pgee.fit: Penalized Generalized Estimating Equations
In pgee.mixed: Penalized Generalized Estimating Equations for Bivariate Mixed Outcomes
Description
Usage
Arguments
Details
Value
Examples
View source: R/estimation_functions.R
Description
Estimate regression coefficients using Penalized Generalized Estimating
Equations (PGEEs). Linear and binary logistic models are currently supported.
In particular, can handle the case of bivariate correlated mixed outcomes, in
which each cluster consists of one continuous outcome and one binary outcome.
Usage
1
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5
Arguments
N
Number of clusters.
m
Cluster size. Assumed equal across all clusters. Should be set to 2
for family=="Mixed".
X
Design matrix. If family=="Mixed", then design matrix for continuous
responses. For family!="Mixed", should have N*m rows. For family=="Mixed",
should have N rows. For standardize=TRUE, the first column should be a
column vector of ones, corresponding to the intercept.
Z
Design matrix for binary responses for family=="Mixed". Should not
be provided for other family types. If not provided for family=="Mixed", is
set equal to X. For family!="Mixed", should have N*m rows. For
family=="Mixed", should have N rows. For standardize=TRUE, the first
column should be a column vector of ones, corresponding to the intercept.
y
Response vector. Don't use this argument for family == "Mixed".
Instead, use arguments yc and yb. Since the cluster size is assumed equal
across clusters, the vector is assumed to have the form c(y_1,
y_2,...,y_N), with y_i = c(y_i1,...,y_im).
yc
Continuous response vector. Use only for family=="Mixed".
yb
Binary (0/1) response vector. Use only for family=="Mixed".
wctype
Working correlation type; one of "Ind", "CS", or "AR1". For
family=="Mixed", "CS" and "AR1" are equivalent.
family
"Gaussian", "Binomial", or "Mixed" (use the last for bivariate
mixed outcomes). Note that for "Binomial", currently only binary outcomes
are supported.
lambda
Tuning parameter(s). A vector of two tuning parameters should
be provided for family=="Mixed" (one for the continuous outcome
coefficients, and one of the binary outcome coefficients). Otherwise, a
single tuning parameter should be provided.
eps
Disturbance in the Linear Quadratic Approximation algorithm.
maxiter
The maximum number of iterations the Newton algorithm tries
before declaring failure to converge.
tol.coef
Converge of the Newton algorithm is declared if two
conditions are met: The L1-norm of the difference of successive iterates
should be less than tol.coef AND the L1-norm of the penalized score should
be less than tol.score.
tol.score
See tol.coef.
init
Vector of initial values for regression coefficients. For
family=="Mixed", should be c(init_c, init_b). Defaults to glm values.
standardize
Standardize the design matrices prior to estimation?
penalty
"SCAD", "MCP", or "LASSO".
weights
Vector of cluster weights. All observations in a cluster are
assumed to have the same weight.
FDR
Should the false discovery rate be estimated for family=="Mixed"?
Currently, FDR cannot be estimated for other family types.
fdr.corr
Association parameter to use in FDR estimation. The default
is to use the association parameter estimated from the PGEEs.
fdr.type
Estimate the FDR for only the coefficients corresponding to
the continuous outcomes ("continuous"), for only the coefficients
corresponding to the binary outcomes ("binary"), or for all coefficients
("all", the default).
Details
pgee.fit estimates the regression coefficients for a single value of the
tuning paramter (or a single pair of tuning parameters in the mixed outcomes
case). To select optimal tuning parameter(s) via k-fold cross validation, see
cv.pgee.
For bivariate mixed outcomes, the false discovery rate can be estimated.
Value
A list
coefficients
Vector of estimated regression
coefficients. For family=="Mixed", this takes the form c(coef_c, coef_b).
vcov
Sandwich formula based covariance matrix of estimated
regression coefficients (other than the intercept(s)). The row/column
names correspond to elements of coefficients.
phi
Estimated dispersion parameter.
alpha
Estimated association parameter.
num_iterations
Number of iterations the Newton algorithm ran.
converge
0=converged, 1=did not converge.
PenScore
Vector of penalized score functions at the estimated
regression coefficients. If the algorithm converges, then these should be
close to zero.
FDR
Estimated FDR for family=="Mixed", if requested.
