mmscore: Score test for association in related people
In GenABEL: genome-wide SNP association analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Score test for association between a trait and genetic polymorphism,
in samples of related individuals
Usage
1
2
Arguments
h2object
An object returned by polygenic polygenic mixed model analysis
routine. The sub-objects used are measuredIDs, residualY, and InvSigma. One can supply
mmscore with a fake h2object, containing these list elements.
data
An object of gwaa.data-class.
ALWAYS PASS THE SAME OBJECT WHICH WAS USED FOR ipolygenic ANALYSIS,
NO SUB-SETTING IN IDs (USE IDSUBSET ARGUMENT FOR SUB-SETTING)!!!
snpsubset
Index, character or logical vector with subset of SNPs to run analysis on.
If missing, all SNPs from data are used for analysis.
idsubset
Index, character or logical vector with subset of IDs to run analysis on.
If missing, all people from data/cc are used for analysis.
strata
Stratification variable. If provieded, scores are computed within strata and
then added up.
times
If more then one, the number of replicas to be used in derivation of
empirical genome-wide significance. NOTE: The structure of the data
is not exchangable, therefore do not use times > 1
unless you are really sure you understand what you are doing!
quiet
do not print warning messages
bcast
If the argument times > 1, progress is reported once in bcast replicas
clambda
If inflation facot Lambda is estimated as lower then one, this parameter
controls if the original P1df (clambda=TRUE) to be reported in Pc1df,
or the original 1df statistics is to be multiplied onto this "deflation"
factor (clambda=FALSE).
If a numeric value is provided, it is used as a correction factor.
propPs
proportion of non-corrected P-values used to estimate the inflation factor Lambda,
passed directly to the estlambda
Details
Score test is performed using the formula
\frac{((G-E[G]) V^{-1} residualY)^2}{(G-E[G]) V^{-1} (G-E[G])}
where G is the vector of genotypes (coded 0, 1, 2) and E[G] is
a vector of (strata-specific) mean genotypic values; V^{-1} is the
InvSigma and residualY are residuals from the trait analysis
with polygenic procedure.
This test is similar to that implemented by Abecasis et al. (see reference).
Value
Object of class scan.gwaa-class; only 1 d.f. test is
implemented currently.
Author(s)
Yurii Aulchenko
References
Chen WM, Abecasis GR. Family-based association tests for genome-wide association
scans. Am J Hum Genet. 2007 Nov;81(5):913-26.
See Also
grammar,
qtscore,
egscore,
plot.scan.gwaa,
scan.gwaa-class
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
# ge03d2 is rather bad data set to demonstrate,
# because this is a population-based study
require(GenABEL.data)
data(ge03d2.clean)
#take half for speed
ge03d2.clean <- ge03d2.clean[1:100,]
gkin <- ibs(ge03d2.clean,w="freq")
h2ht <- polygenic(height ~ sex + age,kin=gkin,ge03d2.clean)
h2ht$est
mm <- mmscore(h2ht,data=ge03d2.clean)
# compute grammar
gr <- qtscore(h2ht$pgres,data=ge03d2.clean,clam=FALSE)
