:
gee(formula = formula2, id = id5, data = cov3, R = correlation,
b = initEstim, tol = tol, maxiter = maxiter, family = family,
corstr = corStruct, Mv = Mv, silent = silent, scale.fix = scale.fix,
scale.value = scale.value)
Summary of Residuals:
Min 1Q Median 3Q Max
-6.8444397 -1.2942113 -0.1217991 1.2103614 9.6129605
Coefficients:
Estimate Naive S.E. Naive z Robust S.E. Robust z
resp1.Intercept -1.981931701 0.19060093 -10.3983319 0.16854252 -11.7592384
resp1.X 1.201184669 0.06298930 19.0696626 0.05514501 21.7822899
resp1.time -0.023195140 0.07998658 -0.2899879 0.07515139 -0.3086455
resp1.X.time 0.009697176 0.02643443 0.3668389 0.02479493 0.3910951
resp2.Intercept -0.721120287 0.14863980 -4.8514615 0.14545212 -4.9577848
resp2.X 0.938931560 0.04932182 19.0368407 0.04754299 19.7491068
resp2.time -0.042618177 0.05964017 -0.7145884 0.06465218 -0.6591916
resp2.X.time 0.016546863 0.01978839 0.8361905 0.02142782 0.7722140
Estimated Scale Parameter: 0.6164724
Number of Iterations: 3
Working Correlation
[,1] [,2] [,3] [,4] [,5]
[1,] 1.00000000 0.848725915 0.694606146 0.513984125 0.053593205
[2,] 0.84872592 1.000000000 0.826221372 0.644746151 0.007159807
[3,] 0.69460615 0.826221372 1.000000000 0.794623005 -0.033635656
[4,] 0.51398413 0.644746151 0.794623005 1.000000000 -0.062693074
[5,] 0.05359321 0.007159807 -0.033635656 -0.062693074 1.000000000
[6,] 0.02665112 0.059073395 0.033098309 -0.005593721 0.802855948
[7,] -0.03363635 0.005957752 0.048941573 0.014020632 0.705999066
[8,] -0.08128953 -0.046425481 0.009958662 0.057843689 0.544878999
[,6] [,7] [,8]
[1,] 0.026651116 -0.033636350 -0.081289528
[2,] 0.059073395 0.005957752 -0.046425481
[3,] 0.033098309 0.048941573 0.009958662
[4,] -0.005593721 0.014020632 0.057843689
[5,] 0.802855948 0.705999066 0.544878999
[6,] 1.000000000 0.848217454 0.724226459
[7,] 0.848217454 1.000000000 0.907250260
[8,] 0.724226459 0.907250260 1.000000000
Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
running glm to get initial regression estimate
resp1.Intercept resp1.X resp1.time resp1.X.time resp2.Intercept
0.027694596 0.279591110 0.018089845 0.005705946 -0.034369118
resp2.X resp2.time resp2.X.time
0.286880761 0.016358894 0.007836619
Multivariate Marginal Models
Version 1.4 (01/2014)
Model:
Link: Identity
Variance to Mean Relation: Gaussian
Correlation Structure: Unstructured
Call:
gee(formula = formula2, id = id5, data = cov3, R = correlation,
b = initEstim, tol = tol, maxiter = maxiter, family = family,
corstr = corStruct, Mv = Mv, silent = silent, scale.fix = scale.fix,
scale.value = scale.value)
Summary of Residuals:
Min 1Q Median 3Q Max
-2.49395337 -0.55649351 -0.01568588 0.52094419 2.90441083
Coefficients:
Estimate Naive S.E. Naive z Robust S.E. Robust z
resp1.Intercept 0.0205385389 0.030692344 0.66917466 0.031445765 0.653141646
resp1.X 0.2814117402 0.015099294 18.63741013 0.014382703 19.565984111
resp1.time 0.0220720659 0.013586065 1.62461060 0.013354275 1.652809007
resp1.X.time 0.0041293419 0.006683752 0.61781798 0.006423078 0.642891465
resp2.Intercept 0.0003028896 0.030123114 0.01005506 0.039575171 0.007653526
resp2.X 0.2801816347 0.014819258 18.90659003 0.019495928 14.371289652
resp2.time 0.0291739038 0.011625151 2.50955062 0.022058970 1.322541523