Examples
1
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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
set.seed(100)
# Gaussian
N <- 100
m <- 10
p <- 10
y <- rnorm(N * m)
# If you want standardize = TRUE, you must provide an intercept.
X <- cbind(1, matrix(rnorm(N * m * (p - 1)), N * m, p - 1))
fit <- pgee.fit(X = X, y = y, N = N, m = m, lambda = 0.5, wctype = "CS",
family = "Gaussian")
str(fit)
fit$coefficients
fit$vcov
# Binary
y <- sample(0:1, N*m, replace = TRUE)
fit <- pgee.fit(X = X, y = y, N = N, m = m, lambda = 0.1, wctype = "CS",
family = "Binomial")
str(fit)
fit$coefficients
fit$vcov
# Bivariate mixed outcomes
# Generate some data
Bc <- c(2.0, 3.0, 1.5, 2.0, rep(0, times = p - 4))
Bb <- c(0.7, -0.7, -0.4, rep(0, times = p - 3))
dat <- gen_mixed_data(Bc, Bc, N, 0.5)
# Estimate regression coefficients and false discovery rate
fit <- pgee.fit(X = dat$X, yc = dat$yc, yb = dat$yb, N = N, m = 2,
wctype = "CS", family = "Mixed", lambda = c(0.1, 0.05),
FDR = TRUE)
str(fit)
fit$coefficients
fit$vcov
Example output
List of 8
$ coefficients : num [1:10] 1.65e-02 3.83e-07 -2.66e-04 -8.06e-06 -3.09e-06 ...
$ vcov : num [1:9, 1:9] 8.61e-13 -1.44e-11 -1.36e-13 -9.17e-14 4.32e-14 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
$ phi : num 1.06
$ alpha : num -0.0112
$ num_iterations: num 13
$ converge : num 0
$ PenScore : num [1:10] -5.03e-16 -4.32e-04 1.24e-01 1.88e-01 1.64e-01 ...
$ FDR : logi NA
[1] 1.647210e-02 3.833171e-07 -2.660433e-04 -8.056127e-06 -3.087420e-06
[6] 8.031320e-07 -6.295737e-04 -6.726526e-03 -4.295715e-07 5.060864e-03
2 3 4 5 6
2 8.613359e-13 -1.443383e-11 -1.359931e-13 -9.165927e-14 4.317532e-14
3 -1.443383e-11 2.523863e-08 4.194025e-12 1.463658e-11 -2.834944e-11
4 -1.359931e-13 4.194025e-12 3.191533e-11 -2.170933e-12 -1.976114e-12
5 -9.165927e-14 1.463658e-11 -2.170933e-12 7.307825e-12 2.608954e-13
6 4.317532e-14 -2.834944e-11 -1.976114e-12 2.608954e-13 1.375238e-12
7 6.422694e-13 6.851341e-10 1.802262e-10 -2.399149e-10 3.363041e-11
8 9.411808e-11 -2.776368e-08 -2.546778e-09 8.121936e-10 3.822077e-10
9 -1.115545e-13 -8.915957e-13 6.852764e-13 4.606714e-13 8.435045e-14
10 3.529888e-10 7.157877e-08 -3.177134e-09 4.235949e-11 7.232707e-11
7 8 9 10
2 6.422694e-13 9.411808e-11 -1.115545e-13 3.529888e-10
3 6.851341e-10 -2.776368e-08 -8.915957e-13 7.157877e-08
4 1.802262e-10 -2.546778e-09 6.852764e-13 -3.177134e-09
5 -2.399149e-10 8.121936e-10 4.606714e-13 4.235949e-11
6 3.363041e-11 3.822077e-10 8.435045e-14 7.232707e-11
7 1.552830e-07 -1.729901e-07 -8.205465e-12 -3.954180e-08
8 -1.729901e-07 1.507694e-05 2.580865e-10 -9.704816e-07
9 -8.205465e-12 2.580865e-10 8.125506e-13 -8.012537e-11
10 -3.954180e-08 -9.704816e-07 -8.012537e-11 1.036791e-05
List of 8
$ coefficients : num [1:10] -9.78e-02 -5.87e-02 -7.56e-02 -2.58e-08 -5.10e-03 ...
$ vcov : num [1:9, 1:9] 1.39e-03 -2.39e-04 4.08e-09 2.34e-05 -2.31e-06 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
$ phi : num 1
$ alpha : num 0.00668
$ num_iterations: num 11
$ converge : num 0
$ PenScore : num [1:10] -3.58e-07 -4.17e-05 -4.92e-05 1.23e-06 6.24e-03 ...