#compute GC
gc <- qtscore(height ~ sex + age,data=ge03d2.clean)
#compare
plot(mm,df="Pc1df",cex=0.5)
add.plot(gc,df="Pc1df",col="red")
add.plot(gr,df="Pc1df",col="lightgreen",cex=1.1)
# can see that mmscore and grammar are quite the same... in contrast to GC
Example output
Loading required package: MASS
Loading required package: GenABEL.data
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
0.007548131 1.147885901 -0.013061168
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] 0.007548131 1.147885901 -0.013061168 0.300000000 0.648103376
Function Value
[1] 55.66681
Gradient:
[1] -0.7970343 -0.9002342 -9.4983582 2.6684209 1.9871480
iteration = 1
Step:
[1] 7.486420e-07 8.455760e-07 8.921661e-06 -2.506406e-06 -1.866497e-06
Parameter:
[1] 0.00754888 1.14788675 -0.01305225 0.29999749 0.64810151
Function Value
[1] 55.66676
Gradient:
[1] -0.5938191 -0.7822453 1.4375897 2.6679804 1.9867985
iteration = 2
Step:
[1] 6.411024e-07 8.260613e-07 -1.420976e-07 -2.767826e-06 -2.061155e-06
Parameter:
[1] 0.007549521 1.147887573 -0.013052388 0.299994726 0.648099449
Function Value
[1] 55.66674
Gradient:
[1] -0.5965473 -0.7837615 1.2894200 2.6679508 1.9863417
iteration = 3
Step:
[1] 0.0008347452 0.0010744655 -0.0001030452 -0.0035973377 -0.0026786097
Parameter:
[1] 0.008384266 1.148962038 -0.013155433 0.296397388 0.645420839
Function Value
[1] 55.65488
Gradient:
[1] -2.285253 -1.676401 -91.362070 2.630593 1.381695
iteration = 4
Step:
[1] 1.322173e-03 1.700842e-03 -9.103538e-05 -5.692279e-03 -4.237766e-03
Parameter:
[1] 0.009706439 1.150662880 -0.013246469 0.290705109 0.641183073
Function Value
[1] 55.64038
Gradient:
[1] -3.3182490 -2.1363395 -149.8012648 2.5667794 0.4018119
iteration = 5
Step:
[1] 0.0026569518 0.0034166055 -0.0001017411 -0.0114327127 -0.0085092693
Parameter:
[1] 0.01236339 1.15407949 -0.01334821 0.27927240 0.63267380
Function Value
[1] 55.61714
Gradient:
[1] -3.551523 -1.986481 -168.151625 2.415280 -1.638642
iteration = 6
Step:
[1] 1.790706e-03 2.301376e-03 -2.328209e-07 -7.700483e-03 -5.727558e-03
Parameter:
[1] 0.01415410 1.15638086 -0.01334844 0.27157191 0.62694625
Function Value
[1] 55.60394
Gradient:
[1] -2.1668397 -0.9869864 -97.4901598 2.2932996 -3.0656584
iteration = 7
Step:
[1] 3.200402e-04 4.099595e-04 5.321961e-05 -1.372949e-03 -1.015214e-03
Parameter:
[1] 0.01447414 1.15679082 -0.01329522 0.27019896 0.62593103
Function Value
[1] 55.6002
Gradient:
[1] -0.7185304 -0.1113436 -20.1306468 2.2667329 -3.3206498
iteration = 8
Step:
[1] -1.718455e-04 -2.218167e-04 2.187891e-05 7.397489e-04 5.564165e-04
Parameter:
[1] 0.01430229 1.15656900 -0.01327334 0.27093871 0.62648745
Function Value
[1] 55.59994
Gradient:
[1] -0.35805603 0.07873818 -0.32076012 2.27692768 -3.17700826
iteration = 9
Step:
[1] -4.370591e-05 -5.678491e-05 2.534223e-06 1.873171e-04 1.446267e-04
Parameter:
[1] 0.01425859 1.15651222 -0.01327081 0.27112603 0.62663208
Function Value
[1] 55.59991
Gradient:
[1] -0.33482824 0.08733884 1.02753420 2.27960852 -3.13980565