resp2.X.time 0.0013941045 0.005719067 0.24376433 0.011165384 0.124859525
Estimated Scale Parameter: 0.6515428
Number of Iterations: 10
Working Correlation
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.00000000 0.78224384 0.636252669 0.48033618 0.06311887 0.01537679
[2,] 0.78224384 1.00000000 0.771044545 0.59733900 0.02188524 0.03315389
[3,] 0.63625267 0.77104455 1.000000000 0.77769384 -0.01476141 -0.01420100
[4,] 0.48033618 0.59733900 0.777693843 1.00000000 -0.11318591 -0.07747520
[5,] 0.06311887 0.02188524 -0.014761412 -0.11318591 1.00000000 0.90204210
[6,] 0.01537679 0.03315389 -0.014201002 -0.07747520 0.90204210 1.00000000
[7,] -0.06688044 -0.03799873 0.029085767 -0.03683402 0.73231105 0.89742346
[8,] -0.11348628 -0.06593866 -0.009127264 0.02623614 0.52183339 0.68778092
[,7] [,8]
[1,] -0.06688044 -0.113486278
[2,] -0.03799873 -0.065938656
[3,] 0.02908577 -0.009127264
[4,] -0.03683402 0.026236144
[5,] 0.73231105 0.521833389
[6,] 0.89742346 0.687780917
[7,] 1.00000000 0.909973804
[8,] 0.90997380 1.000000000
mmm documentation built on May 2, 2019, 2:48 p.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Value Note Author(s) References See Also Examples
Description
fits multivariate marginal models to analyze multivariate longitudinal data, for both continuous and discrete responses
Usage
1 2 3 |
Arguments
formula |
a formula expression, see the examples given below. |
id |
a vector for identification of the clusters. |
data |
an optional data frame. |
correlation |
a user specified square matrix for the working correlation matrix, appropriate when |
initEstim |
user specified initials for the parameter estimates. |
tol |
the tolerance which specifies the convergency of the algorithm. |
maxiter |
the maximum number of iterations to be consumed by the algorithm. |
family |
an object which defines the link and variance function. The possible choices are same with the ones in the |
corStruct |
a character string which defines the structure of the working correlation matrix. For details see the |
Mv |
specifies the lag value, e.g. specification of |
silent |
a logial variable which decides the print of the iterations. |
scale.fix |
a logical variable for fixing the scale parameter to a user specified value. |
scale.value |
a user specified scale parameter value, appropriate when |
Value
Returns an onject of the results. See the examples given below.
Note
Version 1.1.
Author(s)
Ozgur Asar, Ozlem Ilk
References
Asar, O. (2012). On multivariate longitudinal binary data models and their applications in forecasting. MS Thesis, Middle East Technical University. Available online at http://www.lancaster.ac.uk/pg/asar/thesis-Ozgur-Asar
Asar, O., Ilk, O. (2013). mmm: an R package for analyzing multivariate longitudinal data with multivariate marginal models, Computer Methods and Programs in Biomedicine, 112, 649-654.
Liang, K. L., Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
Shelton, B. J., Gilbert, G. H., Liu, B., Fisher, M. (2004). A SAS macro for the analysis of multivariate longitudinal binary outcomes. Computer Methods and Programs in Biomedicine, 76, 163-175.
Zeger, S. L., Liang, K. L (1986). Longitudinal data analysis for discrete and continous outcomes. Biometrics, 42, 121-130.