$ FDR : logi NA
[1] -9.775728e-02 -5.872854e-02 -7.561909e-02 -2.579482e-08 -5.098200e-03
[6] 6.709633e-04 4.849940e-03 2.215454e-02 6.060735e-07 4.823028e-02
2 3 4 5 6
2 1.390546e-03 -2.386341e-04 4.079203e-09 2.339723e-05 -2.313984e-06
3 -2.386341e-04 1.655552e-03 -1.258208e-09 -1.162351e-05 6.927630e-06
4 4.079203e-09 -1.258208e-09 3.193028e-12 9.306620e-10 2.058728e-11
5 2.339723e-05 -1.162351e-05 9.306620e-10 5.886218e-05 -6.298594e-07
6 -2.313984e-06 6.927630e-06 2.058728e-11 -6.298594e-07 1.114552e-06
7 -3.565046e-05 2.382287e-05 1.041267e-09 6.913538e-06 3.362207e-08
8 -6.986897e-05 -2.900527e-05 -2.355404e-09 1.336237e-05 4.538517e-08
9 -3.991919e-09 1.204502e-08 -5.790573e-15 2.937704e-09 -3.516431e-11
10 -1.053045e-04 -7.764264e-05 2.495350e-09 1.598950e-05 -3.252945e-06
7 8 9 10
2 -3.565046e-05 -6.986897e-05 -3.991919e-09 -1.053045e-04
3 2.382287e-05 -2.900527e-05 1.204502e-08 -7.764264e-05
4 1.041267e-09 -2.355404e-09 -5.790573e-15 2.495350e-09
5 6.913538e-06 1.336237e-05 2.937704e-09 1.598950e-05
6 3.362207e-08 4.538517e-08 -3.516431e-11 -3.252945e-06
7 4.297730e-05 4.124194e-06 5.968554e-10 -2.018825e-05
8 4.124194e-06 5.058943e-04 1.856554e-09 1.235802e-04
9 5.968554e-10 1.856554e-09 5.868542e-12 -6.242236e-09
10 -2.018825e-05 1.235802e-04 -6.242236e-09 1.222288e-03
List of 8
$ coefficients : num [1:20] 2.05 3.04 1.50 2.02 -2.93e-05 ...
$ vcov : num [1:18, 1:18] 6.07e-03 -1.99e-03 9.18e-04 1.12e-07 1.10e-08 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:18] "2" "3" "4" "5" ...
.. ..$ : chr [1:18] "2" "3" "4" "5" ...
$ phi : num 0.903
$ alpha : num 0.183
$ num_iterations: num 10
$ converge : num 0
$ PenScore : num [1:20] -5.58e-07 9.31e-08 -2.85e-07 -8.79e-07 4.77e-02 ...
$ FDR : num 0.594
[1] 2.047051e+00 3.040296e+00 1.502942e+00 2.015991e+00 -2.925349e-05
[6] -2.367132e-06 -6.632613e-02 -9.152748e-07 -1.697829e-05 2.473875e-04
[11] 3.373039e+00 3.725877e+00 5.823727e-01 3.954125e+00 -4.312767e-06
[16] -5.340395e-01 -2.219041e-01 1.227100e-08 -5.939249e-01 8.185394e-01
2 3 4 5 6
2 6.067430e-03 -1.994187e-03 9.183373e-04 1.120478e-07 1.095106e-08
3 -1.994187e-03 8.499964e-03 -1.092966e-03 -1.012126e-07 -7.233250e-09
4 9.183373e-04 -1.092966e-03 1.260350e-02 1.008510e-07 -9.366246e-08
5 1.120478e-07 -1.012126e-07 1.008510e-07 6.906804e-10 2.524796e-11
6 1.095106e-08 -7.233250e-09 -9.366246e-08 2.524796e-11 1.415766e-11
7 5.278163e-04 -2.129094e-04 1.719097e-04 -1.105871e-08 -1.030054e-08
8 1.228719e-08 -3.525293e-08 -1.433152e-08 -6.163627e-12 -1.898112e-12
9 8.632915e-08 -1.129494e-07 -5.777191e-08 -4.938664e-11 -1.740980e-11
10 -4.324671e-06 3.419060e-06 -3.843469e-06 -2.464315e-09 -2.041790e-10
12 1.999765e-03 -1.229370e-03 6.040512e-03 7.458440e-07 -5.045008e-08
13 4.639094e-04 9.793754e-03 -1.706723e-03 -1.505214e-07 2.438135e-07
14 -2.183079e-04 -4.902097e-03 1.509391e-02 2.114872e-06 -1.581195e-07
15 5.563223e-09 -9.130134e-09 -1.674314e-09 -4.524822e-13 -4.428578e-13
16 1.469873e-04 8.580838e-03 3.479823e-04 1.819400e-07 5.758183e-07
17 -8.998121e-04 -2.775425e-03 -5.546974e-04 1.804347e-07 -2.432032e-07
18 -2.113816e-09 1.115609e-09 9.205544e-10 2.456952e-13 -6.624567e-14
19 -3.400299e-03 -3.688318e-04 3.636519e-03 -4.749089e-07 -1.252001e-07
20 7.295800e-04 -1.086563e-03 1.550250e-03 -3.656149e-07 -3.219096e-08
7 8 9 10 12