iteration = 10
Step:
[1] -8.239764e-05 -1.084886e-04 4.557309e-06 3.510771e-04 2.842010e-04
Parameter:
[1] 0.01417619 1.15640373 -0.01326625 0.27147711 0.62691628
Function Value
[1] 55.59986
Gradient:
[1] -0.2963599 0.1003585 3.2826027 2.2845664 -3.0667127
iteration = 11
Step:
[1] -1.125355e-04 -1.519010e-04 6.387447e-06 4.741788e-04 4.181545e-04
Parameter:
[1] 0.01406365 1.15625183 -0.01325987 0.27195129 0.62733443
Function Value
[1] 55.59972
Gradient:
[1] -0.2410546 0.1194671 6.5118233 2.2910729 -2.9591862
iteration = 12
Step:
[1] -1.694592e-04 -2.394344e-04 1.018578e-05 6.988233e-04 7.156662e-04
Parameter:
[1] 0.01389419 1.15601240 -0.01324968 0.27265011 0.62805010
Function Value
[1] 55.59936
Gradient:
[1] -0.1476295 0.1533271 11.9219868 2.3001185 -2.7752158
iteration = 13
Step:
[1] -2.161574e-04 -3.363418e-04 1.464905e-05 8.474317e-04 1.161466e-03
Parameter:
[1] 0.01367804 1.15567605 -0.01323503 0.27349754 0.62921156
Function Value
[1] 55.59845
Gradient:
[1] 0.001112454 0.211353186 20.419473287 2.309517370 -2.476852991
iteration = 14
Step:
[1] -2.088932e-04 -4.252463e-04 1.953791e-05 6.764875e-04 1.927817e-03
Parameter:
[1] 0.01346914 1.15525081 -0.01321549 0.27417403 0.63113938
Function Value
[1] 55.5961
Gradient:
[1] 0.2404947 0.3153472 33.7968048 2.3118226 -1.9823419
iteration = 15
Step:
[1] 3.369304e-05 -3.592887e-04 1.987934e-05 -7.174267e-04 3.127760e-03
Parameter:
[1] 0.01350284 1.15489152 -0.01319561 0.27345660 0.63426714
Function Value
[1] 55.59023
Gradient:
[1] 0.6095535 0.5025264 53.6679393 2.2831436 -1.1823416
iteration = 16
Step:
[1] 9.517540e-04 2.484439e-04 2.110652e-06 -5.483508e-03 4.790299e-03
Parameter:
[1] 0.01445459 1.15513996 -0.01319350 0.26797309 0.63905744
Function Value
[1] 55.57644
Gradient:
[1] 1.12710099 0.83201768 79.66540174 2.16314918 0.03686374
iteration = 17
Step:
[1] 3.276493e-03 2.152326e-03 -6.180635e-05 -1.703339e-02 6.065806e-03
Parameter:
[1] 0.01773108 1.15729229 -0.01325531 0.25093971 0.64512324
Function Value
[1] 55.54862
Gradient:
[1] 1.680746 1.348176 102.947639 1.841034 1.573250
iteration = 18
Step:
[1] 0.0067836239 0.0054898838 -0.0001817005 -0.0337960053 0.0042469873
Parameter:
[1] 0.02451471 1.16278217 -0.01343701 0.21714370 0.64937023
Function Value
[1] 55.50832
Gradient:
[1] 1.903909 1.949905 101.515793 1.243283 2.667115
iteration = 19
Step:
[1] 0.0074591773 0.0068599564 -0.0002434808 -0.0359910848 -0.0019551940
Parameter:
[1] 0.03197388 1.16964213 -0.01368049 0.18115262 0.64741504
Function Value
[1] 55.47725
Gradient:
[1] 1.4808321 2.2839731 63.6782829 0.6107532 2.2529371
iteration = 20
Step:
[1] 0.0028906328 0.0032049549 -0.0001284514 -0.0131711102 -0.0051624919
Parameter:
[1] 0.03486452 1.17284708 -0.01380894 0.16798151 0.64225255
Function Value
[1] 55.46738
Gradient:
[1] 0.7967717 2.1623817 20.4515645 0.3685095 1.0282386
iteration = 21
Step:
[1] -2.784684e-04 7.698159e-05 -1.399989e-05 1.816475e-03 -2.620404e-03
Parameter:
[1] 0.03458605 1.17292407 -0.01382294 0.16979798 0.63963214
Function Value
