polygenic: Estimation of polygenic model
In GenABEL: genome-wide SNP association analysis
Description
Usage
Arguments
Details
Value
Note
Author(s)
References
See Also
Examples
Description
This function maximises the likelihood of the data under
polygenic model with covariates an reports twice negative
maximum likelihood estimates and the inverse of the
variance-covariance matrix at the point of ML.
Usage
1
2
3
4
5
6
7
polygenic(formula, kinship.matrix, data, fixh2,
starth2 = 0.3, trait.type = "gaussian",
opt.method = "nlm", scaleh2 = 1, quiet = FALSE,
steptol = 1e-08, gradtol = 1e-08, optimbou = 8,
fglschecks = TRUE, maxnfgls = 8, maxdiffgls = 1e-04,
patchBasedOnFGLS = TRUE, llfun = "polylik_eigen",
eigenOfRel, ...)
Arguments
formula
Formula describing fixed effects to be
used in the analysis, e.g. y ~ a + b means that outcome
(y) depends on two covariates, a and b. If no covariates
used in the analysis, skip the right-hand side of the
equation.
kinship.matrix
Kinship matrix, as provided by e.g.
ibs(,weight="freq"), or estimated outside of GenABEL from
pedigree data.
data
An (optional) object of
gwaa.data-class or a data frame with
outcome and covariates
fixh2
Optional value of heritability to be used,
instead of maximisation. The uses of this option are
two-fold: (a) testing significance of heritability and
(b) using a priori known heritability to derive the rest
of MLEs and var.-cov. matrix.
starth2
Starting value for h2 estimate
trait.type
"gaussian" or "binomial"
opt.method
"nlm" or "optim". These two use
different optimisation functions. We suggest using the
default nlm, although optim
may give better results in some situations
scaleh2
Only relevant when "nlm" optimisation
function is used. "scaleh2" is the heritability scaling
parameter, regulating how "big" are parameter changes in
h2 with respect to changes in other parameters. As other
parameters are estimated from previous regression, these
are expected to change little from the initial estimate.
The default value of 1000 proved to work rather well
under a range of conditions.
quiet
If FALSE (default), details of optimisation
process are reported
steptol
steptal parameter of "nlm"
gradtol
gradtol parameter of "nlm"
optimbou
fixed effects boundary scale parameter
for 'optim'
fglschecks
additional check for convergence on/off
(convergence between estimates obtained and that from
FGLS)
maxnfgls
number of fgls checks to perform
maxdiffgls
max difference allowed in fgls checks
patchBasedOnFGLS
if FGLS checks not passed,
'patch' fixed effect estimates based on FGLS expectation
llfun
function to compute likelihood (default
'polylik_eigen', also available – but not recommended –
'polylik')
eigenOfRel
results of eigen(relationship matrix =
2*kinship.matrix). Passing this can decrease
computational time substantially if multiple traits are
analysed using the same kinship matrix. This option will
not work if any NA's are found in the trait and/or
covariates and if the dimensions of the 'eigen'-object,
trait, covariates, kinship do not match.
...
Optional arguments to be passed to
nlm or (optim) minimisation
function
Details
One of the major uses of this function is to estimate
residuals of the trait and the inverse of the
variance-covariance matrix for further use in analysis
with mmscore and grammar.
Also, it can be used for a variant of GRAMMAR analysis,
which allows for permutations for GW significance by use
of environmental residuals as an analysis trait with
qtscore.
"Environmental residuals" (not to be mistaken with just
"residuals") are the residual where both the effect of
covariates AND the estimated polygenic effect (breeding
values) are factored out. This thus provides an estimate
of the trait value contributed by environment (or,
turning this other way around, the part of the trait not
explained by covariates and by the polygene). Polygenic
residuals are estimated as
σ^2 V^{-1} (Y - (\hat{μ} + \hat{β} C_1
+ ...))
where sigma^2 is the residual variance,
V^{-1} is the InvSigma (inverse of the var-cov
matrix at the maximum of polygenic model) and (Y -
(\hat{μ} + \hat{β} C_1 + ...)) is the trait values
adjusted for covariates (also at at the maximum of
polygenic model likelihood).
It can also be used for heritability analysis. If you
want to test significance of heritability, estimate the
model and write down the function minimum reported at the
"h2an" element of the output (this is twice the negative
MaxLikelihood). Then do a next round of estimation, but
set fixh2=0. The difference between your function minima
gives a test distributed as chi-squared with 1 d.f.
The way to compute the likelihood is partly based on the
paper of Thompson (see refs), namely instead of taking
the inverse of the var-cov matrix every time,
eigenvectors of the inverse of G (taken only once) are
used.
Value
A list with values
h2an
A list supplied by the
nlm minimisation routine. Of particular
interest are elements "estimate" containing parameter
maximal likelihood estimates (MLEs) (order: mean, betas
for covariates, heritability, (polygenic + residual
variance)). The value of twice negative maximum
log-likelihood is returned as h2an\$minimum.
esth2
Estimate (or fixed value) of heritability
residualY
Residuals from analysis, based on
covariate effects only; NOTE: these are NOT grammar
"environmental residuals"!
pgresidualY
Environmental residuals from analysis,
based on covariate effects and predicted breeding value.
grresidualY
GRAMMAR+ transformed trait
residuals
grammarGamma
list with GRAMMAR-gamma
correction factors
InvSigma
Inverse of the
variance-covariance matrix, computed at the MLEs – these
are used in mmscore and
grammar functions.
call
The details
of call
measuredIDs
Logical values for IDs who
were used in analysis (traits and all covariates
measured) == TRUE
convFGLS
was convergence
achieved according to FGLS criterionE
Note
Presence of twins may complicate your analysis. Check the
kinship matrix for singularities, or rather use
check.marker for identification of twin
samples. Take special care in interpretation.
If a trait (no covariates) is used, make sure that the
order of IDs in the kinship.matrix is exactly the same as
in the outcome
Please note that there is alternative to 'polygenic',
polygenic_hglm, which is faster than
polygenic() with the llfun='polylik' option, but slightly
slower than the default polygenic().
Author(s)
Yurii Aulchenko, Gulnara Svischeva
References
Thompson EA, Shaw RG (1990) Pedigree analysis for
quantitative traits: variance components without matrix
inversion. Biometrics 46, 399-413.
for original GRAMMAR
Aulchenko YS, de Koning DJ, Haley C. Genomewide rapid
association using mixed model and regression: a fast and
simple method for genome-wide pedigree-based quantitative
trait loci association analysis. Genetics. 2007
177(1):577-85.
for GRAMMAR-GC
Amin N, van Duijn CM, Aulchenko YS. A genomic background
based method for association analysis in related
individuals. PLoS ONE. 2007 Dec 5;2(12):e1274.
for GRAMMAR-Gamma
Svischeva G, Axenovich TI, Belonogova NM, van Duijn CM,
Aulchenko YS. Rapid variance components-based method for
whole-genome association analysis. Nature Genetics. 2012
44:1166-1170. doi:10.1038/ng.2410
for GRAMMAR+ transformation
Belonogova NM, Svishcheva GR, van Duijn CM, Aulchenko YS,
Axenovich TI (2013) Region-Based Association Analysis of
Human Quantitative Traits in Related Individuals. PLoS
ONE 8(6): e65395. doi:10.1371/journal.pone.0065395
See Also
polygenic_hglm, mmscore,
grammar
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
# note that procedure runs on CLEAN data
require(GenABEL.data)
data(ge03d2ex.clean)
gkin <- ibs(ge03d2ex.clean,w="freq")
h2ht <- polygenic(height ~ sex + age, kin=gkin, ge03d2ex.clean)
# estimate of heritability
h2ht$esth2
# other parameters
h2ht$h2an
# the minimum twice negative log-likelihood
h2ht$h2an$minimum
# twice maximum log-likelihood
-h2ht$h2an$minimum
# for binary trait (experimental)
h2dm <- polygenic(dm2 ~ sex + age, kin=gkin, ge03d2ex.clean, trait="binomial")
# estimated parameters
h2dm$h2an
Example output
Loading required package: MASS
Loading required package: GenABEL.data
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
-0.03595906 1.35161070 -0.01526032
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] -0.03595906 1.35161070 -0.01526032 0.30000000 0.56541567
Function Value
[1] 44.96445
Gradient:
[1] 0.6952411 -4.9601763 -1.0986500 -7.4497076 7.7513129
iteration = 1
Step:
[1] -5.201715e-05 3.711147e-04 8.219974e-05 5.573786e-04 -5.799444e-04
Parameter:
[1] -0.03601108 1.35198181 -0.01517812 0.30055738 0.56483573
Function Value
[1] 44.95909
Gradient:
[1] 3.107222 -3.511972 121.907800 -7.432526 7.555024
iteration = 2
Step:
[1] -0.0056803906 0.0391389920 -0.0004557513 0.0589434941 -0.0613165833
Parameter:
[1] -0.04169147 1.39112081 -0.01563388 0.35950087 0.50351915
Function Value
[1] 44.63419
Gradient:
[1] 0.1555315 -2.8746362 -43.4451610 -6.8388025 -17.7974660
iteration = 3
Step:
[1] 0.0018629761 -0.0130601242 0.0001444049 -0.0195093144 0.0215087235
Parameter:
[1] -0.03982849 1.37806068 -0.01548947 0.33999156 0.52502787
Function Value
[1] 44.53947
Gradient:
[1] 1.011636 -3.226584 5.550631 -7.085987 -7.490362
iteration = 4
Step:
[1] -2.994997e-04 1.837261e-03 -1.748087e-05 2.931252e-03 -1.889602e-03