2 5.278163e-04 1.228719e-08 8.632915e-08 -4.324671e-06 1.999765e-03
3 -2.129094e-04 -3.525293e-08 -1.129494e-07 3.419060e-06 -1.229370e-03
4 1.719097e-04 -1.433152e-08 -5.777191e-08 -3.843469e-06 6.040512e-03
5 -1.105871e-08 -6.163627e-12 -4.938664e-11 -2.464315e-09 7.458440e-07
6 -1.030054e-08 -1.898112e-12 -1.740980e-11 -2.041790e-10 -5.045008e-08
7 1.161352e-03 1.142078e-08 9.199996e-08 -1.123398e-07 3.982237e-04
8 1.142078e-08 5.249917e-12 7.388985e-12 1.069282e-10 -1.086270e-08
9 9.199996e-08 7.388985e-12 2.731616e-10 7.432086e-10 2.378787e-07
10 -1.123398e-07 1.069282e-10 7.432086e-10 5.508336e-08 1.121240e-05
12 3.982237e-04 -1.086270e-08 2.378787e-07 1.121240e-05 4.357038e-01
13 -2.099369e-04 8.122335e-09 -2.650940e-07 -6.196575e-06 -9.242782e-03
14 9.231346e-04 3.339292e-08 2.429992e-06 1.681701e-05 5.602406e-01
15 4.405135e-09 -9.965784e-15 -8.227181e-15 -4.624539e-12 1.156936e-07
16 -1.648790e-03 -7.788926e-08 -1.562993e-06 -1.947880e-05 -1.313660e-01
17 2.327306e-03 3.131309e-09 7.656904e-07 3.154618e-06 -5.515750e-02
18 -6.864954e-10 -6.942618e-14 7.173760e-13 2.993692e-13 4.849884e-08
19 4.613168e-04 9.107466e-08 7.453231e-07 -8.924857e-07 -1.491422e-01
20 -9.581017e-05 -2.416204e-08 -2.228102e-07 5.021345e-06 1.243623e-01
13 14 15 16 17
2 4.639094e-04 -2.183079e-04 5.563223e-09 1.469873e-04 -8.998121e-04
3 9.793754e-03 -4.902097e-03 -9.130134e-09 8.580838e-03 -2.775425e-03
4 -1.706723e-03 1.509391e-02 -1.674314e-09 3.479823e-04 -5.546974e-04
5 -1.505214e-07 2.114872e-06 -4.524822e-13 1.819400e-07 1.804347e-07
6 2.438135e-07 -1.581195e-07 -4.428578e-13 5.758183e-07 -2.432032e-07
7 -2.099369e-04 9.231346e-04 4.405135e-09 -1.648790e-03 2.327306e-03
8 8.122335e-09 3.339292e-08 -9.965784e-15 -7.788926e-08 3.131309e-09
9 -2.650940e-07 2.429992e-06 -8.227181e-15 -1.562993e-06 7.656904e-07
10 -6.196575e-06 1.681701e-05 -4.624539e-12 -1.947880e-05 3.154618e-06
12 -9.242782e-03 5.602406e-01 1.156936e-07 -1.313660e-01 -5.515750e-02
13 2.024047e-01 -6.651392e-02 2.646102e-07 5.317334e-03 -4.446412e-02
14 -6.651392e-02 1.000502e+00 -1.459658e-07 -3.418954e-01 9.393061e-04
15 2.646102e-07 -1.459658e-07 2.993054e-12 -1.033343e-07 -1.192904e-07
16 5.317334e-03 -3.418954e-01 -1.033343e-07 4.571472e-01 -7.272123e-02
17 -4.446412e-02 9.393061e-04 -1.192904e-07 -7.272123e-02 1.550194e-01
18 -2.684176e-08 1.114626e-07 -9.608794e-14 -4.538110e-08 3.130715e-08
19 -6.188868e-02 -2.134241e-01 -9.419478e-08 1.009501e-01 6.735619e-02
20 -2.166507e-02 1.750626e-01 1.896163e-08 -1.903459e-02 -2.118618e-02
18 19 20
2 -2.113816e-09 -3.400299e-03 7.295800e-04
3 1.115609e-09 -3.688318e-04 -1.086563e-03
4 9.205544e-10 3.636519e-03 1.550250e-03
5 2.456952e-13 -4.749089e-07 -3.656149e-07
6 -6.624567e-14 -1.252001e-07 -3.219096e-08
7 -6.864954e-10 4.613168e-04 -9.581017e-05
8 -6.942618e-14 9.107466e-08 -2.416204e-08
9 7.173760e-13 7.453231e-07 -2.228102e-07
10 2.993692e-13 -8.924857e-07 5.021345e-06
12 4.849884e-08 -1.491422e-01 1.243623e-01
13 -2.684176e-08 -6.188868e-02 -2.166507e-02
14 1.114626e-07 -2.134241e-01 1.750626e-01
15 -9.608794e-14 -9.419478e-08 1.896163e-08
16 -4.538110e-08 1.009501e-01 -1.903459e-02
17 3.130715e-08 6.735619e-02 -2.118618e-02
18 6.498689e-14 5.871319e-09 1.206831e-08
19 5.871319e-09 2.745129e-01 -7.139645e-02
20 1.206831e-08 -7.139645e-02 8.965196e-02
pgee.mixed documentation built on May 2, 2019, 8:35 a.m.