[1] 55.46605
Gradient:
[1] 0.4379634 1.9641385 1.3430362 0.3986591 0.3972916
iteration = 22
Step:
[1] -3.270487e-04 -2.478646e-04 6.965651e-06 1.653009e-03 -3.538327e-04
Parameter:
[1] 0.03425900 1.17267620 -0.01381598 0.17145099 0.63927831
Function Value
[1] 55.46599
Gradient:
[1] 0.3932840 1.9176692 -0.4484865 0.4286262 0.3127178
iteration = 23
Step:
[1] -4.784184e-05 -4.278825e-05 1.572686e-06 2.324103e-04 -1.091682e-05
Parameter:
[1] 0.03421116 1.17263341 -0.01381440 0.17168340 0.63926739
Function Value
[1] 55.46598
Gradient:
[1] 0.3960711 1.9156881 -0.2012953 0.4328866 0.3102883
iteration = 24
Step:
[1] -1.406266e-04 -1.321138e-04 4.869115e-06 6.735665e-04 -2.933668e-05
Parameter:
[1] 0.03407053 1.17250130 -0.01380953 0.17235697 0.63923806
Function Value
[1] 55.46596
Gradient:
[1] 0.4076997 1.9113822 0.7141092 0.4452625 0.3038118
iteration = 25
Step:
[1] -1.815508e-04 -1.840437e-04 6.479897e-06 8.490960e-04 -3.921052e-05
Parameter:
[1] 0.03388898 1.17231726 -0.01380305 0.17320606 0.63919885
Function Value
[1] 55.46591
Gradient:
[1] 0.4236033 1.9053465 1.9495757 0.4609188 0.2951103
iteration = 26
Step:
[1] -3.225709e-04 -3.642812e-04 1.191606e-05 1.451990e-03 -7.162228e-05
Parameter:
[1] 0.03356641 1.17195297 -0.01379114 0.17465805 0.63912722
Function Value
[1] 55.46578
Gradient:
[1] 0.4517300 1.8917948 4.1526063 0.4878503 0.2791383
iteration = 27
Step:
[1] -5.038233e-04 -6.636859e-04 1.958371e-05 2.123960e-03 -1.157051e-04
Parameter:
[1] 0.03306259 1.17128929 -0.01377155 0.17678201 0.63901152
Function Value
[1] 55.46544
Gradient:
[1] 0.4943032 1.8628450 7.5580409 0.5276727 0.2531846
iteration = 28
Step:
[1] -8.114959e-04 -1.314954e-03 3.404951e-05 3.047291e-03 -1.959979e-04
Parameter:
[1] 0.03225109 1.16997433 -0.01373750 0.17982930 0.63881552
Function Value
[1] 55.46459
Gradient:
[1] 0.5588927 1.7957351 12.9263366 0.5860254 0.2089235
iteration = 29
Step:
[1] -1.217899e-03 -2.598422e-03 5.747866e-05 3.623872e-03 -3.192569e-04
Parameter:
[1] 0.03103319 1.16737591 -0.01368003 0.18345317 0.63849626
Function Value
[1] 55.46253
Gradient:
[1] 0.6454119 1.6428073 20.6703392 0.6589926 0.1363922
iteration = 30
Step:
[1] -1.577059e-03 -4.933296e-03 9.050034e-05 2.309101e-03 -4.794377e-04
Parameter:
[1] 0.02945613 1.16244262 -0.01358953 0.18576227 0.63801683
Function Value
[1] 55.45794
Gradient:
[1] 0.73090743 1.31355169 29.89105404 0.71690174 0.02728338
iteration = 31
Step:
[1] -0.0012317179 -0.0077383457 0.0001106893 -0.0041004734 -0.0005461381
Parameter:
[1] 0.02822441 1.15470427 -0.01347884 0.18166180 0.63747069
Function Value
[1] 55.44984
Gradient:
[1] 0.73299201 0.73221144 35.14431806 0.67059315 -0.09679972
iteration = 32
Step:
[1] 5.698054e-04 -7.445375e-03 6.254506e-05 -1.485675e-02 -2.392295e-04
Parameter:
[1] 0.02879422 1.14725889 -0.01341629 0.16680505 0.63723146
Function Value
[1] 55.44095
Gradient:
[1] 0.55641337 0.08627239 27.60362614 0.42842279 -0.15516839
iteration = 33
Step:
[1] 2.159426e-03 -1.776175e-03 -3.622574e-05 -1.612610e-02 3.043072e-04