Parameter:
[1] -0.04012799 1.37989794 -0.01550695 0.34292281 0.52313827
Function Value
[1] 44.52749
Gradient:
[1] 0.9640696 -3.1335755 2.5363639 -7.0480591 -8.3212282
iteration = 5
Step:
[1] -0.0024710671 0.0141878257 -0.0001288244 0.0234295749 -0.0100040555
Parameter:
[1] -0.04259906 1.39408577 -0.01563578 0.36635239 0.51313421
Function Value
[1] 44.43237
Gradient:
[1] 0.6645141 -2.3289872 -16.7405295 -6.7102443 -12.9213073
iteration = 6
Step:
[1] -0.0034887192 0.0186767407 -0.0001586064 0.0320319929 -0.0066370511
Parameter:
[1] -0.04608778 1.41276251 -0.01579438 0.39838438 0.50649716
Function Value
[1] 44.29205
Gradient:
[1] 0.434841 -1.101415 -32.878705 -6.206905 -16.232392
iteration = 7
Step:
[1] -0.0083824716 0.0424238096 -0.0003400073 0.0750898987 -0.0032228593
Parameter:
[1] -0.05447025 1.45518632 -0.01613439 0.47347428 0.50327430
Function Value
[1] 43.9565
Gradient:
[1] 0.2351745 1.9975845 -51.3453032 -5.0223199 -18.4659207
iteration = 8
Step:
[1] -0.0094453882 0.0445536478 -0.0003308165 0.0821760264 0.0116543804
Parameter:
[1] -0.06391564 1.49973997 -0.01646521 0.55565030 0.51492868
Function Value
[1] 43.58117
Gradient:
[1] 0.5808767 5.5383725 -40.0186002 -3.9310594 -14.0381792
iteration = 9
Step:
[1] -0.0058783413 0.0239988528 -0.0001573366 0.0484418571 0.0221591395
Parameter:
[1] -0.06979398 1.52373882 -0.01662254 0.60409216 0.53708782
Function Value
[1] 43.34279
Gradient:
[1] 1.051246 7.349500 -16.605703 -3.642096 -5.229185
iteration = 10
Step:
[1] -1.158292e-03 1.756650e-03 6.728088e-06 7.518883e-03 1.300087e-02
Parameter:
[1] -0.07095227 1.52549547 -0.01661582 0.61161104 0.55008869
Function Value
[1] 43.29157
Gradient:
[1] 1.2567523 7.3859214 -3.9416819 -3.7778617 -0.2132411
iteration = 11
Step:
[1] -1.177800e-04 -1.724444e-03 2.472415e-05 -4.189617e-04 3.868139e-03
Parameter:
[1] -0.07107005 1.52377103 -0.01659109 0.61119208 0.55395683
Function Value
[1] 43.28242
Gradient:
[1] 1.342678 7.225841 1.754204 -3.838303 1.270675
iteration = 12
Step:
[1] -2.898677e-04 -2.807326e-03 3.975047e-05 1.080056e-05 3.640250e-03
Parameter:
[1] -0.07135992 1.52096370 -0.01655134 0.61120288 0.55759708
Function Value
[1] 43.26933
Gradient:
[1] 1.361838 6.920845 4.765588 -3.870127 2.636419
iteration = 13
Step:
[1] -1.248027e-03 -6.035858e-03 9.903974e-05 3.872902e-03 5.921292e-03
Parameter:
[1] -0.07260794 1.51492784 -0.01645230 0.61507578 0.56351837
Function Value
[1] 43.23549
Gradient:
[1] 1.467064 6.284171 14.956889 -3.829444 4.722074
iteration = 14
Step:
[1] -0.003667111 -0.010338786 0.000193242 0.015963932 0.007831988
Parameter:
[1] -0.07627506 1.50458906 -0.01625906 0.63103972 0.57135036
Function Value
[1] 43.16296
Gradient:
[1] 1.304292 4.918091 16.850343 -3.559436 7.135861
iteration = 15
Step:
[1] -0.0086120418 -0.0148080383 0.0003485246 0.0432997412 0.0080067358
Parameter:
[1] -0.08488710 1.48978102 -0.01591053 0.67433946 0.57935709
Function Value
[1] 43.02931
Gradient:
[1] 1.339562 2.899138 37.143789 -2.798269 8.803389
iteration = 16
Step:
[1] -0.0135627829 -0.0116172745 0.0003872629 0.0752708151 0.0024409612
Parameter:
[1] -0.09844988 1.47816374 -0.01552327 0.74961027 0.58179805
Function Value
[1] 42.86704
Gradient:
[1] -0.2311334 -0.1894086 -16.1612798 -1.5413494 7.4262848
iteration = 17
Step:
[1] -0.0121374504 0.0030276774 0.0002412749 0.0754016688 -0.0052203932
Parameter:
[1] -0.1105873 1.4811914 -0.0152820 0.8250119 0.5765777
Function Value
[1] 42.76368
Gradient:
[1] 3.0988223 0.9230727 165.8923264 -0.6038011 2.8933417
iteration = 18
Step:
[1] -1.193064e-02 1.500920e-02 -8.709254e-05 8.100285e-02 -4.051641e-03
Parameter:
[1] -0.12251797 1.49620062 -0.01536909 0.90601479 0.57252602
Function Value
[1] 42.7415
Gradient:
[1] -25.196607 -15.161577 -1208.005117 -1.512464 -2.525064
iteration = 19
Step:
[1] -5.024815e-03 6.766438e-03 8.668581e-06 3.437199e-02 -5.908472e-04
Parameter:
[1] -0.12754279 1.50296706 -0.01536042 0.94038678 0.57193517
Function Value
[1] 42.66949
Gradient:
[1] -43.816646 -25.735535 -2107.566022 -4.461268 -4.814848
iteration = 20
Step:
[1] -6.727971e-03 8.226600e-03 1.406721e-05 4.552273e-02 -6.173578e-04
Parameter:
[1] -0.13427076 1.51119366 -0.01534635 0.98590951 0.57131781
Function Value
[1] 42.43899
Gradient:
[1] -2.184576e+02 -1.263053e+02 -1.057406e+04 6.603956e-01 -9.174241e+00
iteration = 21
Step:
[1] -1.571452e-04 2.488553e-04 1.107746e-06 1.099544e-03 -5.839027e-05
Parameter:
[1] -0.13442790 1.51144251 -0.01534525 0.98700906 0.57125942
Function Value
[1] 42.43301
Gradient:
[1] -235.625791 -136.196181 -11406.280852 4.424992 -9.378391
iteration = 22
Step:
[1] -4.598765e-04 2.113960e-03 1.876863e-06 4.034224e-03 2.353895e-04
Parameter:
[1] -0.13488778 1.51355647 -0.01534337 0.99104328 0.57149481
Function Value
[1] 42.23814
Gradient:
[1] -303.14149 -174.95881 -14673.75621 15.34813 -9.78877
iteration = 23
Step:
[1] -4.762620e-04 2.286486e-03 2.810688e-06 4.252874e-03 7.929576e-05
Parameter:
[1] -0.13536404 1.51584296 -0.01534056 0.99529616 0.57157411
Function Value
[1] 42.04943
Gradient:
[1] -492.91950 -284.20853 -23858.07348 103.41617 -10.75527
iteration = 24
Step:
[1] -4.880739e-05 8.052088e-04 -1.281772e-06 7.754507e-04 2.914410e-04
Parameter:
[1] -0.13541285 1.51664817 -0.01534184 0.99607161 0.57186555
Function Value
[1] 41.9555
Gradient:
[1] -553.81021 -319.24373 -26800.66105 141.37753 -10.83452
iteration = 25
Step:
[1] -5.817446e-05 3.629908e-03 -1.135983e-05 2.511617e-03 1.930430e-03
Parameter:
[1] -0.1354710 1.5202781 -0.0153532 0.9985832 0.5737960
Function Value
[1] 41.6486
Gradient:
[1] -1112.25314 -640.91055 -53759.09134 861.17589 -11.48326
iteration = 26
Step:
[1] 3.152763e-04 5.808994e-03 -4.048516e-05 6.614566e-04 1.947813e-02
Parameter:
[1] -0.13515575 1.52608707 -0.01539368 0.99924468 0.59327411
Function Value
[1] 40.05337
Gradient:
[1] -1153.825163 -664.287358 -55518.442458 417.864667 -3.036911
iteration = 27
Step:
[1] 7.914019e-05 9.297012e-04 -1.026842e-05 1.121967e-04 1.794036e-04
Parameter:
[1] -0.13507661 1.52701677 -0.01540395 0.99935688 0.59345351
Function Value
[1] 39.96911
Gradient:
[1] -1285.334290 -740.027916 -61813.664680 605.314683 -3.111495
iteration = 28
Step:
[1] 4.883655e-04 5.054683e-03 -6.185446e-05 3.141007e-04 5.701953e-04
Parameter:
[1] -0.13458824 1.53207145 -0.01546581 0.99967098 0.59402371
Function Value
[1] 39.72506
Gradient:
[1] -2048.838072 -1179.789650 -98298.564222 2448.057715 -3.654304
iteration = 29
Step:
[1] 1.214517e-04 1.276153e-03 -1.452827e-05 7.376215e-05 6.570941e-04
Parameter:
[1] -0.13446679 1.53334761 -0.01548034 0.99974474 0.59468080
Function Value
[1] 39.61036
Gradient:
[1] -2.411351e+03 -1.388711e+03 -1.155454e+05 3.694601e+03 -3.673803e+00
iteration = 30
Step:
[1] 7.452209e-05 7.672971e-04 -8.911639e-06 2.939784e-05 4.996318e-04
Parameter:
[1] -0.13439227 1.53411490 -0.01548925 0.99977414 0.59518043
Function Value
[1] 39.518
Gradient:
[1] -2.581160e+03 -1.486559e+03 -1.235815e+05 4.304559e+03 -3.560188e+00
iteration = 31
Step:
[1] 2.626547e-04 2.543459e-03 -3.242419e-05 5.485978e-05 8.812888e-04
Parameter:
[1] -0.13412961 1.53665836 -0.01552167 0.99982900 0.59606172
Function Value
[1] 39.37919
Gradient:
[1] -3.063640e+03 -1.764532e+03 -1.464272e+05 6.484346e+03 -3.505848e+00
iteration = 32
Step:
[1] -4.850160e-04 -4.027918e-03 6.994311e-05 1.291776e-04 5.521813e-03
Parameter:
[1] -0.13461463 1.53263044 -0.01545173 0.99995818 0.60158353
Function Value
[1] 38.5911
Gradient:
[1] -7.015695e+03 -4.044164e+03 -3.307688e+05 4.239322e+04 -2.747247e+00
iteration = 33
Step:
[1] -0.0036846213 -0.0331472710 0.0004729021 -0.0001385644 0.0097942344
Parameter:
[1] -0.13829925 1.49948317 -0.01497883 0.99981961 0.61137777
Function Value
[1] 37.71216
Gradient:
[1] -1176.042376 -679.935038 -54772.439345 -3683.879832 4.168696
iteration = 34
Step:
[1] 3.077973e-04 2.883885e-03 -4.095993e-05 5.731157e-06 1.596461e-05
Parameter:
[1] -0.13799145 1.50236706 -0.01501979 0.99982534 0.61139373
Function Value
[1] 37.71183
Gradient:
[1] -1261.023533 -728.643945 -58829.900330 -3587.156500 4.120981
iteration = 35
Step:
[1] 2.197557e-04 2.046782e-03 -2.907519e-05 4.230519e-06 3.375284e-05
Parameter:
[1] -0.13777170 1.50441384 -0.01504886 0.99982957 0.61142749
Function Value
[1] 37.71178
Gradient:
[1] -1323.662715 -764.555241 -61817.199961 -3511.308969 4.090928
iteration = 36
Step:
[1] -2.570604e-04 -2.373342e-03 3.376401e-05 -4.865204e-06 -6.183080e-05
Parameter:
[1] -0.1380288 1.5020405 -0.0150151 0.9998247 0.6113657
Function Value
[1] 37.71152
Gradient:
[1] -1252.311200 -723.571453 -60880.544794 -3360.513025 4.118845
iteration = 37
Step:
[1] -8.613738e-04 1.035953e-03 6.909211e-06 1.960728e-05 -9.759670e-03
Parameter:
[1] -0.13889013 1.50307645 -0.01500819 0.99984431 0.60160598
Function Value
[1] 37.51618
Gradient:
[1] -1257.166645 -726.276998 -61115.097604 -4067.154715 1.236159
iteration = 38
Step:
[1] -4.997227e-03 1.508595e-02 -6.728274e-05 1.496902e-04 -5.013312e-02
Parameter:
[1] -0.14388736 1.51816240 -0.01507547 0.99999401 0.55147287
Function Value
[1] 34.53783
Gradient:
[1] -5980.33896 -3448.23574 -290875.51455 44010.32035 -17.30548
iteration = 39
Parameter:
[1] -0.14388736 1.51816240 -0.01507547 0.99999401 0.55147287
Function Value
[1] 34.53783
Gradient:
[1] -5980.33896 -3448.23574 -290875.51455 44010.32035 -17.30548
Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.