See Also
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 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 | #########################
## Binary data example ##
#########################
data(motherStress)
fit1<-mmm(formula=cbind(stress,illness)~married+education+
employed+chlth+mhlth+race+csex+housize+bstress+billness+
week,id=motherStress$id,data=motherStress,family=binomial,corStruct="exchangeable")
summary(fit1)
########################
## Count data example ##
########################
## First we illustrate how the data set is simulated
## Then the R script to analyze the data set by mmm is given
## Note: no need to run the script to generate the data set, unless of interest
## Not run:
### Generating the data by the help of 'corcounts' package
# loading the package 'corcounts'
library("corcounts")
# setting the seed to 12
set.seed(12)
# number of subjects in the study
n1 <- 500
# defining the response and covariate families (Poi indicates Poisson distribution)
margins <- c("Poi","Poi","Poi","Poi","Poi","Poi","Poi","Poi","Poi")
# the means of the responses and covariate. while 5 and 8 are the means of the responses
# 20 is the mean of the time independent covariate
mu <- c(5, 8, 20, 5, 8, 5, 8, 5, 8)
# the correlation structure which 'corcounts' uses to generate correlated count data
# (unstr indicates unstructured correlation structure)
corstr <- "unstr"
# the correlation matrix corcounts assumes the correlated count data have
corpar<-matrix(c(1,0.4,0.6,0.9,0.37,0.8,0.34,0.7,0.31,
0.4,1,0.6,0.37,0.9,0.34,0.8,0.31,0.7,
0.6,0.6,1,0.6,0.6,0.6,0.6,0.6,0.6,
0.9,0.37,0.6,1,0.4,0.9,0.37,0.8,0.34,
0.37,0.9,0.6,0.4,1,0.37,0.9,0.34,0.8,
0.8,0.34,0.6,0.9,0.37,1,0.4,0.9,0.37,
0.34,0.8,0.6,0.37,0.9,0.4,1,0.37,0.9,
0.7,0.31,0.6,0.8,0.34,0.9,0.37,1,0.4,
0.31,0.7,0.6,0.34,0.8,0.37,0.9,0.4,1),ncol=9,byrow=T)
# generating the correlated count data by 'rcounts' function avaiable in 'corcounts'
data1 <- rcounts(N=n1,margins=margins,mu=mu,corstr=corstr,corpar=corpar)
### The reconstruction of the generated correlated count data to
### the longitudinal data (long) format
# seperating the bivariate responses measured at the first time
# point and the time independent covariate
time11<-data1[,1:3]
# seperating the bivariate responses measured at the second time
# point and combining them with the time independent covariate
time12<-cbind(data1[,4:5],data1[,3])
# seperating the bivariate responses measured at the third time
# point and combining them with the time independent covariate
time13<-cbind(data1[,6:7],data1[,3])
# seperating the bivariate responses measured at the fourth time
# point and combining them with the time independent covariate
time14<-cbind(data1[,8:9],data1[,3])
# combining the data for all the time points
data12<-rbind(time11,time12,time13,time14)
# constructing the time variable
time1<-matrix(rep(seq(1:4),each=n1))
# constructing the id variable
id1<-matrix(rep(seq(1:n1),4))
# combining the id of the subjects, the simulated data and the time variable
data13<-cbind(id1,data12,time1)
# reconstructing the data subject by subject which 'mmm' expects it has
data14<-NULL
for (i in 1:n1) data14<-rbind(data14,data13[data13[,1]==i,])
### Data manipulations on the covariates
# taking natural logarithm of the time independent covariate
data14[,4]<-log(data14[,4])
# standardizing time variable
data14[,5]<-scale(data14[,5])
# adding the interaction of the time independent covariate
# and time as a new covariate
multiLongCount<-as.data.frame(cbind(data14,data14[,4]*data14[,5]))
names(multiLongCount)<-c("ID","resp1","resp2","X","time","X.time")
## End(Not run)
### R script to analyze the count data set
### It is already stored in mmm pacakge
data(multiLongCount)
fit2<-mmm(formula=cbind(resp1,resp2)~X+time+X.time,
id=multiLongCount$ID,data=multiLongCount,family=poisson,corStruct="unstructured")
summary(fit2)
#############################
## Continuous data example ##
#############################
## First we illustrate how the data set is simulated
## Then the R script to analyze the data set by mmm is given
## Note: no need to run the script to generate the data set, unless of interest
## Not run:
### Generating the data by the help of mvtnorm package
# loading package 'mvtnorm'
library("mvtnorm")
# number of subjects in the study
n2<-500