Parameter:
[1] 0.03095365 1.14548272 -0.01345252 0.15067895 0.63753577
Function Value
[1] 55.43664
Gradient:
[1] 0.30839294 -0.16767397 11.28189554 0.14077256 -0.09577193
iteration = 34
Step:
[1] 1.329174e-03 1.693987e-03 -5.186797e-05 -5.691026e-03 3.438891e-04
Parameter:
[1] 0.03228282 1.14717671 -0.01350439 0.14498793 0.63787965
Function Value
[1] 55.43592
Gradient:
[1] 0.18565946 -0.10103569 1.74549687 0.03155287 -0.01987298
iteration = 35
Step:
[1] 2.406597e-04 8.303781e-04 -1.505240e-05 -2.357704e-04 8.198753e-05
Parameter:
[1] 0.03252348 1.14800709 -0.01351944 0.14475216 0.63796164
Function Value
[1] 55.43588
Gradient:
[1] 0.166314294 -0.048618401 -0.034773834 0.024763821 -0.000102375
iteration = 36
Step:
[1] 2.176200e-06 9.103215e-05 -1.007243e-06 1.235977e-04 -6.863360e-07
Parameter:
[1] 0.03252566 1.14809812 -0.01352044 0.14487575 0.63796096
Function Value
[1] 55.43588
Gradient:
[1] 1.671713e-01 -4.137046e-02 -2.856078e-02 2.674685e-02 -4.596501e-05
iteration = 37
Step:
[1] -1.453098e-06 5.199941e-06 -6.803913e-09 1.576172e-05 -1.088528e-06
Parameter:
[1] 0.03252420 1.14810332 -0.01352045 0.14489152 0.63795987
Function Value
[1] 55.43588
Gradient:
[1] 0.1675834369 -0.0407589183 -0.0060234129 0.0270183165 -0.0002847145
iteration = 38
Step:
[1] -7.018031e-06 2.132072e-05 5.795043e-09 6.557846e-05 -4.917844e-06
Parameter:
[1] 0.03251718 1.14812464 -0.01352045 0.14495709 0.63795495
Function Value
[1] 55.43588
Gradient:
[1] 0.169520021 -0.038109858 0.100900948 0.028149842 -0.001373564
iteration = 39
Step:
[1] -1.025201e-05 2.604498e-05 4.079207e-08 7.848309e-05 -6.020541e-06
Parameter:
[1] 0.03250693 1.14815068 -0.01352040 0.14503558 0.63794893
Function Value
[1] 55.43588
Gradient:
[1] 0.171911353 -0.034856335 0.234380977 0.029505991 -0.002709768
iteration = 40
Step:
[1] -2.379585e-05 4.832576e-05 1.612808e-07 1.416707e-04 -1.099602e-05
Parameter:
[1] 0.03248314 1.14819901 -0.01352024 0.14517725 0.63793793
Function Value
[1] 55.43588
Gradient:
[1] 0.176225797 -0.028884274 0.479667349 0.031960639 -0.005153083
iteration = 41
Step:
[1] -4.975047e-05 7.664985e-05 4.670112e-07 2.152422e-04 -1.693579e-05
Parameter:
[1] 0.03243339 1.14827566 -0.01351978 0.14539249 0.63792100
Function Value
[1] 55.43588
Gradient:
[1] 0.182681902 -0.019620962 0.858509395 0.035707693 -0.008920978
iteration = 42
Step:
[1] -1.155539e-04 1.304495e-04 1.336277e-06 3.422457e-04 -2.750061e-05
Parameter:
[1] 0.03231783 1.14840611 -0.01351844 0.14573474 0.63789350
Function Value
[1] 55.43587
Gradient:
[1] 0.19263973 -0.00441388 1.47517113 0.04171345 -0.01505077
iteration = 43
Step:
[1] -2.700496e-04 2.181017e-04 3.580838e-06 5.123954e-04 -4.267814e-05
Parameter:
[1] 0.03204778 1.14862421 -0.01351486 0.14624713 0.63785082
Function Value
[1] 55.43585
Gradient:
[1] 0.20670809 0.01961264 2.43536878 0.05083264 -0.02459187
iteration = 44
Step:
[1] -6.375624e-04 3.638714e-04 9.251417e-06 7.092973e-04 -6.317613e-05
Parameter:
[1] 0.03141022 1.14898808 -0.01350561 0.14695643 0.63778764