difFGLS:
[1] 0.1438866 1.5181628 0.0150402
fixed effect betas changed to FGLS-betas for re-estimation
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] -7.250237e-07 -4.180867e-07 -3.526983e-05 9.999940e-01 5.514729e-01
Function Value
[1] 172.985
Gradient:
[1] 21.39558 -172.36984 81479.68470 -182035.74323 -268.35463
iteration = 1
Step:
[1] -2.703002e-10 2.177627e-09 -1.029370e-06 2.299741e-06 3.390247e-09
Parameter:
[1] -7.252940e-07 -4.159090e-07 -3.629920e-05 9.999963e-01 5.514729e-01
Function Value
[1] 172.6428
Gradient:
[1] -5554.4953 -3392.9377 -140236.1148 -262282.5545 -268.6098
iteration = 2
Step:
[1] 7.941777e-10 9.124004e-10 -1.664463e-07 4.592674e-07 6.591203e-10
Parameter:
[1] -7.244998e-07 -4.149966e-07 -3.646565e-05 9.999968e-01 5.514729e-01
Function Value
[1] 172.5864
Gradient:
[1] -7371.9159 -4442.8849 -210347.7719 -271499.3653 -268.7475
iteration = 3
Step:
[1] 1.293685e-08 8.558506e-09 -7.623648e-08 2.860451e-07 1.563140e-09
Parameter:
[1] -7.115630e-07 -4.064381e-07 -3.654189e-05 9.999971e-01 5.514729e-01
Function Value
[1] 172.5462
Gradient:
[1] -8600.0836 -5152.6135 -255826.4738 -274825.1718 -268.8418
iteration = 4
Step:
[1] 4.468662e-08 2.874172e-08 -8.846557e-08 4.464591e-07 4.174900e-09
Parameter:
[1] -6.668764e-07 -3.776964e-07 -3.663035e-05 9.999975e-01 5.514729e-01
Function Value
[1] 172.4752
Gradient:
[1] -10825.8889 -6439.1582 -335345.8142 -268133.3274 -269.0097
iteration = 5
Step:
[1] 2.565799e-07 1.634779e-07 -1.633817e-07 1.280177e-06 2.165055e-08
Parameter:
[1] -4.102964e-07 -2.142185e-07 -3.679373e-05 9.999988e-01 5.514729e-01
Function Value
[1] 172.3173
Gradient:
[1] -24612.3641 -14410.0061 -808097.4807 2260957.4104 -270.0145
iteration = 6
Step:
[1] 4.686870e-08 3.427485e-08 1.245002e-07 -5.587739e-07 1.067738e-08
Parameter:
[1] -3.634277e-07 -1.799436e-07 -3.666923e-05 9.999982e-01 5.514729e-01
Function Value
[1] 172.3054
Gradient:
[1] -15524.6733 -9156.8070 -487173.3472 -147023.0020 -269.3152
iteration = 7
Step:
[1] 4.349374e-07 2.815183e-07 1.441202e-07 2.995798e-08 4.341239e-08
Parameter:
[1] 7.150968e-08 1.015747e-07 -3.652511e-05 9.999982e-01 5.514730e-01
Function Value
[1] 172.1833
Gradient:
[1] -14003.2608 -8279.9597 -408615.7019 -280481.7433 -269.1244
iteration = 8
Step:
[1] 8.227897e-06 5.266223e-06 2.162161e-06 8.336993e-07 7.306458e-07
Parameter:
[1] 8.299407e-06 5.367798e-06 -3.436295e-05 9.999991e-01 5.514737e-01
Function Value
[1] 171.8232
Gradient:
[1] 25284.9856 14349.9774 1746837.4447 2161826.8315 -269.6327
iteration = 9
Step:
[1] -2.830714e-06 -1.826299e-06 -8.838457e-07 -3.471264e-07 -2.734530e-07
Parameter:
[1] 5.468693e-06 3.541499e-06 -3.524680e-05 9.999987e-01 5.514734e-01
Function Value
[1] 171.4498
Gradient:
[1] 3206.5172 1633.1726 532322.6384 -1480528.7173 -268.3798
iteration = 10
Step:
[1] 4.808095e-07 2.550995e-07 -3.446460e-07 1.197499e-07 -3.738298e-08
Parameter:
[1] 5.949502e-06 3.796599e-06 -3.559144e-05 9.999989e-01 5.514734e-01
Function Value
[1] 171.3448
Gradient:
[1] -2235.0938 -1508.8450 306534.6177 -1951739.0936 -268.3683
iteration = 11
Step:
[1] 7.382568e-07 4.096077e-07 -3.576726e-07 1.507269e-07 -3.014743e-08
Parameter:
[1] 6.687759e-06 4.206206e-06 -3.594912e-05 9.999990e-01 5.514733e-01
Function Value
[1] 171.3071
Gradient:
[1] -9328.2472 -5605.6778 23660.7024 2677876.0962 -268.5534
iteration = 12
Step:
[1] -2.183609e-07 -8.367507e-08 1.742902e-07 -2.322627e-08 6.603415e-08
Parameter:
[1] 6.469398e-06 4.122531e-06 -3.577483e-05 9.999990e-01 5.514734e-01
Function Value
[1] 171.2646
Gradient:
[1] -6016.2472 -3645.5854 -292032.4657 -9052.6643 -268.4355
iteration = 13
Step:
[1] -3.665899e-07 -1.138747e-07 2.957366e-07 -3.924904e-08 1.513485e-07
Parameter:
[1] 6.102808e-06 4.008656e-06 -3.547909e-05 9.999989e-01 5.514736e-01
Function Value
[1] 171.2574
Gradient:
[1] -389.8093 -401.0869 -18326.3318 -9053.2454 -268.3544
iteration = 14
Parameter:
[1] 6.102808e-06 4.008656e-06 -3.547909e-05 9.999989e-01 5.514736e-01
Function Value
[1] 171.2574
Gradient:
[1] -389.8093 -401.0869 -18326.3318 -9053.2454 -268.3544
Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.