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Description Usage Arguments Details Value Examples
View source: R/estimation_functions.R
Description
Estimate regression coefficients using Penalized Generalized Estimating Equations (PGEEs). Linear and binary logistic models are currently supported. In particular, can handle the case of bivariate correlated mixed outcomes, in which each cluster consists of one continuous outcome and one binary outcome.
Usage
1 2 3 4 5 |
Arguments
N |
Number of clusters. |
m |
Cluster size. Assumed equal across all clusters. Should be set to 2 for family=="Mixed". |
X |
Design matrix. If family=="Mixed", then design matrix for continuous responses. For family!="Mixed", should have N*m rows. For family=="Mixed", should have N rows. For standardize=TRUE, the first column should be a column vector of ones, corresponding to the intercept. |
Z |
Design matrix for binary responses for family=="Mixed". Should not be provided for other family types. If not provided for family=="Mixed", is set equal to X. For family!="Mixed", should have N*m rows. For family=="Mixed", should have N rows. For standardize=TRUE, the first column should be a column vector of ones, corresponding to the intercept. |
y |
Response vector. Don't use this argument for family == "Mixed". Instead, use arguments yc and yb. Since the cluster size is assumed equal across clusters, the vector is assumed to have the form c(y_1, y_2,...,y_N), with y_i = c(y_i1,...,y_im). |
yc |
Continuous response vector. Use only for family=="Mixed". |
yb |
Binary (0/1) response vector. Use only for family=="Mixed". |
wctype |
Working correlation type; one of "Ind", "CS", or "AR1". For family=="Mixed", "CS" and "AR1" are equivalent. |
family |
"Gaussian", "Binomial", or "Mixed" (use the last for bivariate mixed outcomes). Note that for "Binomial", currently only binary outcomes are supported. |
lambda |
Tuning parameter(s). A vector of two tuning parameters should be provided for family=="Mixed" (one for the continuous outcome coefficients, and one of the binary outcome coefficients). Otherwise, a single tuning parameter should be provided. |
eps |
Disturbance in the Linear Quadratic Approximation algorithm. |
maxiter |
The maximum number of iterations the Newton algorithm tries before declaring failure to converge. |
tol.coef |
Converge of the Newton algorithm is declared if two conditions are met: The L1-norm of the difference of successive iterates should be less than tol.coef AND the L1-norm of the penalized score should be less than tol.score. |
tol.score |
See |
init |
Vector of initial values for regression coefficients. For family=="Mixed", should be c(init_c, init_b). Defaults to glm values. |
standardize |
Standardize the design matrices prior to estimation? |
penalty |
"SCAD", "MCP", or "LASSO". |
weights |
Vector of cluster weights. All observations in a cluster are assumed to have the same weight. |
FDR |
Should the false discovery rate be estimated for family=="Mixed"? Currently, FDR cannot be estimated for other family types. |
fdr.corr |
Association parameter to use in FDR estimation. The default is to use the association parameter estimated from the PGEEs. |
fdr.type |
Estimate the FDR for only the coefficients corresponding to the continuous outcomes ("continuous"), for only the coefficients corresponding to the binary outcomes ("binary"), or for all coefficients ("all", the default). |
Details
pgee.fit estimates the regression coefficients for a single value of the
tuning paramter (or a single pair of tuning parameters in the mixed outcomes
case). To select optimal tuning parameter(s) via k-fold cross validation, see
cv.pgee.
For bivariate mixed outcomes, the false discovery rate can be estimated.
Value
A list
coefficients |
Vector of estimated regression coefficients. For family=="Mixed", this takes the form c(coef_c, coef_b). |
vcov |
Sandwich formula based covariance matrix of estimated
regression coefficients (other than the intercept(s)). The row/column
names correspond to elements of |
phi |
Estimated dispersion parameter. |
alpha |
Estimated association parameter. |
num_iterations |
Number of iterations the Newton algorithm ran. |
converge |
0=converged, 1=did not converge. |
PenScore |
Vector of penalized score functions at the estimated regression coefficients. If the algorithm converges, then these should be close to zero. |
FDR |
Estimated FDR for family=="Mixed", if requested. |
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 | set.seed(100)
# Gaussian
N <- 100
m <- 10
p <- 10
y <- rnorm(N * m)