Function Value
[1] 55.43579
Gradient:
[1] 0.22388539 0.05628653 3.86427760 0.06380475 -0.03878446
iteration = 45
Step:
[1] -1.427347e-03 5.666489e-04 2.202241e-05 7.662118e-04 -7.978570e-05
Parameter:
[1] 0.02998287 1.14955473 -0.01348359 0.14772264 0.63770786
Function Value
[1] 55.43566
Gradient:
[1] 0.23598767 0.10546101 5.68621928 0.07880081 -0.05686896
iteration = 46
Step:
[1] -2.735302e-03 7.121201e-04 4.418494e-05 2.288645e-04 -6.016317e-05
Parameter:
[1] 0.02724757 1.15026685 -0.01343940 0.14795151 0.63764769
Function Value
[1] 55.43541
Gradient:
[1] 0.21945948 0.15005929 7.10202634 0.08636999 -0.07088492
iteration = 47
Step:
[1] -3.608464e-03 4.539553e-04 6.087765e-05 -1.309925e-03 4.062775e-05
Parameter:
[1] 0.02363911 1.15072081 -0.01337852 0.14664158 0.63768832
Function Value
[1] 55.43509
Gradient:
[1] 0.14641570 0.14459199 6.29046136 0.06882706 -0.06266988
iteration = 48
Step:
[1] -2.169158e-03 -2.347575e-04 3.930104e-05 -2.473445e-03 1.497573e-04
Parameter:
[1] 0.02146995 1.15048605 -0.01333922 0.14416813 0.63783808
Function Value
[1] 55.43489
Gradient:
[1] 0.04942878 0.07431887 3.02524417 0.02943145 -0.02998014
iteration = 49
Step:
[1] 5.557258e-05 -4.539996e-04 1.416156e-06 -1.461011e-03 1.104264e-04
Parameter:
[1] 0.02152552 1.15003205 -0.01333781 0.14270712 0.63794850
Function Value
[1] 55.43484
Gradient:
[1] 0.003353335 0.015154033 0.567880448 0.004341068 -0.005494222
iteration = 50
Step:
[1] 3.836532e-04 -1.617514e-04 -5.891470e-06 -2.342879e-04 2.407737e-05
Parameter:
[1] 0.02190918 1.14987030 -0.01334370 0.14247284 0.63797258
Function Value
[1] 55.43484
Gradient:
[1] -1.228557e-03 4.846942e-04 8.041553e-03 -1.853309e-04 -2.093969e-05
iteration = 51
Step:
[1] -4.062326e-04 -1.327259e-05 8.100931e-06 -1.626987e-05 1.338393e-07
Parameter:
[1] 0.02150294 1.14985702 -0.01333560 0.14245657 0.63797272
Function Value
[1] 55.43484
Gradient:
[1] 2.118476e-05 2.484121e-04 -2.034779e-02 3.547563e-04 -1.413970e-04
iteration = 52
Step:
[1] -2.230488e-05 -3.600743e-06 4.673192e-07 -2.107057e-05 7.438154e-07
Parameter:
[1] 0.02148064 1.14985342 -0.01333513 0.14243550 0.63797346
Function Value
[1] 55.43484
Gradient:
[1] -3.952927e-05 -2.804369e-05 -1.970639e-03 2.897963e-05 1.439702e-06
iteration = 53
Step:
[1] -7.615441e-08 2.402892e-08 2.612985e-09 -1.534459e-06 1.329647e-08
Parameter:
[1] 0.02148056 1.14985345 -0.01333513 0.14243396 0.63797347
Function Value
[1] 55.43484
Gradient:
[1] -9.626717e-06 -6.582133e-06 -4.536789e-04 1.316529e-06 1.798171e-06
iteration = 54
Step:
[1] 5.077235e-08 1.172134e-08 -6.731285e-10 -6.724250e-08 -5.737773e-09
Parameter:
[1] 0.02148061 1.14985346 -0.01333513 0.14243389 0.63797347
Function Value
[1] 55.43484
Gradient:
[1] -1.126423e-06 -6.620630e-07 -5.630881e-05 -4.806822e-08 2.609468e-07
iteration = 55
Parameter:
[1] 0.02148062 1.14985346 -0.01333513 0.14243390 0.63797347
Function Value
[1] 55.43484
Gradient:
[1] -3.829825e-08 -1.476881e-08 -2.150529e-06 -1.111999e-08 1.193712e-08
Successive iterates within tolerance.