difFGLS:
[1] 6.827759e-06 4.426701e-06 2.128240e-07
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning message:
In polygenic(height ~ sex + age, kin = gkin, ge03d2ex.clean) :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
[1] 0.9999989
$minimum
[1] 698.2069
$estimate
[1] 1.702026e+02 3.962819e-05 -3.507340e-04 9.999989e-01 5.389340e+01
$gradient
[1] -389.8093 -401.0869 -18326.3318 -9053.2454 -268.3544
$code
[1] 3
$iterations
[1] 14
[1] 698.2069
[1] -698.2069
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
-0.68387860 0.56774460 0.01787041
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] -0.68387860 0.56774460 0.01787041 0.30000000 4.51763042
Function Value
[1] 180.6698
Gradient:
[1] 0.0009084147 -0.0356880037 -0.4256702937 -4.4684565523 24.3849166591
iteration = 1
Step:
[1] -8.242247e-05 3.238051e-03 3.862201e-02 4.054329e-01 -2.212497e+00
Parameter:
[1] -0.68396103 0.57098265 0.05649242 0.70543294 2.30513301
Function Value
[1] 117.1616
Gradient:
[1] 8.519400 3.326277 347.254448 28.042685 39.447832
iteration = 2
Step:
[1] -0.14369299 -0.05610285 -5.85698852 -0.47298367 -0.66534928
Parameter:
[1] -0.8276540 0.5148798 -5.8004961 0.2324493 1.6397837
Function Value
[1] 109.6195
Gradient:
[1] 0.00000 0.00000 0.00000 43.90581 38.98239
iteration = 3
Step:
[1] -2.816365e-05 -1.099609e-05 -1.147963e-03 -2.419883e-02 -2.153337e-02
Parameter:
[1] -0.8276822 0.5148688 -5.8016441 0.2082504 1.6182504
Function Value
[1] 107.7294
Gradient:
[1] 0.00000 0.00000 0.00000 42.26395 39.75974
iteration = 4
Step:
[1] -0.0001760877 -0.0000687509 -0.0071774107 -0.1492786046 -0.3129398878
Parameter:
[1] -0.82785827 0.51480005 -5.80882147 0.05897184 1.30531047
Function Value
[1] 88.34065
Gradient:
[1] 0.00000 0.00000 0.00000 40.18280 45.02935
iteration = 5
Step:
[1] -1.666106e-05 -6.505070e-06 -6.791120e-04 -1.412435e-02 -2.961737e-02
Parameter:
[1] -0.82787493 0.51479354 -5.80950059 0.04484749 1.27569310
Function Value
[1] 86.43301
Gradient:
[1] 0.00000 0.00000 0.00000 40.20546 45.45210
iteration = 6
Step:
[1] -1.661784e-05 -6.488194e-06 -6.773502e-04 -1.408770e-02 -2.954091e-02
Parameter:
[1] -0.82789155 0.51478705 -5.81017794 0.03075978 1.24615219
Function Value
[1] 84.51764
Gradient:
[1] 0.00000 0.00000 0.00000 40.26049 45.84853
iteration = 7
Step:
[1] -1.656779e-05 -6.468656e-06 -6.753105e-04 -1.404528e-02 -2.945226e-02
Parameter:
[1] -0.82790812 0.51478058 -5.81085325 0.01671451 1.21669993
Function Value
[1] 82.59579
Gradient:
[1] 0.00000 0.00000 0.00000 40.34675 46.21406
iteration = 8
Step:
[1] -1.650629e-05 -6.444642e-06 -6.728034e-04 -1.399313e-02 -2.934316e-02
Parameter:
[1] -0.827924622 0.514774140 -5.811526050 0.002721372 1.187356776
Function Value
[1] 80.66945
Gradient:
[1] 0.00000 0.00000 0.00000 40.46308 46.54336
iteration = 9
Step:
[1] -1.642822e-06 -6.414162e-07 -6.696214e-05 -1.392695e-03 -2.920455e-03
Parameter:
[1] -0.827926265 0.514773498 -5.811593012 0.001328677 1.184436321
Function Value
[1] 80.47711
Gradient:
[1] 0.00000 0.00000 0.00000 40.47629 46.57400
iteration = 10
Step:
[1] -1.641932e-07 -6.410685e-08 -6.692584e-06 -1.391940e-04 -2.918873e-04
Parameter:
[1] -0.827926429 0.514773434 -5.811599705 0.001189483 1.184144433
Function Value
[1] 80.45788
Gradient:
[1] 0.00000 0.00000 0.00000 40.47763 46.57704
iteration = 11
Step:
[1] -1.641841e-07 -6.410332e-08 -6.692216e-06 -1.391864e-04 -2.918713e-04
Parameter:
[1] -0.827926593 0.514773370 -5.811606397 0.001050296 1.183852562
Function Value
[1] 80.43865
Gradient:
[1] 0.00000 0.00000 0.00000 40.47897 46.58008
iteration = 12
Step:
[1] -1.641751e-07 -6.409979e-08 -6.691847e-06 -1.391787e-04 -2.918552e-04
Parameter:
[1] -0.8279267572 0.5147733061 -5.8116130889 0.0009111176 1.1835607067
Function Value
[1] 80.41942
Gradient:
[1] 0.00000 0.00000 0.00000 40.48031 46.58311
iteration = 13
Step:
[1] -1.641660e-07 -6.409625e-08 -6.691477e-06 -1.391710e-04 -2.918391e-04
Parameter:
[1] -0.8279269213 0.5147732420 -5.8116197803 0.0007719466 1.1832688675
Function Value
[1] 80.4002
Gradient:
[1] 0.00000 0.00000 0.00000 40.48166 46.58613
iteration = 14
Step:
[1] -1.641569e-07 -6.409269e-08 -6.691107e-06 -1.391633e-04 -2.918230e-04
Parameter:
[1] -0.8279270855 0.5147731779 -5.8116264714 0.0006327833 1.1829770446
Function Value
[1] 80.38097
Gradient:
[1] 0.00000 0.00000 0.00000 40.48300 46.58916
iteration = 15
Step:
[1] -1.641478e-07 -6.408913e-08 -6.690735e-06 -1.391556e-04 -2.918068e-04
Parameter:
[1] -0.8279272496 0.5147731138 -5.8116331622 0.0004936278 1.1826852378
Function Value
[1] 80.36174
Gradient:
[1] 0.00000 0.00000 0.00000 40.48436 46.59218
iteration = 16
Step:
[1] -1.641387e-07 -6.408557e-08 -6.690362e-06 -1.391478e-04 -2.917905e-04
Parameter:
[1] -0.82792741 0.51477305 -5.81163985 0.00035448 1.18239345
Function Value
[1] 80.34251
Gradient:
[1] 0.00000 0.00000 0.00000 40.48571 46.59519
iteration = 17
Step:
[1] -1.641295e-07 -6.408199e-08 -6.689989e-06 -1.391400e-04 -2.917743e-04
Parameter:
[1] -0.8279275779 0.5147729856 -5.8116465425 0.0002153399 1.1821016730
Function Value
[1] 80.32328
Gradient:
[1] 0.00000 0.00000 0.00000 40.48707 46.59820
iteration = 18
Step:
[1] -1.641203e-07 -6.407840e-08 -6.689615e-06 -1.391323e-04 -2.917579e-04
Parameter:
[1] -8.279277e-01 5.147729e-01 -5.811653e+00 7.620769e-05 1.181810e+00
Function Value
[1] 80.30405
Gradient:
[1] 0.00000 0.00000 0.00000 40.48842 46.60120
iteration = 19
Step:
[1] -1.641111e-08 -6.407481e-09 -6.689239e-07 -1.391244e-05 -2.917416e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811654e+00 6.229525e-05 1.181781e+00
Function Value
[1] 80.30213
Gradient:
[1] 0.00000 0.00000 0.00000 40.48856 46.60150
iteration = 20
Step:
[1] -1.641102e-08 -6.407445e-09 -6.689202e-07 -1.391237e-05 -2.917399e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811655e+00 4.838288e-05 1.181752e+00
Function Value
[1] 80.30021
Gradient:
[1] 0.0000 0.0000 0.0000 40.4887 46.6018
iteration = 21
Step:
[1] -1.641092e-08 -6.407409e-09 -6.689164e-07 -1.391229e-05 -2.917383e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811655e+00 3.447059e-05 1.181722e+00
Function Value
[1] 80.29828
Gradient:
[1] 0.00000 0.00000 0.00000 40.48883 46.60210
iteration = 22
Step:
[1] -1.641083e-08 -6.407373e-09 -6.689126e-07 -1.391221e-05 -2.917367e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811656e+00 2.055838e-05 1.181693e+00
Function Value
[1] 80.29636
Gradient:
[1] 0.00000 0.00000 0.00000 40.48897 46.60240
iteration = 23
Step:
[1] -1.641074e-08 -6.407337e-09 -6.689089e-07 -1.391213e-05 -2.917350e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 6.646253e-06 1.181664e+00
Function Value
[1] 80.29444
Gradient:
[1] 0.00000 0.00000 0.00000 40.48911 46.60270
iteration = 24
Step:
[1] -1.641065e-09 -6.407300e-10 -6.689051e-08 -1.391205e-06 -2.917334e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 5.255047e-06 1.181661e+00
Function Value
[1] 80.29424
Gradient:
[1] 0.00000 0.00000 0.00000 40.48912 46.60273
iteration = 25
Step:
[1] -1.641064e-09 -6.407297e-10 -6.689047e-08 -1.391205e-06 -2.917332e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 3.863843e-06 1.181658e+00
Function Value
[1] 80.29405
Gradient:
[1] 0.00000 0.00000 0.00000 40.48913 46.60276
iteration = 26
Step:
[1] -1.641063e-09 -6.407294e-10 -6.689044e-08 -1.391204e-06 -2.917331e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 2.472639e-06 1.181655e+00
Function Value
[1] 80.29386
Gradient:
[1] 0.00000 0.00000 0.00000 40.48915 46.60279
iteration = 27
Step:
[1] -1.641062e-09 -6.407289e-10 -6.689040e-08 -1.391203e-06 -2.917329e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.081436e-06 1.181652e+00
Function Value
[1] 80.29367
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60282
iteration = 28
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689036e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 9.423159e-07 1.181652e+00
Function Value
[1] 80.29365
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60283
iteration = 29
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689036e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 8.031957e-07 1.181652e+00
Function Value
[1] 80.29363
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60283
iteration = 30
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689035e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 6.640754e-07 1.181652e+00
Function Value
[1] 80.29361
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60283
iteration = 31
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689035e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 5.249553e-07 1.181651e+00
Function Value
[1] 80.29359
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60284
iteration = 32
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689034e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 3.858351e-07 1.181651e+00
Function Value
[1] 80.29357
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60284
iteration = 33
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689034e-09 -1.391202e-07 -2.917326e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 2.467149e-07 1.181651e+00
Function Value
[1] 80.29355
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60284
iteration = 34
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689034e-09 -1.391202e-07 -2.917326e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.075947e-07 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 35
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 9.368269e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 36
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 7.977067e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 37
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 6.585866e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 38
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 5.194664e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 39
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 3.803462e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 40
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 2.412261e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 41
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.021059e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 42
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.021059e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 -506861.07675 46.60285
Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.
difFGLS:
[1] 1.1763440 0.3818257 5.8156840
fixed effect betas changed to FGLS-betas for re-estimation
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] 3.484162e-01 1.329472e-01 4.027072e-03 1.021059e-08 1.181650e+00
Function Value
[1] 42.21514
Gradient:
[1] 1.3966371 -0.5273326 36.2719095 3.2599153 78.8275636
iteration = 1
Step:
[1] -4.978551e-11 1.879769e-11 -1.292975e-09 -1.162053e-10 -2.809944e-09
Parameter:
[1] 3.484162e-01 1.329472e-01 4.027071e-03 1.009439e-08 1.181650e+00
Function Value
[1] 42.21514
Gradient:
[1] 1.396637 -0.527333 36.271877 3.259915 78.827564
iteration = 2
Parameter:
[1] 3.484162e-01 1.329472e-01 4.027071e-03 1.006132e-08 1.181650e+00
Function Value
[1] 42.21514
Gradient:
[1] 1.3966363 -0.5273331 36.2718680 3.2599151 78.8275638
Successive iterates within tolerance.
Current iterate is probably solution.
difFGLS:
[1] 6.492118e-11 3.201203e-11 1.661003e-09
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning messages:
1: In polygenic(dm2 ~ sex + age, kin = gkin, ge03d2ex.clean, trait = "binomial") :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
2: In sqrt(fi) : NaNs produced
$minimum
[1] -51.17526
$estimate
[1] 3.484162e-01 1.329472e-01 4.027071e-03 1.006132e-08 1.181650e+00
$gradient
[1] 1.3966363 -0.5273331 36.2718680 3.2599151 78.8275638
$code
[1] 2
$iterations
[1] 2
GenABEL documentation built on May 30, 2017, 3:36 a.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 Details Value Note Author(s) References See Also Examples
Description
This function maximises the likelihood of the data under polygenic model with covariates an reports twice negative maximum likelihood estimates and the inverse of the variance-covariance matrix at the point of ML.