# If you want standardize = TRUE, you must provide an intercept.
X <- cbind(1, matrix(rnorm(N * m * (p - 1)), N * m, p - 1))
fit <- pgee.fit(X = X, y = y, N = N, m = m, lambda = 0.5, wctype = "CS",
family = "Gaussian")
str(fit)
fit$coefficients
fit$vcov
# Binary
y <- sample(0:1, N*m, replace = TRUE)
fit <- pgee.fit(X = X, y = y, N = N, m = m, lambda = 0.1, wctype = "CS",
family = "Binomial")
str(fit)
fit$coefficients
fit$vcov
# Bivariate mixed outcomes
# Generate some data
Bc <- c(2.0, 3.0, 1.5, 2.0, rep(0, times = p - 4))
Bb <- c(0.7, -0.7, -0.4, rep(0, times = p - 3))
dat <- gen_mixed_data(Bc, Bc, N, 0.5)
# Estimate regression coefficients and false discovery rate
fit <- pgee.fit(X = dat$X, yc = dat$yc, yb = dat$yb, N = N, m = 2,
wctype = "CS", family = "Mixed", lambda = c(0.1, 0.05),
FDR = TRUE)
str(fit)
fit$coefficients
fit$vcov
|
Example output
List of 8
$ coefficients : num [1:10] 1.65e-02 3.83e-07 -2.66e-04 -8.06e-06 -3.09e-06 ...
$ vcov : num [1:9, 1:9] 8.61e-13 -1.44e-11 -1.36e-13 -9.17e-14 4.32e-14 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
$ phi : num 1.06
$ alpha : num -0.0112
$ num_iterations: num 13
$ converge : num 0
$ PenScore : num [1:10] -5.03e-16 -4.32e-04 1.24e-01 1.88e-01 1.64e-01 ...
$ FDR : logi NA
[1] 1.647210e-02 3.833171e-07 -2.660433e-04 -8.056127e-06 -3.087420e-06
[6] 8.031320e-07 -6.295737e-04 -6.726526e-03 -4.295715e-07 5.060864e-03
2 3 4 5 6
2 8.613359e-13 -1.443383e-11 -1.359931e-13 -9.165927e-14 4.317532e-14
3 -1.443383e-11 2.523863e-08 4.194025e-12 1.463658e-11 -2.834944e-11
4 -1.359931e-13 4.194025e-12 3.191533e-11 -2.170933e-12 -1.976114e-12
5 -9.165927e-14 1.463658e-11 -2.170933e-12 7.307825e-12 2.608954e-13
6 4.317532e-14 -2.834944e-11 -1.976114e-12 2.608954e-13 1.375238e-12
7 6.422694e-13 6.851341e-10 1.802262e-10 -2.399149e-10 3.363041e-11
8 9.411808e-11 -2.776368e-08 -2.546778e-09 8.121936e-10 3.822077e-10
9 -1.115545e-13 -8.915957e-13 6.852764e-13 4.606714e-13 8.435045e-14
10 3.529888e-10 7.157877e-08 -3.177134e-09 4.235949e-11 7.232707e-11
7 8 9 10
2 6.422694e-13 9.411808e-11 -1.115545e-13 3.529888e-10
3 6.851341e-10 -2.776368e-08 -8.915957e-13 7.157877e-08
4 1.802262e-10 -2.546778e-09 6.852764e-13 -3.177134e-09
5 -2.399149e-10 8.121936e-10 4.606714e-13 4.235949e-11
6 3.363041e-11 3.822077e-10 8.435045e-14 7.232707e-11
7 1.552830e-07 -1.729901e-07 -8.205465e-12 -3.954180e-08
8 -1.729901e-07 1.507694e-05 2.580865e-10 -9.704816e-07
9 -8.205465e-12 2.580865e-10 8.125506e-13 -8.012537e-11
10 -3.954180e-08 -9.704816e-07 -8.012537e-11 1.036791e-05
List of 8
$ coefficients : num [1:10] -9.78e-02 -5.87e-02 -7.56e-02 -2.58e-08 -5.10e-03 ...
$ vcov : num [1:9, 1:9] 1.39e-03 -2.39e-04 4.08e-09 2.34e-05 -2.31e-06 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
.. ..$ : chr [1:9] "2" "3" "4" "5" ...
$ phi : num 1
$ alpha : num 0.00668
$ num_iterations: num 11
$ converge : num 0
$ PenScore : num [1:10] -3.58e-07 -4.17e-05 -4.92e-05 1.23e-06 6.24e-03 ...