Current iterate is probably solution.
difFGLS:
[1] 9.821324e-12 9.881451e-11 3.340536e-12
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning message:
In polygenic(height ~ sex + age, kin = gkin, ge03d2.clean) :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
[1] 0.1424339
Warning message:
In mmscore(h2ht, data = ge03d2.clean) : Lambda estimated < 1, set to 1
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 Author(s) References See Also Examples
Description
Score test for association between a trait and genetic polymorphism, in samples of related individuals
Usage
1 2 |
Arguments
h2object |
An object returned by |
data |
An object of |
snpsubset |
Index, character or logical vector with subset of SNPs to run analysis on.
If missing, all SNPs from |
idsubset |
Index, character or logical vector with subset of IDs to run analysis on.
If missing, all people from |
strata |
Stratification variable. If provieded, scores are computed within strata and then added up. |
times |
If more then one, the number of replicas to be used in derivation of empirical genome-wide significance. NOTE: The structure of the data is not exchangable, therefore do not use times > 1 unless you are really sure you understand what you are doing! |
quiet |
do not print warning messages |
bcast |
If the argument times > 1, progress is reported once in bcast replicas |
clambda |
If inflation facot Lambda is estimated as lower then one, this parameter controls if the original P1df (clambda=TRUE) to be reported in Pc1df, or the original 1df statistics is to be multiplied onto this "deflation" factor (clambda=FALSE). If a numeric value is provided, it is used as a correction factor. |
propPs |
proportion of non-corrected P-values used to estimate the inflation factor Lambda,
passed directly to the |
Details
Score test is performed using the formula
\frac{((G-E[G]) V^{-1} residualY)^2}{(G-E[G]) V^{-1} (G-E[G])}
where G is the vector of genotypes (coded 0, 1, 2) and E[G] is
a vector of (strata-specific) mean genotypic values; V^{-1} is the
InvSigma and residualY are residuals from the trait analysis
with polygenic procedure.
This test is similar to that implemented by Abecasis et al. (see reference).
Value
Object of class scan.gwaa-class; only 1 d.f. test is
implemented currently.
Author(s)
Yurii Aulchenko
References
Chen WM, Abecasis GR. Family-based association tests for genome-wide association scans. Am J Hum Genet. 2007 Nov;81(5):913-26.
See Also
grammar,
qtscore,
egscore,
plot.scan.gwaa,
scan.gwaa-class
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | # ge03d2 is rather bad data set to demonstrate,
# because this is a population-based study
require(GenABEL.data)
data(ge03d2.clean)
#take half for speed
ge03d2.clean <- ge03d2.clean[1:100,]
gkin <- ibs(ge03d2.clean,w="freq")
h2ht <- polygenic(height ~ sex + age,kin=gkin,ge03d2.clean)
h2ht$est
mm <- mmscore(h2ht,data=ge03d2.clean)
# compute grammar
gr <- qtscore(h2ht$pgres,data=ge03d2.clean,clam=FALSE)
#compute GC
gc <- qtscore(height ~ sex + age,data=ge03d2.clean)
#compare
plot(mm,df="Pc1df",cex=0.5)
add.plot(gc,df="Pc1df",col="red")
add.plot(gr,df="Pc1df",col="lightgreen",cex=1.1)
# can see that mmscore and grammar are quite the same... in contrast to GC
|
Example output
Loading required package: MASS