# setting the seed to 12
set.seed(12)
# specifying the correlation matrix which 'mvtnorm' assumes the correlated data have
cormat<-matrix(c(1,0.4,0.6,0.9,0.37,0.8,0.34,0.7,0.31,
0.4,1,0.6,0.37,0.9,0.34,0.8,0.31,0.7,
0.6,0.6,1,0.6,0.6,0.6,0.6,0.6,0.6,
0.9,0.37,0.6,1,0.4,0.9,0.37,0.8,0.34,
0.37,0.9,0.6,0.4,1,0.37,0.9,0.34,0.8,
0.8,0.34,0.6,0.9,0.37,1,0.4,0.9,0.37,
0.34,0.8,0.6,0.37,0.9,0.4,1,0.37,0.9,
0.7,0.31,0.6,0.8,0.34,0.9,0.37,1,0.4,
0.31,0.7,0.6,0.34,0.8,0.37,0.9,0.4,1),ncol=9,byrow=T)
# variances of the responses and time independent covariate
# while 0.97 and 1.1 correspond to the variances of the bivariate responses
# 4 corresponds to the variance of the time independent covariate
variance<-c(0.97,1.1,4,0.97,1.1,0.97,1.1,0.97,1.1)
# constructing the (diaonal) standard deviation matrix
std<-diag(sqrt(variance),9)
# constructing the variance covariance matrix, sigma
sigma<-std
# generating the correlated continuous data utilizing 'rmvnorm' function available
# in 'mvtnorm'; method="svd" indicates use of 'singular value decomposition method
data2<-rmvnorm(n2,mean = rep(0,nrow(sigma)),sigma=sigma,method="svd")
### The reconstruction of the generated correlated continuous data to the
### longitudinal data (long) format
# seperating the bivariate responses measured at first time point
# and the time independent covariate
time21<-data2[,1:3]
# seperating the bivariate responses measured at second time point
# and combining them with the time independent covariate
time22<-cbind(data2[,4:5],data2[,3])
# seperating the bivariate responses measured at third time point
# and combining them with the time independent covariate
time23<-cbind(data2[,6:7],data2[,3])
# seperating the bivariate responses measured at fourth time point
# and combining them with the time independent covariate
time24<-cbind(data2[,8:9],data2[,3])
# combining the data for all the time points
data22<-rbind(time21,time22,time23,time24)
# constructing the time variable
time2<-matrix(rep(seq(1:4),each=n2))
# constructing the id variable
id2<-matrix(rep(seq(1:n2),4))
# combining the id of the subjects, the generated data and the time variable
data23<-cbind(id2,data22,time2)
# reconstructing the data subject by subject which 'mmm' expects it has
data24<-NULL
for (i in 1:n2) data24<-rbind(data24,data23[data23[,1]==i,])
### Data manipulations on the covariates
# standardizing the time variable
data24[,5]<-scale(data24[,5])
# adding the interaction of the time independent covariate
# and time as a new covariate
multiLongGaussian<-as.data.frame(cbind(data24,data24[,4]*data24[,5]))
names(multiLongGaussian)<-c("ID","resp1","resp2","X","time","X.time")
## End(Not run)
### R script to analyze the continuous data set
### It is already stored in mmm pacakge
data(multiLongGaussian)
fit3<-mmm(formula=cbind(resp1,resp2)~X+time+X.time,
id=multiLongGaussian$ID,data=multiLongGaussian,family=gaussian,corStruct="unstructured")
summary(fit3)
|
Example output
Loading required package: gee
Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
running glm to get initial regression estimate
stress.Intercept stress.married stress.education stress.employed
-2.180720871 0.019430701 0.378751056 -0.642639022
stress.chlth stress.mhlth stress.race stress.csex
-0.254767051 -0.185567901 0.061986473 -0.007871376
stress.housize stress.bstress stress.billness stress.week
0.033264472 3.882818003 0.766096223 -0.430352406
illness.Intercept illness.married illness.education illness.employed
-1.615583265 0.508179899 -0.035048178 -0.218950724
illness.chlth illness.mhlth illness.race illness.csex
-0.388314564 0.002553814 0.133293195 0.040354347
illness.housize illness.bstress illness.billness illness.week
-0.615464854 0.224095099 1.930771378 -0.194958339
Multivariate Marginal Models
Version 1.4 (01/2014)
Model:
Link: Logit
Variance to Mean Relation: Binomial
Correlation Structure: Exchangeable
Call:
gee(formula = formula2, id = id5, data = cov3, R = correlation,
b = initEstim, tol = tol, maxiter = maxiter, family = family,
corstr = corStruct, Mv = Mv, silent = silent, scale.fix = scale.fix,
scale.value = scale.value)
Summary of Residuals:
Min 1Q Median 3Q Max
-0.54684804 -0.11674926 -0.07385203 -0.04499435 0.97009440
Coefficients:
Estimate Naive S.E. Naive z Robust S.E. Robust z