$ FDR : logi NA
[1] -9.775728e-02 -5.872854e-02 -7.561909e-02 -2.579482e-08 -5.098200e-03
[6] 6.709633e-04 4.849940e-03 2.215454e-02 6.060735e-07 4.823028e-02
2 3 4 5 6
2 1.390546e-03 -2.386341e-04 4.079203e-09 2.339723e-05 -2.313984e-06
3 -2.386341e-04 1.655552e-03 -1.258208e-09 -1.162351e-05 6.927630e-06
4 4.079203e-09 -1.258208e-09 3.193028e-12 9.306620e-10 2.058728e-11
5 2.339723e-05 -1.162351e-05 9.306620e-10 5.886218e-05 -6.298594e-07
6 -2.313984e-06 6.927630e-06 2.058728e-11 -6.298594e-07 1.114552e-06
7 -3.565046e-05 2.382287e-05 1.041267e-09 6.913538e-06 3.362207e-08
8 -6.986897e-05 -2.900527e-05 -2.355404e-09 1.336237e-05 4.538517e-08
9 -3.991919e-09 1.204502e-08 -5.790573e-15 2.937704e-09 -3.516431e-11
10 -1.053045e-04 -7.764264e-05 2.495350e-09 1.598950e-05 -3.252945e-06
7 8 9 10
2 -3.565046e-05 -6.986897e-05 -3.991919e-09 -1.053045e-04
3 2.382287e-05 -2.900527e-05 1.204502e-08 -7.764264e-05
4 1.041267e-09 -2.355404e-09 -5.790573e-15 2.495350e-09
5 6.913538e-06 1.336237e-05 2.937704e-09 1.598950e-05
6 3.362207e-08 4.538517e-08 -3.516431e-11 -3.252945e-06
7 4.297730e-05 4.124194e-06 5.968554e-10 -2.018825e-05
8 4.124194e-06 5.058943e-04 1.856554e-09 1.235802e-04
9 5.968554e-10 1.856554e-09 5.868542e-12 -6.242236e-09
10 -2.018825e-05 1.235802e-04 -6.242236e-09 1.222288e-03
List of 8
$ coefficients : num [1:20] 2.05 3.04 1.50 2.02 -2.93e-05 ...
$ vcov : num [1:18, 1:18] 6.07e-03 -1.99e-03 9.18e-04 1.12e-07 1.10e-08 ...
..- attr(*, "dimnames")=List of 2
.. ..$ : chr [1:18] "2" "3" "4" "5" ...
.. ..$ : chr [1:18] "2" "3" "4" "5" ...
$ phi : num 0.903
$ alpha : num 0.183
$ num_iterations: num 10
$ converge : num 0
$ PenScore : num [1:20] -5.58e-07 9.31e-08 -2.85e-07 -8.79e-07 4.77e-02 ...
$ FDR : num 0.594
[1] 2.047051e+00 3.040296e+00 1.502942e+00 2.015991e+00 -2.925349e-05
[6] -2.367132e-06 -6.632613e-02 -9.152748e-07 -1.697829e-05 2.473875e-04
[11] 3.373039e+00 3.725877e+00 5.823727e-01 3.954125e+00 -4.312767e-06
[16] -5.340395e-01 -2.219041e-01 1.227100e-08 -5.939249e-01 8.185394e-01
2 3 4 5 6
2 6.067430e-03 -1.994187e-03 9.183373e-04 1.120478e-07 1.095106e-08
3 -1.994187e-03 8.499964e-03 -1.092966e-03 -1.012126e-07 -7.233250e-09
4 9.183373e-04 -1.092966e-03 1.260350e-02 1.008510e-07 -9.366246e-08
5 1.120478e-07 -1.012126e-07 1.008510e-07 6.906804e-10 2.524796e-11
6 1.095106e-08 -7.233250e-09 -9.366246e-08 2.524796e-11 1.415766e-11
7 5.278163e-04 -2.129094e-04 1.719097e-04 -1.105871e-08 -1.030054e-08
8 1.228719e-08 -3.525293e-08 -1.433152e-08 -6.163627e-12 -1.898112e-12
9 8.632915e-08 -1.129494e-07 -5.777191e-08 -4.938664e-11 -1.740980e-11
10 -4.324671e-06 3.419060e-06 -3.843469e-06 -2.464315e-09 -2.041790e-10
12 1.999765e-03 -1.229370e-03 6.040512e-03 7.458440e-07 -5.045008e-08
13 4.639094e-04 9.793754e-03 -1.706723e-03 -1.505214e-07 2.438135e-07
14 -2.183079e-04 -4.902097e-03 1.509391e-02 2.114872e-06 -1.581195e-07
15 5.563223e-09 -9.130134e-09 -1.674314e-09 -4.524822e-13 -4.428578e-13
16 1.469873e-04 8.580838e-03 3.479823e-04 1.819400e-07 5.758183e-07
17 -8.998121e-04 -2.775425e-03 -5.546974e-04 1.804347e-07 -2.432032e-07
18 -2.113816e-09 1.115609e-09 9.205544e-10 2.456952e-13 -6.624567e-14
19 -3.400299e-03 -3.688318e-04 3.636519e-03 -4.749089e-07 -1.252001e-07
20 7.295800e-04 -1.086563e-03 1.550250e-03 -3.656149e-07 -3.219096e-08
7 8 9 10 12