Usage
1 2 3 4 5 6 7 | polygenic(formula, kinship.matrix, data, fixh2,
starth2 = 0.3, trait.type = "gaussian",
opt.method = "nlm", scaleh2 = 1, quiet = FALSE,
steptol = 1e-08, gradtol = 1e-08, optimbou = 8,
fglschecks = TRUE, maxnfgls = 8, maxdiffgls = 1e-04,
patchBasedOnFGLS = TRUE, llfun = "polylik_eigen",
eigenOfRel, ...)
|
Arguments
formula |
Formula describing fixed effects to be used in the analysis, e.g. y ~ a + b means that outcome (y) depends on two covariates, a and b. If no covariates used in the analysis, skip the right-hand side of the equation. |
kinship.matrix |
Kinship matrix, as provided by e.g. ibs(,weight="freq"), or estimated outside of GenABEL from pedigree data. |
data |
An (optional) object of
|
fixh2 |
Optional value of heritability to be used, instead of maximisation. The uses of this option are two-fold: (a) testing significance of heritability and (b) using a priori known heritability to derive the rest of MLEs and var.-cov. matrix. |
starth2 |
Starting value for h2 estimate |
trait.type |
"gaussian" or "binomial" |
opt.method |
"nlm" or "optim". These two use
different optimisation functions. We suggest using the
default |
scaleh2 |
Only relevant when "nlm" optimisation function is used. "scaleh2" is the heritability scaling parameter, regulating how "big" are parameter changes in h2 with respect to changes in other parameters. As other parameters are estimated from previous regression, these are expected to change little from the initial estimate. The default value of 1000 proved to work rather well under a range of conditions. |
quiet |
If FALSE (default), details of optimisation process are reported |
steptol |
steptal parameter of "nlm" |
gradtol |
gradtol parameter of "nlm" |
optimbou |
fixed effects boundary scale parameter for 'optim' |
fglschecks |
additional check for convergence on/off (convergence between estimates obtained and that from FGLS) |
maxnfgls |
number of fgls checks to perform |
maxdiffgls |
max difference allowed in fgls checks |
patchBasedOnFGLS |
if FGLS checks not passed, 'patch' fixed effect estimates based on FGLS expectation |
llfun |
function to compute likelihood (default 'polylik_eigen', also available – but not recommended – 'polylik') |
eigenOfRel |
results of eigen(relationship matrix = 2*kinship.matrix). Passing this can decrease computational time substantially if multiple traits are analysed using the same kinship matrix. This option will not work if any NA's are found in the trait and/or covariates and if the dimensions of the 'eigen'-object, trait, covariates, kinship do not match. |
... |
Optional arguments to be passed to
|
Details
One of the major uses of this function is to estimate
residuals of the trait and the inverse of the
variance-covariance matrix for further use in analysis
with mmscore and grammar.
Also, it can be used for a variant of GRAMMAR analysis,
which allows for permutations for GW significance by use
of environmental residuals as an analysis trait with
qtscore.
"Environmental residuals" (not to be mistaken with just "residuals") are the residual where both the effect of covariates AND the estimated polygenic effect (breeding values) are factored out. This thus provides an estimate of the trait value contributed by environment (or, turning this other way around, the part of the trait not explained by covariates and by the polygene). Polygenic residuals are estimated as
σ^2 V^{-1} (Y - (\hat{μ} + \hat{β} C_1 + ...))
where sigma^2 is the residual variance, V^{-1} is the InvSigma (inverse of the var-cov matrix at the maximum of polygenic model) and (Y - (\hat{μ} + \hat{β} C_1 + ...)) is the trait values adjusted for covariates (also at at the maximum of polygenic model likelihood).
It can also be used for heritability analysis. If you want to test significance of heritability, estimate the model and write down the function minimum reported at the "h2an" element of the output (this is twice the negative MaxLikelihood). Then do a next round of estimation, but set fixh2=0. The difference between your function minima gives a test distributed as chi-squared with 1 d.f.
The way to compute the likelihood is partly based on the paper of Thompson (see refs), namely instead of taking the inverse of the var-cov matrix every time, eigenvectors of the inverse of G (taken only once) are used.
Value
A list with values
h2an |
A list supplied by the
|
esth2 |
Estimate (or fixed value) of heritability |
residualY |
Residuals from analysis, based on covariate effects only; NOTE: these are NOT grammar "environmental residuals"! |
pgresidualY |
Environmental residuals from analysis, based on covariate effects and predicted breeding value. |
grresidualY |
GRAMMAR+ transformed trait residuals |
grammarGamma |
list with GRAMMAR-gamma correction factors |
InvSigma |
Inverse of the
variance-covariance matrix, computed at the MLEs – these
are used in |
call |
The details of call |
measuredIDs |
Logical values for IDs who were used in analysis (traits and all covariates measured) == TRUE |
convFGLS |
was convergence achieved according to FGLS criterionE |
Note
Presence of twins may complicate your analysis. Check the
kinship matrix for singularities, or rather use
check.marker for identification of twin
samples. Take special care in interpretation.
If a trait (no covariates) is used, make sure that the order of IDs in the kinship.matrix is exactly the same as in the outcome
Please note that there is alternative to 'polygenic',
polygenic_hglm, which is faster than
polygenic() with the llfun='polylik' option, but slightly
slower than the default polygenic().
Author(s)
Yurii Aulchenko, Gulnara Svischeva
References
Thompson EA, Shaw RG (1990) Pedigree analysis for quantitative traits: variance components without matrix inversion. Biometrics 46, 399-413.
for original GRAMMAR
Aulchenko YS, de Koning DJ, Haley C. Genomewide rapid association using mixed model and regression: a fast and simple method for genome-wide pedigree-based quantitative trait loci association analysis. Genetics. 2007 177(1):577-85.
for GRAMMAR-GC
Amin N, van Duijn CM, Aulchenko YS. A genomic background based method for association analysis in related individuals. PLoS ONE. 2007 Dec 5;2(12):e1274.
for GRAMMAR-Gamma
Svischeva G, Axenovich TI, Belonogova NM, van Duijn CM, Aulchenko YS. Rapid variance components-based method for whole-genome association analysis. Nature Genetics. 2012 44:1166-1170. doi:10.1038/ng.2410
for GRAMMAR+ transformation
Belonogova NM, Svishcheva GR, van Duijn CM, Aulchenko YS, Axenovich TI (2013) Region-Based Association Analysis of Human Quantitative Traits in Related Individuals. PLoS ONE 8(6): e65395. doi:10.1371/journal.pone.0065395
See Also
polygenic_hglm, mmscore,
grammar
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | # note that procedure runs on CLEAN data
require(GenABEL.data)
data(ge03d2ex.clean)
gkin <- ibs(ge03d2ex.clean,w="freq")
h2ht <- polygenic(height ~ sex + age, kin=gkin, ge03d2ex.clean)
# estimate of heritability
h2ht$esth2
# other parameters
h2ht$h2an
# the minimum twice negative log-likelihood
h2ht$h2an$minimum
# twice maximum log-likelihood
-h2ht$h2an$minimum
# for binary trait (experimental)
h2dm <- polygenic(dm2 ~ sex + age, kin=gkin, ge03d2ex.clean, trait="binomial")
# estimated parameters
h2dm$h2an
|
Example output
Loading required package: MASS
Loading required package: GenABEL.data
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
-0.03595906 1.35161070 -0.01526032
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] -0.03595906 1.35161070 -0.01526032 0.30000000 0.56541567
Function Value
[1] 44.96445
Gradient:
[1] 0.6952411 -4.9601763 -1.0986500 -7.4497076 7.7513129
iteration = 1
Step:
[1] -5.201715e-05 3.711147e-04 8.219974e-05 5.573786e-04 -5.799444e-04
Parameter:
[1] -0.03601108 1.35198181 -0.01517812 0.30055738 0.56483573
Function Value
[1] 44.95909
Gradient:
[1] 3.107222 -3.511972 121.907800 -7.432526 7.555024
iteration = 2
Step:
[1] -0.0056803906 0.0391389920 -0.0004557513 0.0589434941 -0.0613165833
Parameter:
[1] -0.04169147 1.39112081 -0.01563388 0.35950087 0.50351915
Function Value
[1] 44.63419
Gradient:
[1] 0.1555315 -2.8746362 -43.4451610 -6.8388025 -17.7974660
iteration = 3
Step:
[1] 0.0018629761 -0.0130601242 0.0001444049 -0.0195093144 0.0215087235
Parameter:
[1] -0.03982849 1.37806068 -0.01548947 0.33999156 0.52502787
Function Value
[1] 44.53947
Gradient:
[1] 1.011636 -3.226584 5.550631 -7.085987 -7.490362
iteration = 4
Step:
[1] -2.994997e-04 1.837261e-03 -1.748087e-05 2.931252e-03 -1.889602e-03
Parameter:
[1] -0.04012799 1.37989794 -0.01550695 0.34292281 0.52313827
Function Value
[1] 44.52749
Gradient:
[1] 0.9640696 -3.1335755 2.5363639 -7.0480591 -8.3212282
iteration = 5
Step:
[1] -0.0024710671 0.0141878257 -0.0001288244 0.0234295749 -0.0100040555
Parameter:
[1] -0.04259906 1.39408577 -0.01563578 0.36635239 0.51313421
Function Value
[1] 44.43237
Gradient:
[1] 0.6645141 -2.3289872 -16.7405295 -6.7102443 -12.9213073
iteration = 6
Step:
[1] -0.0034887192 0.0186767407 -0.0001586064 0.0320319929 -0.0066370511
Parameter:
[1] -0.04608778 1.41276251 -0.01579438 0.39838438 0.50649716
Function Value
[1] 44.29205
Gradient:
[1] 0.434841 -1.101415 -32.878705 -6.206905 -16.232392
iteration = 7
Step:
[1] -0.0083824716 0.0424238096 -0.0003400073 0.0750898987 -0.0032228593
Parameter:
[1] -0.05447025 1.45518632 -0.01613439 0.47347428 0.50327430
Function Value
[1] 43.9565
Gradient:
[1] 0.2351745 1.9975845 -51.3453032 -5.0223199 -18.4659207
iteration = 8
Step:
[1] -0.0094453882 0.0445536478 -0.0003308165 0.0821760264 0.0116543804
Parameter:
[1] -0.06391564 1.49973997 -0.01646521 0.55565030 0.51492868
Function Value
[1] 43.58117
Gradient:
[1] 0.5808767 5.5383725 -40.0186002 -3.9310594 -14.0381792
iteration = 9
Step:
[1] -0.0058783413 0.0239988528 -0.0001573366 0.0484418571 0.0221591395
Parameter:
[1] -0.06979398 1.52373882 -0.01662254 0.60409216 0.53708782
Function Value
[1] 43.34279
Gradient:
[1] 1.051246 7.349500 -16.605703 -3.642096 -5.229185
iteration = 10
Step:
[1] -1.158292e-03 1.756650e-03 6.728088e-06 7.518883e-03 1.300087e-02
Parameter:
[1] -0.07095227 1.52549547 -0.01661582 0.61161104 0.55008869
Function Value
[1] 43.29157
Gradient:
[1] 1.2567523 7.3859214 -3.9416819 -3.7778617 -0.2132411
iteration = 11
Step:
[1] -1.177800e-04 -1.724444e-03 2.472415e-05 -4.189617e-04 3.868139e-03
Parameter:
[1] -0.07107005 1.52377103 -0.01659109 0.61119208 0.55395683
Function Value
[1] 43.28242
Gradient:
[1] 1.342678 7.225841 1.754204 -3.838303 1.270675
iteration = 12
Step:
[1] -2.898677e-04 -2.807326e-03 3.975047e-05 1.080056e-05 3.640250e-03
Parameter:
[1] -0.07135992 1.52096370 -0.01655134 0.61120288 0.55759708
Function Value
[1] 43.26933
Gradient:
[1] 1.361838 6.920845 4.765588 -3.870127 2.636419
iteration = 13
Step:
[1] -1.248027e-03 -6.035858e-03 9.903974e-05 3.872902e-03 5.921292e-03
Parameter:
[1] -0.07260794 1.51492784 -0.01645230 0.61507578 0.56351837
Function Value
[1] 43.23549
Gradient:
[1] 1.467064 6.284171 14.956889 -3.829444 4.722074
iteration = 14
Step:
[1] -0.003667111 -0.010338786 0.000193242 0.015963932 0.007831988
Parameter:
[1] -0.07627506 1.50458906 -0.01625906 0.63103972 0.57135036
Function Value
[1] 43.16296
Gradient:
[1] 1.304292 4.918091 16.850343 -3.559436 7.135861
iteration = 15
Step:
[1] -0.0086120418 -0.0148080383 0.0003485246 0.0432997412 0.0080067358
Parameter:
[1] -0.08488710 1.48978102 -0.01591053 0.67433946 0.57935709
Function Value
[1] 43.02931
Gradient:
[1] 1.339562 2.899138 37.143789 -2.798269 8.803389
iteration = 16
Step:
[1] -0.0135627829 -0.0116172745 0.0003872629 0.0752708151 0.0024409612
Parameter:
[1] -0.09844988 1.47816374 -0.01552327 0.74961027 0.58179805
Function Value
[1] 42.86704
Gradient:
[1] -0.2311334 -0.1894086 -16.1612798 -1.5413494 7.4262848
iteration = 17
Step:
[1] -0.0121374504 0.0030276774 0.0002412749 0.0754016688 -0.0052203932
Parameter:
[1] -0.1105873 1.4811914 -0.0152820 0.8250119 0.5765777
Function Value
[1] 42.76368
Gradient:
[1] 3.0988223 0.9230727 165.8923264 -0.6038011 2.8933417
iteration = 18
Step:
[1] -1.193064e-02 1.500920e-02 -8.709254e-05 8.100285e-02 -4.051641e-03
Parameter:
[1] -0.12251797 1.49620062 -0.01536909 0.90601479 0.57252602
Function Value
[1] 42.7415
Gradient:
[1] -25.196607 -15.161577 -1208.005117 -1.512464 -2.525064
iteration = 19
Step:
[1] -5.024815e-03 6.766438e-03 8.668581e-06 3.437199e-02 -5.908472e-04
Parameter:
[1] -0.12754279 1.50296706 -0.01536042 0.94038678 0.57193517
Function Value
[1] 42.66949
Gradient:
[1] -43.816646 -25.735535 -2107.566022 -4.461268 -4.814848
iteration = 20
Step:
[1] -6.727971e-03 8.226600e-03 1.406721e-05 4.552273e-02 -6.173578e-04
Parameter:
[1] -0.13427076 1.51119366 -0.01534635 0.98590951 0.57131781
Function Value
[1] 42.43899
Gradient:
[1] -2.184576e+02 -1.263053e+02 -1.057406e+04 6.603956e-01 -9.174241e+00
iteration = 21
Step:
[1] -1.571452e-04 2.488553e-04 1.107746e-06 1.099544e-03 -5.839027e-05
Parameter:
[1] -0.13442790 1.51144251 -0.01534525 0.98700906 0.57125942
Function Value
[1] 42.43301
Gradient:
[1] -235.625791 -136.196181 -11406.280852 4.424992 -9.378391
iteration = 22
Step:
[1] -4.598765e-04 2.113960e-03 1.876863e-06 4.034224e-03 2.353895e-04
Parameter:
[1] -0.13488778 1.51355647 -0.01534337 0.99104328 0.57149481
Function Value
[1] 42.23814
Gradient:
[1] -303.14149 -174.95881 -14673.75621 15.34813 -9.78877
iteration = 23
Step:
[1] -4.762620e-04 2.286486e-03 2.810688e-06 4.252874e-03 7.929576e-05
Parameter:
[1] -0.13536404 1.51584296 -0.01534056 0.99529616 0.57157411
Function Value
[1] 42.04943
Gradient:
[1] -492.91950 -284.20853 -23858.07348 103.41617 -10.75527
iteration = 24
Step:
[1] -4.880739e-05 8.052088e-04 -1.281772e-06 7.754507e-04 2.914410e-04
Parameter:
[1] -0.13541285 1.51664817 -0.01534184 0.99607161 0.57186555
Function Value
[1] 41.9555
Gradient:
[1] -553.81021 -319.24373 -26800.66105 141.37753 -10.83452
iteration = 25
Step:
[1] -5.817446e-05 3.629908e-03 -1.135983e-05 2.511617e-03 1.930430e-03
Parameter:
[1] -0.1354710 1.5202781 -0.0153532 0.9985832 0.5737960
Function Value
[1] 41.6486
Gradient:
[1] -1112.25314 -640.91055 -53759.09134 861.17589 -11.48326
iteration = 26
Step:
[1] 3.152763e-04 5.808994e-03 -4.048516e-05 6.614566e-04 1.947813e-02
Parameter:
[1] -0.13515575 1.52608707 -0.01539368 0.99924468 0.59327411
Function Value
[1] 40.05337
Gradient:
[1] -1153.825163 -664.287358 -55518.442458 417.864667 -3.036911
iteration = 27
Step:
[1] 7.914019e-05 9.297012e-04 -1.026842e-05 1.121967e-04 1.794036e-04
Parameter:
[1] -0.13507661 1.52701677 -0.01540395 0.99935688 0.59345351
Function Value
[1] 39.96911
Gradient:
[1] -1285.334290 -740.027916 -61813.664680 605.314683 -3.111495
iteration = 28
Step:
[1] 4.883655e-04 5.054683e-03 -6.185446e-05 3.141007e-04 5.701953e-04
Parameter:
[1] -0.13458824 1.53207145 -0.01546581 0.99967098 0.59402371
Function Value
[1] 39.72506
Gradient:
[1] -2048.838072 -1179.789650 -98298.564222 2448.057715 -3.654304
iteration = 29
Step:
[1] 1.214517e-04 1.276153e-03 -1.452827e-05 7.376215e-05 6.570941e-04
Parameter:
[1] -0.13446679 1.53334761 -0.01548034 0.99974474 0.59468080
Function Value
[1] 39.61036
Gradient:
[1] -2.411351e+03 -1.388711e+03 -1.155454e+05 3.694601e+03 -3.673803e+00
iteration = 30
Step:
[1] 7.452209e-05 7.672971e-04 -8.911639e-06 2.939784e-05 4.996318e-04
Parameter:
[1] -0.13439227 1.53411490 -0.01548925 0.99977414 0.59518043
Function Value
[1] 39.518
Gradient:
[1] -2.581160e+03 -1.486559e+03 -1.235815e+05 4.304559e+03 -3.560188e+00
iteration = 31
Step:
[1] 2.626547e-04 2.543459e-03 -3.242419e-05 5.485978e-05 8.812888e-04
Parameter:
[1] -0.13412961 1.53665836 -0.01552167 0.99982900 0.59606172
Function Value
[1] 39.37919
Gradient:
[1] -3.063640e+03 -1.764532e+03 -1.464272e+05 6.484346e+03 -3.505848e+00
iteration = 32
Step:
[1] -4.850160e-04 -4.027918e-03 6.994311e-05 1.291776e-04 5.521813e-03
Parameter:
[1] -0.13461463 1.53263044 -0.01545173 0.99995818 0.60158353
Function Value
[1] 38.5911
Gradient:
[1] -7.015695e+03 -4.044164e+03 -3.307688e+05 4.239322e+04 -2.747247e+00
iteration = 33
Step:
[1] -0.0036846213 -0.0331472710 0.0004729021 -0.0001385644 0.0097942344
Parameter:
[1] -0.13829925 1.49948317 -0.01497883 0.99981961 0.61137777
Function Value
[1] 37.71216
Gradient:
[1] -1176.042376 -679.935038 -54772.439345 -3683.879832 4.168696
iteration = 34
Step:
[1] 3.077973e-04 2.883885e-03 -4.095993e-05 5.731157e-06 1.596461e-05
Parameter:
[1] -0.13799145 1.50236706 -0.01501979 0.99982534 0.61139373
Function Value
[1] 37.71183
Gradient:
[1] -1261.023533 -728.643945 -58829.900330 -3587.156500 4.120981
iteration = 35
Step:
[1] 2.197557e-04 2.046782e-03 -2.907519e-05 4.230519e-06 3.375284e-05
Parameter:
[1] -0.13777170 1.50441384 -0.01504886 0.99982957 0.61142749
Function Value
[1] 37.71178
Gradient:
[1] -1323.662715 -764.555241 -61817.199961 -3511.308969 4.090928
iteration = 36
Step:
[1] -2.570604e-04 -2.373342e-03 3.376401e-05 -4.865204e-06 -6.183080e-05
Parameter:
[1] -0.1380288 1.5020405 -0.0150151 0.9998247 0.6113657
Function Value
[1] 37.71152
Gradient:
[1] -1252.311200 -723.571453 -60880.544794 -3360.513025 4.118845
iteration = 37
Step:
[1] -8.613738e-04 1.035953e-03 6.909211e-06 1.960728e-05 -9.759670e-03
Parameter:
[1] -0.13889013 1.50307645 -0.01500819 0.99984431 0.60160598
Function Value
[1] 37.51618
Gradient:
[1] -1257.166645 -726.276998 -61115.097604 -4067.154715 1.236159
iteration = 38
Step:
[1] -4.997227e-03 1.508595e-02 -6.728274e-05 1.496902e-04 -5.013312e-02
Parameter:
[1] -0.14388736 1.51816240 -0.01507547 0.99999401 0.55147287
Function Value
[1] 34.53783
Gradient:
[1] -5980.33896 -3448.23574 -290875.51455 44010.32035 -17.30548
iteration = 39
Parameter:
[1] -0.14388736 1.51816240 -0.01507547 0.99999401 0.55147287
Function Value
[1] 34.53783
Gradient:
[1] -5980.33896 -3448.23574 -290875.51455 44010.32035 -17.30548
Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.