stress.Intercept -2.138108065 0.3864089 -5.53327797 0.4152241 -5.14928699
stress.married -0.005031438 0.2173216 -0.02315204 0.2356163 -0.02135437
stress.education 0.364051429 0.2376232 1.53205358 0.2254810 1.61455489
stress.employed -0.646912681 0.2452896 -2.63734225 0.2499109 -2.58857330
stress.chlth -0.260979015 0.1327819 -1.96547162 0.1330329 -1.96176319
stress.mhlth -0.171999294 0.1291866 -1.33140241 0.1234630 -1.39312376
stress.race -0.014867099 0.2265020 -0.06563783 0.2416023 -0.06153541
stress.csex -0.043166175 0.2038832 -0.21172011 0.2199978 -0.19621185
stress.housize 0.061457566 0.2250456 0.27308935 0.2393628 0.25675489
stress.bstress 3.894148584 0.6901308 5.64262421 0.7109605 5.47730640
stress.billness 0.858467730 0.6690715 1.28307325 0.7082821 1.21204219
stress.week -0.429332576 0.1450881 -2.95911583 0.1621079 -2.64843753
illness.Intercept -1.576188192 0.3745326 -4.20841404 0.4780402 -3.29718757
illness.married 0.499098985 0.2203245 2.26529081 0.2660131 1.87621960
illness.education -0.055276625 0.2319788 -0.23828304 0.2871428 -0.19250570
illness.employed -0.218074096 0.2387195 -0.91351607 0.3287659 -0.66331115
illness.chlth -0.400065494 0.1310395 -3.05301349 0.1561921 -2.56136874
illness.mhlth 0.025130852 0.1263277 0.19893375 0.1657948 0.15157805
illness.race 0.019617144 0.2262809 0.08669376 0.2442925 0.08030186
illness.csex 0.018774821 0.1999519 0.09389666 0.2457134 0.07640943
illness.housize -0.564393489 0.2221188 -2.54095363 0.2585483 -2.18293280
illness.bstress 0.061179972 0.7384118 0.08285346 0.9805477 0.06239367
illness.billness 2.175750375 0.6618790 3.28723267 0.7521979 2.89252395
illness.week -0.194479469 0.1441036 -1.34958082 0.2158324 -0.90106704
Estimated Scale Parameter: 0.9907396
Number of Iterations: 5
Working Correlation
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
[7,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[13,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[19,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[7,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
[13,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[19,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[7,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[13,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
[19,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[,19] [,20] [,21] [,22] [,23] [,24]
[1,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[2,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[3,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[4,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[5,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[6,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[7,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[8,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[9,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[10,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[11,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[12,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[13,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[14,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[15,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[16,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[17,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[18,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[19,] 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523
[20,] 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523 0.07040523
[21,] 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523 0.07040523
[22,] 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523 0.07040523
[23,] 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000 0.07040523
[24,] 0.07040523 0.07040523 0.07040523 0.07040523 0.07040523 1.00000000
Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
running glm to get initial regression estimate
resp1.Intercept resp1.X resp1.time resp1.X.time resp2.Intercept
-1.975302855 1.199162395 -0.021954619 0.009498535 -0.687791871
resp2.X resp2.time resp2.X.time
0.926931138 -0.037415199 0.014558684
Multivariate Marginal Models
Version 1.4 (01/2014)
Model:
Link: Logarithm
Variance to Mean Relation: Poisson
Correlation Structure: Unstructured
Call:
gee(formula = formula2, id = id5, data = cov3, R = correlation,
b = initEstim, tol = tol, maxiter = maxiter, family = family,
corstr = corStruct, Mv = Mv, silent = silent, scale.fix = scale.fix,
scale.value = scale.value)
Summary of Residuals:
Min 1Q Median 3Q Max
-6.8444397 -1.2942113 -0.1217991 1.2103614 9.6129605
Coefficients:
Estimate Naive S.E. Naive z Robust S.E. Robust z
resp1.Intercept -1.981931701 0.19060093 -10.3983319 0.16854252 -11.7592384
resp1.X 1.201184669 0.06298930 19.0696626 0.05514501 21.7822899
resp1.time -0.023195140 0.07998658 -0.2899879 0.07515139 -0.3086455
resp1.X.time 0.009697176 0.02643443 0.3668389 0.02479493 0.3910951
resp2.Intercept -0.721120287 0.14863980 -4.8514615 0.14545212 -4.9577848
resp2.X 0.938931560 0.04932182 19.0368407 0.04754299 19.7491068
resp2.time -0.042618177 0.05964017 -0.7145884 0.06465218 -0.6591916
resp2.X.time 0.016546863 0.01978839 0.8361905 0.02142782 0.7722140
Estimated Scale Parameter: 0.6164724
Number of Iterations: 3
Working Correlation
[,1] [,2] [,3] [,4] [,5]
[1,] 1.00000000 0.848725915 0.694606146 0.513984125 0.053593205
[2,] 0.84872592 1.000000000 0.826221372 0.644746151 0.007159807
[3,] 0.69460615 0.826221372 1.000000000 0.794623005 -0.033635656
[4,] 0.51398413 0.644746151 0.794623005 1.000000000 -0.062693074
[5,] 0.05359321 0.007159807 -0.033635656 -0.062693074 1.000000000
[6,] 0.02665112 0.059073395 0.033098309 -0.005593721 0.802855948
[7,] -0.03363635 0.005957752 0.048941573 0.014020632 0.705999066
[8,] -0.08128953 -0.046425481 0.009958662 0.057843689 0.544878999
[,6] [,7] [,8]
[1,] 0.026651116 -0.033636350 -0.081289528
[2,] 0.059073395 0.005957752 -0.046425481
[3,] 0.033098309 0.048941573 0.009958662
[4,] -0.005593721 0.014020632 0.057843689
[5,] 0.802855948 0.705999066 0.544878999
[6,] 1.000000000 0.848217454 0.724226459
[7,] 0.848217454 1.000000000 0.907250260
[8,] 0.724226459 0.907250260 1.000000000
Beginning Cgee S-function, @(#) geeformula.q 4.13 98/01/27
running glm to get initial regression estimate
resp1.Intercept resp1.X resp1.time resp1.X.time resp2.Intercept
0.027694596 0.279591110 0.018089845 0.005705946 -0.034369118
resp2.X resp2.time resp2.X.time
0.286880761 0.016358894 0.007836619
Multivariate Marginal Models
Version 1.4 (01/2014)
Model:
Link: Identity
Variance to Mean Relation: Gaussian
Correlation Structure: Unstructured
Call:
gee(formula = formula2, id = id5, data = cov3, R = correlation,
b = initEstim, tol = tol, maxiter = maxiter, family = family,
corstr = corStruct, Mv = Mv, silent = silent, scale.fix = scale.fix,
scale.value = scale.value)
Summary of Residuals:
Min 1Q Median 3Q Max
-2.49395337 -0.55649351 -0.01568588 0.52094419 2.90441083
Coefficients:
Estimate Naive S.E. Naive z Robust S.E. Robust z
resp1.Intercept 0.0205385389 0.030692344 0.66917466 0.031445765 0.653141646
resp1.X 0.2814117402 0.015099294 18.63741013 0.014382703 19.565984111
resp1.time 0.0220720659 0.013586065 1.62461060 0.013354275 1.652809007
resp1.X.time 0.0041293419 0.006683752 0.61781798 0.006423078 0.642891465
resp2.Intercept 0.0003028896 0.030123114 0.01005506 0.039575171 0.007653526
resp2.X 0.2801816347 0.014819258 18.90659003 0.019495928 14.371289652
resp2.time 0.0291739038 0.011625151 2.50955062 0.022058970 1.322541523
resp2.X.time 0.0013941045 0.005719067 0.24376433 0.011165384 0.124859525
Estimated Scale Parameter: 0.6515428
Number of Iterations: 10
Working Correlation
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 1.00000000 0.78224384 0.636252669 0.48033618 0.06311887 0.01537679
[2,] 0.78224384 1.00000000 0.771044545 0.59733900 0.02188524 0.03315389
[3,] 0.63625267 0.77104455 1.000000000 0.77769384 -0.01476141 -0.01420100
[4,] 0.48033618 0.59733900 0.777693843 1.00000000 -0.11318591 -0.07747520
[5,] 0.06311887 0.02188524 -0.014761412 -0.11318591 1.00000000 0.90204210
[6,] 0.01537679 0.03315389 -0.014201002 -0.07747520 0.90204210 1.00000000
[7,] -0.06688044 -0.03799873 0.029085767 -0.03683402 0.73231105 0.89742346
[8,] -0.11348628 -0.06593866 -0.009127264 0.02623614 0.52183339 0.68778092
[,7] [,8]
[1,] -0.06688044 -0.113486278
[2,] -0.03799873 -0.065938656
[3,] 0.02908577 -0.009127264
[4,] -0.03683402 0.026236144
[5,] 0.73231105 0.521833389
[6,] 0.89742346 0.687780917
[7,] 1.00000000 0.909973804
[8,] 0.90997380 1.000000000
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.