2 5.278163e-04 1.228719e-08 8.632915e-08 -4.324671e-06 1.999765e-03
3 -2.129094e-04 -3.525293e-08 -1.129494e-07 3.419060e-06 -1.229370e-03
4 1.719097e-04 -1.433152e-08 -5.777191e-08 -3.843469e-06 6.040512e-03
5 -1.105871e-08 -6.163627e-12 -4.938664e-11 -2.464315e-09 7.458440e-07
6 -1.030054e-08 -1.898112e-12 -1.740980e-11 -2.041790e-10 -5.045008e-08
7 1.161352e-03 1.142078e-08 9.199996e-08 -1.123398e-07 3.982237e-04
8 1.142078e-08 5.249917e-12 7.388985e-12 1.069282e-10 -1.086270e-08
9 9.199996e-08 7.388985e-12 2.731616e-10 7.432086e-10 2.378787e-07
10 -1.123398e-07 1.069282e-10 7.432086e-10 5.508336e-08 1.121240e-05
12 3.982237e-04 -1.086270e-08 2.378787e-07 1.121240e-05 4.357038e-01
13 -2.099369e-04 8.122335e-09 -2.650940e-07 -6.196575e-06 -9.242782e-03
14 9.231346e-04 3.339292e-08 2.429992e-06 1.681701e-05 5.602406e-01
15 4.405135e-09 -9.965784e-15 -8.227181e-15 -4.624539e-12 1.156936e-07
16 -1.648790e-03 -7.788926e-08 -1.562993e-06 -1.947880e-05 -1.313660e-01
17 2.327306e-03 3.131309e-09 7.656904e-07 3.154618e-06 -5.515750e-02
18 -6.864954e-10 -6.942618e-14 7.173760e-13 2.993692e-13 4.849884e-08
19 4.613168e-04 9.107466e-08 7.453231e-07 -8.924857e-07 -1.491422e-01
20 -9.581017e-05 -2.416204e-08 -2.228102e-07 5.021345e-06 1.243623e-01
13 14 15 16 17
2 4.639094e-04 -2.183079e-04 5.563223e-09 1.469873e-04 -8.998121e-04
3 9.793754e-03 -4.902097e-03 -9.130134e-09 8.580838e-03 -2.775425e-03
4 -1.706723e-03 1.509391e-02 -1.674314e-09 3.479823e-04 -5.546974e-04
5 -1.505214e-07 2.114872e-06 -4.524822e-13 1.819400e-07 1.804347e-07
6 2.438135e-07 -1.581195e-07 -4.428578e-13 5.758183e-07 -2.432032e-07
7 -2.099369e-04 9.231346e-04 4.405135e-09 -1.648790e-03 2.327306e-03
8 8.122335e-09 3.339292e-08 -9.965784e-15 -7.788926e-08 3.131309e-09
9 -2.650940e-07 2.429992e-06 -8.227181e-15 -1.562993e-06 7.656904e-07
10 -6.196575e-06 1.681701e-05 -4.624539e-12 -1.947880e-05 3.154618e-06
12 -9.242782e-03 5.602406e-01 1.156936e-07 -1.313660e-01 -5.515750e-02
13 2.024047e-01 -6.651392e-02 2.646102e-07 5.317334e-03 -4.446412e-02
14 -6.651392e-02 1.000502e+00 -1.459658e-07 -3.418954e-01 9.393061e-04
15 2.646102e-07 -1.459658e-07 2.993054e-12 -1.033343e-07 -1.192904e-07
16 5.317334e-03 -3.418954e-01 -1.033343e-07 4.571472e-01 -7.272123e-02
17 -4.446412e-02 9.393061e-04 -1.192904e-07 -7.272123e-02 1.550194e-01
18 -2.684176e-08 1.114626e-07 -9.608794e-14 -4.538110e-08 3.130715e-08
19 -6.188868e-02 -2.134241e-01 -9.419478e-08 1.009501e-01 6.735619e-02
20 -2.166507e-02 1.750626e-01 1.896163e-08 -1.903459e-02 -2.118618e-02
18 19 20
2 -2.113816e-09 -3.400299e-03 7.295800e-04
3 1.115609e-09 -3.688318e-04 -1.086563e-03
4 9.205544e-10 3.636519e-03 1.550250e-03
5 2.456952e-13 -4.749089e-07 -3.656149e-07
6 -6.624567e-14 -1.252001e-07 -3.219096e-08
7 -6.864954e-10 4.613168e-04 -9.581017e-05
8 -6.942618e-14 9.107466e-08 -2.416204e-08
9 7.173760e-13 7.453231e-07 -2.228102e-07
10 2.993692e-13 -8.924857e-07 5.021345e-06
12 4.849884e-08 -1.491422e-01 1.243623e-01
13 -2.684176e-08 -6.188868e-02 -2.166507e-02
14 1.114626e-07 -2.134241e-01 1.750626e-01
15 -9.608794e-14 -9.419478e-08 1.896163e-08
16 -4.538110e-08 1.009501e-01 -1.903459e-02
17 3.130715e-08 6.735619e-02 -2.118618e-02
18 6.498689e-14 5.871319e-09 1.206831e-08
19 5.871319e-09 2.745129e-01 -7.139645e-02
20 1.206831e-08 -7.139645e-02 8.965196e-02
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