difFGLS:
[1] 0.1438866 1.5181628 0.0150402
fixed effect betas changed to FGLS-betas for re-estimation
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] -7.250237e-07 -4.180867e-07 -3.526983e-05 9.999940e-01 5.514729e-01
Function Value
[1] 172.985
Gradient:
[1] 21.39558 -172.36984 81479.68470 -182035.74323 -268.35463
iteration = 1
Step:
[1] -2.703002e-10 2.177627e-09 -1.029370e-06 2.299741e-06 3.390247e-09
Parameter:
[1] -7.252940e-07 -4.159090e-07 -3.629920e-05 9.999963e-01 5.514729e-01
Function Value
[1] 172.6428
Gradient:
[1] -5554.4953 -3392.9377 -140236.1148 -262282.5545 -268.6098
iteration = 2
Step:
[1] 7.941777e-10 9.124004e-10 -1.664463e-07 4.592674e-07 6.591203e-10
Parameter:
[1] -7.244998e-07 -4.149966e-07 -3.646565e-05 9.999968e-01 5.514729e-01
Function Value
[1] 172.5864
Gradient:
[1] -7371.9159 -4442.8849 -210347.7719 -271499.3653 -268.7475
iteration = 3
Step:
[1] 1.293685e-08 8.558506e-09 -7.623648e-08 2.860451e-07 1.563140e-09
Parameter:
[1] -7.115630e-07 -4.064381e-07 -3.654189e-05 9.999971e-01 5.514729e-01
Function Value
[1] 172.5462
Gradient:
[1] -8600.0836 -5152.6135 -255826.4738 -274825.1718 -268.8418
iteration = 4
Step:
[1] 4.468662e-08 2.874172e-08 -8.846557e-08 4.464591e-07 4.174900e-09
Parameter:
[1] -6.668764e-07 -3.776964e-07 -3.663035e-05 9.999975e-01 5.514729e-01
Function Value
[1] 172.4752
Gradient:
[1] -10825.8889 -6439.1582 -335345.8142 -268133.3274 -269.0097
iteration = 5
Step:
[1] 2.565799e-07 1.634779e-07 -1.633817e-07 1.280177e-06 2.165055e-08
Parameter:
[1] -4.102964e-07 -2.142185e-07 -3.679373e-05 9.999988e-01 5.514729e-01
Function Value
[1] 172.3173
Gradient:
[1] -24612.3641 -14410.0061 -808097.4807 2260957.4104 -270.0145
iteration = 6
Step:
[1] 4.686870e-08 3.427485e-08 1.245002e-07 -5.587739e-07 1.067738e-08
Parameter:
[1] -3.634277e-07 -1.799436e-07 -3.666923e-05 9.999982e-01 5.514729e-01
Function Value
[1] 172.3054
Gradient:
[1] -15524.6733 -9156.8070 -487173.3472 -147023.0020 -269.3152
iteration = 7
Step:
[1] 4.349374e-07 2.815183e-07 1.441202e-07 2.995798e-08 4.341239e-08
Parameter:
[1] 7.150968e-08 1.015747e-07 -3.652511e-05 9.999982e-01 5.514730e-01
Function Value
[1] 172.1833
Gradient:
[1] -14003.2608 -8279.9597 -408615.7019 -280481.7433 -269.1244
iteration = 8
Step:
[1] 8.227897e-06 5.266223e-06 2.162161e-06 8.336993e-07 7.306458e-07
Parameter:
[1] 8.299407e-06 5.367798e-06 -3.436295e-05 9.999991e-01 5.514737e-01
Function Value
[1] 171.8232
Gradient:
[1] 25284.9856 14349.9774 1746837.4447 2161826.8315 -269.6327
iteration = 9
Step:
[1] -2.830714e-06 -1.826299e-06 -8.838457e-07 -3.471264e-07 -2.734530e-07
Parameter:
[1] 5.468693e-06 3.541499e-06 -3.524680e-05 9.999987e-01 5.514734e-01
Function Value
[1] 171.4498
Gradient:
[1] 3206.5172 1633.1726 532322.6384 -1480528.7173 -268.3798
iteration = 10
Step:
[1] 4.808095e-07 2.550995e-07 -3.446460e-07 1.197499e-07 -3.738298e-08
Parameter:
[1] 5.949502e-06 3.796599e-06 -3.559144e-05 9.999989e-01 5.514734e-01
Function Value
[1] 171.3448
Gradient:
[1] -2235.0938 -1508.8450 306534.6177 -1951739.0936 -268.3683
iteration = 11
Step:
[1] 7.382568e-07 4.096077e-07 -3.576726e-07 1.507269e-07 -3.014743e-08
Parameter:
[1] 6.687759e-06 4.206206e-06 -3.594912e-05 9.999990e-01 5.514733e-01
Function Value
[1] 171.3071
Gradient:
[1] -9328.2472 -5605.6778 23660.7024 2677876.0962 -268.5534
iteration = 12
Step:
[1] -2.183609e-07 -8.367507e-08 1.742902e-07 -2.322627e-08 6.603415e-08
Parameter:
[1] 6.469398e-06 4.122531e-06 -3.577483e-05 9.999990e-01 5.514734e-01
Function Value
[1] 171.2646
Gradient:
[1] -6016.2472 -3645.5854 -292032.4657 -9052.6643 -268.4355
iteration = 13
Step:
[1] -3.665899e-07 -1.138747e-07 2.957366e-07 -3.924904e-08 1.513485e-07
Parameter:
[1] 6.102808e-06 4.008656e-06 -3.547909e-05 9.999989e-01 5.514736e-01
Function Value
[1] 171.2574
Gradient:
[1] -389.8093 -401.0869 -18326.3318 -9053.2454 -268.3544
iteration = 14
Parameter:
[1] 6.102808e-06 4.008656e-06 -3.547909e-05 9.999989e-01 5.514736e-01
Function Value
[1] 171.2574
Gradient:
[1] -389.8093 -401.0869 -18326.3318 -9053.2454 -268.3544
Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.
difFGLS:
[1] 6.827759e-06 4.426701e-06 2.128240e-07
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning message:
In polygenic(height ~ sex + age, kin = gkin, ge03d2ex.clean) :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
[1] 0.9999989
$minimum
[1] 698.2069
$estimate
[1] 1.702026e+02 3.962819e-05 -3.507340e-04 9.999989e-01 5.389340e+01
$gradient
[1] -389.8093 -401.0869 -18326.3318 -9053.2454 -268.3544
$code
[1] 3
$iterations
[1] 14
[1] 698.2069
[1] -698.2069
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
-0.68387860 0.56774460 0.01787041
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] -0.68387860 0.56774460 0.01787041 0.30000000 4.51763042
Function Value
[1] 180.6698
Gradient:
[1] 0.0009084147 -0.0356880037 -0.4256702937 -4.4684565523 24.3849166591
iteration = 1
Step:
[1] -8.242247e-05 3.238051e-03 3.862201e-02 4.054329e-01 -2.212497e+00
Parameter:
[1] -0.68396103 0.57098265 0.05649242 0.70543294 2.30513301
Function Value
[1] 117.1616
Gradient:
[1] 8.519400 3.326277 347.254448 28.042685 39.447832
iteration = 2
Step:
[1] -0.14369299 -0.05610285 -5.85698852 -0.47298367 -0.66534928
Parameter:
[1] -0.8276540 0.5148798 -5.8004961 0.2324493 1.6397837
Function Value
[1] 109.6195
Gradient:
[1] 0.00000 0.00000 0.00000 43.90581 38.98239
iteration = 3
Step:
[1] -2.816365e-05 -1.099609e-05 -1.147963e-03 -2.419883e-02 -2.153337e-02
Parameter:
[1] -0.8276822 0.5148688 -5.8016441 0.2082504 1.6182504
Function Value
[1] 107.7294
Gradient:
[1] 0.00000 0.00000 0.00000 42.26395 39.75974
iteration = 4
Step:
[1] -0.0001760877 -0.0000687509 -0.0071774107 -0.1492786046 -0.3129398878
Parameter:
[1] -0.82785827 0.51480005 -5.80882147 0.05897184 1.30531047
Function Value
[1] 88.34065
Gradient:
[1] 0.00000 0.00000 0.00000 40.18280 45.02935
iteration = 5
Step:
[1] -1.666106e-05 -6.505070e-06 -6.791120e-04 -1.412435e-02 -2.961737e-02
Parameter:
[1] -0.82787493 0.51479354 -5.80950059 0.04484749 1.27569310
Function Value
[1] 86.43301
Gradient:
[1] 0.00000 0.00000 0.00000 40.20546 45.45210
iteration = 6
Step:
[1] -1.661784e-05 -6.488194e-06 -6.773502e-04 -1.408770e-02 -2.954091e-02
Parameter:
[1] -0.82789155 0.51478705 -5.81017794 0.03075978 1.24615219
Function Value
[1] 84.51764
Gradient:
[1] 0.00000 0.00000 0.00000 40.26049 45.84853
iteration = 7
Step:
[1] -1.656779e-05 -6.468656e-06 -6.753105e-04 -1.404528e-02 -2.945226e-02
Parameter:
[1] -0.82790812 0.51478058 -5.81085325 0.01671451 1.21669993
Function Value
[1] 82.59579
Gradient:
[1] 0.00000 0.00000 0.00000 40.34675 46.21406
iteration = 8
Step:
[1] -1.650629e-05 -6.444642e-06 -6.728034e-04 -1.399313e-02 -2.934316e-02
Parameter:
[1] -0.827924622 0.514774140 -5.811526050 0.002721372 1.187356776
Function Value
[1] 80.66945
Gradient:
[1] 0.00000 0.00000 0.00000 40.46308 46.54336
iteration = 9
Step:
[1] -1.642822e-06 -6.414162e-07 -6.696214e-05 -1.392695e-03 -2.920455e-03
Parameter:
[1] -0.827926265 0.514773498 -5.811593012 0.001328677 1.184436321
Function Value
[1] 80.47711
Gradient:
[1] 0.00000 0.00000 0.00000 40.47629 46.57400
iteration = 10
Step:
[1] -1.641932e-07 -6.410685e-08 -6.692584e-06 -1.391940e-04 -2.918873e-04
Parameter:
[1] -0.827926429 0.514773434 -5.811599705 0.001189483 1.184144433
Function Value
[1] 80.45788
Gradient:
[1] 0.00000 0.00000 0.00000 40.47763 46.57704
iteration = 11
Step:
[1] -1.641841e-07 -6.410332e-08 -6.692216e-06 -1.391864e-04 -2.918713e-04
Parameter:
[1] -0.827926593 0.514773370 -5.811606397 0.001050296 1.183852562
Function Value
[1] 80.43865
Gradient:
[1] 0.00000 0.00000 0.00000 40.47897 46.58008
iteration = 12
Step:
[1] -1.641751e-07 -6.409979e-08 -6.691847e-06 -1.391787e-04 -2.918552e-04
Parameter:
[1] -0.8279267572 0.5147733061 -5.8116130889 0.0009111176 1.1835607067
Function Value
[1] 80.41942
Gradient:
[1] 0.00000 0.00000 0.00000 40.48031 46.58311
iteration = 13
Step:
[1] -1.641660e-07 -6.409625e-08 -6.691477e-06 -1.391710e-04 -2.918391e-04
Parameter:
[1] -0.8279269213 0.5147732420 -5.8116197803 0.0007719466 1.1832688675
Function Value
[1] 80.4002
Gradient:
[1] 0.00000 0.00000 0.00000 40.48166 46.58613
iteration = 14
Step:
[1] -1.641569e-07 -6.409269e-08 -6.691107e-06 -1.391633e-04 -2.918230e-04
Parameter:
[1] -0.8279270855 0.5147731779 -5.8116264714 0.0006327833 1.1829770446
Function Value
[1] 80.38097
Gradient:
[1] 0.00000 0.00000 0.00000 40.48300 46.58916
iteration = 15
Step:
[1] -1.641478e-07 -6.408913e-08 -6.690735e-06 -1.391556e-04 -2.918068e-04
Parameter:
[1] -0.8279272496 0.5147731138 -5.8116331622 0.0004936278 1.1826852378
Function Value
[1] 80.36174
Gradient:
[1] 0.00000 0.00000 0.00000 40.48436 46.59218
iteration = 16
Step:
[1] -1.641387e-07 -6.408557e-08 -6.690362e-06 -1.391478e-04 -2.917905e-04
Parameter:
[1] -0.82792741 0.51477305 -5.81163985 0.00035448 1.18239345
Function Value
[1] 80.34251
Gradient:
[1] 0.00000 0.00000 0.00000 40.48571 46.59519
iteration = 17
Step:
[1] -1.641295e-07 -6.408199e-08 -6.689989e-06 -1.391400e-04 -2.917743e-04
Parameter:
[1] -0.8279275779 0.5147729856 -5.8116465425 0.0002153399 1.1821016730
Function Value
[1] 80.32328
Gradient:
[1] 0.00000 0.00000 0.00000 40.48707 46.59820
iteration = 18
Step:
[1] -1.641203e-07 -6.407840e-08 -6.689615e-06 -1.391323e-04 -2.917579e-04
Parameter:
[1] -8.279277e-01 5.147729e-01 -5.811653e+00 7.620769e-05 1.181810e+00
Function Value
[1] 80.30405
Gradient:
[1] 0.00000 0.00000 0.00000 40.48842 46.60120
iteration = 19
Step:
[1] -1.641111e-08 -6.407481e-09 -6.689239e-07 -1.391244e-05 -2.917416e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811654e+00 6.229525e-05 1.181781e+00
Function Value
[1] 80.30213
Gradient:
[1] 0.00000 0.00000 0.00000 40.48856 46.60150
iteration = 20
Step:
[1] -1.641102e-08 -6.407445e-09 -6.689202e-07 -1.391237e-05 -2.917399e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811655e+00 4.838288e-05 1.181752e+00
Function Value
[1] 80.30021
Gradient:
[1] 0.0000 0.0000 0.0000 40.4887 46.6018
iteration = 21
Step:
[1] -1.641092e-08 -6.407409e-09 -6.689164e-07 -1.391229e-05 -2.917383e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811655e+00 3.447059e-05 1.181722e+00
Function Value
[1] 80.29828
Gradient:
[1] 0.00000 0.00000 0.00000 40.48883 46.60210
iteration = 22
Step:
[1] -1.641083e-08 -6.407373e-09 -6.689126e-07 -1.391221e-05 -2.917367e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811656e+00 2.055838e-05 1.181693e+00
Function Value
[1] 80.29636
Gradient:
[1] 0.00000 0.00000 0.00000 40.48897 46.60240
iteration = 23
Step:
[1] -1.641074e-08 -6.407337e-09 -6.689089e-07 -1.391213e-05 -2.917350e-05
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 6.646253e-06 1.181664e+00
Function Value
[1] 80.29444
Gradient:
[1] 0.00000 0.00000 0.00000 40.48911 46.60270
iteration = 24
Step:
[1] -1.641065e-09 -6.407300e-10 -6.689051e-08 -1.391205e-06 -2.917334e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 5.255047e-06 1.181661e+00
Function Value
[1] 80.29424
Gradient:
[1] 0.00000 0.00000 0.00000 40.48912 46.60273
iteration = 25
Step:
[1] -1.641064e-09 -6.407297e-10 -6.689047e-08 -1.391205e-06 -2.917332e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 3.863843e-06 1.181658e+00
Function Value
[1] 80.29405
Gradient:
[1] 0.00000 0.00000 0.00000 40.48913 46.60276
iteration = 26
Step:
[1] -1.641063e-09 -6.407294e-10 -6.689044e-08 -1.391204e-06 -2.917331e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 2.472639e-06 1.181655e+00
Function Value
[1] 80.29386
Gradient:
[1] 0.00000 0.00000 0.00000 40.48915 46.60279
iteration = 27
Step:
[1] -1.641062e-09 -6.407289e-10 -6.689040e-08 -1.391203e-06 -2.917329e-06
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.081436e-06 1.181652e+00
Function Value
[1] 80.29367
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60282
iteration = 28
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689036e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 9.423159e-07 1.181652e+00
Function Value
[1] 80.29365
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60283
iteration = 29
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689036e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 8.031957e-07 1.181652e+00
Function Value
[1] 80.29363
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60283
iteration = 30
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689035e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 6.640754e-07 1.181652e+00
Function Value
[1] 80.29361
Gradient:
[1] 0.00000 0.00000 0.00000 40.48916 46.60283
iteration = 31
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689035e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 5.249553e-07 1.181651e+00
Function Value
[1] 80.29359
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60284
iteration = 32
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689034e-09 -1.391202e-07 -2.917327e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 3.858351e-07 1.181651e+00
Function Value
[1] 80.29357
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60284
iteration = 33
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689034e-09 -1.391202e-07 -2.917326e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 2.467149e-07 1.181651e+00
Function Value
[1] 80.29355
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60284
iteration = 34
Step:
[1] -1.641061e-10 -6.407286e-11 -6.689034e-09 -1.391202e-07 -2.917326e-07
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.075947e-07 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 35
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 9.368269e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 36
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 7.977067e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 37
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 6.585866e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 38
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 5.194664e-08 1.181650e+00
Function Value
[1] 80.29353
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 39
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 3.803462e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 40
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 2.412261e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 41
Step:
[1] -1.641065e-11 -6.407319e-12 -6.689032e-10 -1.391202e-08 -2.917326e-08
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.021059e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 40.48917 46.60285
iteration = 42
Parameter:
[1] -8.279278e-01 5.147729e-01 -5.811657e+00 1.021059e-08 1.181650e+00
Function Value
[1] 80.29352
Gradient:
[1] 0.00000 0.00000 0.00000 -506861.07675 46.60285
Last global step failed to locate a point lower than x.
Either x is an approximate local minimum of the function,
the function is too non-linear for this algorithm,
or steptol is too large.
difFGLS:
[1] 1.1763440 0.3818257 5.8156840
fixed effect betas changed to FGLS-betas for re-estimation
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] 3.484162e-01 1.329472e-01 4.027072e-03 1.021059e-08 1.181650e+00
Function Value
[1] 42.21514
Gradient:
[1] 1.3966371 -0.5273326 36.2719095 3.2599153 78.8275636
iteration = 1
Step:
[1] -4.978551e-11 1.879769e-11 -1.292975e-09 -1.162053e-10 -2.809944e-09
Parameter:
[1] 3.484162e-01 1.329472e-01 4.027071e-03 1.009439e-08 1.181650e+00
Function Value
[1] 42.21514
Gradient:
[1] 1.396637 -0.527333 36.271877 3.259915 78.827564
iteration = 2
Parameter:
[1] 3.484162e-01 1.329472e-01 4.027071e-03 1.006132e-08 1.181650e+00
Function Value
[1] 42.21514
Gradient:
[1] 1.3966363 -0.5273331 36.2718680 3.2599151 78.8275638
Successive iterates within tolerance.
Current iterate is probably solution.
difFGLS:
[1] 6.492118e-11 3.201203e-11 1.661003e-09
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning messages:
1: In polygenic(dm2 ~ sex + age, kin = gkin, ge03d2ex.clean, trait = "binomial") :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
2: In sqrt(fi) : NaNs produced
$minimum
[1] -51.17526
$estimate
[1] 3.484162e-01 1.329472e-01 4.027071e-03 1.006132e-08 1.181650e+00
$gradient
[1] 1.3966363 -0.5273331 36.2718680 3.2599151 78.8275638
$code
[1] 2
$iterations
[1] 2
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.