Loading required package: GenABEL.data
LM estimates of fixed parameters:
desmat(Intercept) desmatsex desmatage
0.007548131 1.147885901 -0.013061168
iteration = 0
Step:
[1] 0 0 0 0 0
Parameter:
[1] 0.007548131 1.147885901 -0.013061168 0.300000000 0.648103376
Function Value
[1] 55.66681
Gradient:
[1] -0.7970343 -0.9002342 -9.4983582 2.6684209 1.9871480
iteration = 1
Step:
[1] 7.486420e-07 8.455760e-07 8.921661e-06 -2.506406e-06 -1.866497e-06
Parameter:
[1] 0.00754888 1.14788675 -0.01305225 0.29999749 0.64810151
Function Value
[1] 55.66676
Gradient:
[1] -0.5938191 -0.7822453 1.4375897 2.6679804 1.9867985
iteration = 2
Step:
[1] 6.411024e-07 8.260613e-07 -1.420976e-07 -2.767826e-06 -2.061155e-06
Parameter:
[1] 0.007549521 1.147887573 -0.013052388 0.299994726 0.648099449
Function Value
[1] 55.66674
Gradient:
[1] -0.5965473 -0.7837615 1.2894200 2.6679508 1.9863417
iteration = 3
Step:
[1] 0.0008347452 0.0010744655 -0.0001030452 -0.0035973377 -0.0026786097
Parameter:
[1] 0.008384266 1.148962038 -0.013155433 0.296397388 0.645420839
Function Value
[1] 55.65488
Gradient:
[1] -2.285253 -1.676401 -91.362070 2.630593 1.381695
iteration = 4
Step:
[1] 1.322173e-03 1.700842e-03 -9.103538e-05 -5.692279e-03 -4.237766e-03
Parameter:
[1] 0.009706439 1.150662880 -0.013246469 0.290705109 0.641183073
Function Value
[1] 55.64038
Gradient:
[1] -3.3182490 -2.1363395 -149.8012648 2.5667794 0.4018119
iteration = 5
Step:
[1] 0.0026569518 0.0034166055 -0.0001017411 -0.0114327127 -0.0085092693
Parameter:
[1] 0.01236339 1.15407949 -0.01334821 0.27927240 0.63267380
Function Value
[1] 55.61714
Gradient:
[1] -3.551523 -1.986481 -168.151625 2.415280 -1.638642
iteration = 6
Step:
[1] 1.790706e-03 2.301376e-03 -2.328209e-07 -7.700483e-03 -5.727558e-03
Parameter:
[1] 0.01415410 1.15638086 -0.01334844 0.27157191 0.62694625
Function Value
[1] 55.60394
Gradient:
[1] -2.1668397 -0.9869864 -97.4901598 2.2932996 -3.0656584
iteration = 7
Step:
[1] 3.200402e-04 4.099595e-04 5.321961e-05 -1.372949e-03 -1.015214e-03
Parameter:
[1] 0.01447414 1.15679082 -0.01329522 0.27019896 0.62593103
Function Value
[1] 55.6002
Gradient:
[1] -0.7185304 -0.1113436 -20.1306468 2.2667329 -3.3206498
iteration = 8
Step:
[1] -1.718455e-04 -2.218167e-04 2.187891e-05 7.397489e-04 5.564165e-04
Parameter:
[1] 0.01430229 1.15656900 -0.01327334 0.27093871 0.62648745
Function Value
[1] 55.59994
Gradient:
[1] -0.35805603 0.07873818 -0.32076012 2.27692768 -3.17700826
iteration = 9
Step:
[1] -4.370591e-05 -5.678491e-05 2.534223e-06 1.873171e-04 1.446267e-04
Parameter:
[1] 0.01425859 1.15651222 -0.01327081 0.27112603 0.62663208
Function Value
[1] 55.59991
Gradient:
[1] -0.33482824 0.08733884 1.02753420 2.27960852 -3.13980565
iteration = 10
Step:
[1] -8.239764e-05 -1.084886e-04 4.557309e-06 3.510771e-04 2.842010e-04
Parameter:
[1] 0.01417619 1.15640373 -0.01326625 0.27147711 0.62691628
Function Value
[1] 55.59986
Gradient:
[1] -0.2963599 0.1003585 3.2826027 2.2845664 -3.0667127
iteration = 11
Step:
[1] -1.125355e-04 -1.519010e-04 6.387447e-06 4.741788e-04 4.181545e-04
Parameter:
[1] 0.01406365 1.15625183 -0.01325987 0.27195129 0.62733443
Function Value
[1] 55.59972
Gradient:
[1] -0.2410546 0.1194671 6.5118233 2.2910729 -2.9591862
iteration = 12
Step:
[1] -1.694592e-04 -2.394344e-04 1.018578e-05 6.988233e-04 7.156662e-04
Parameter:
[1] 0.01389419 1.15601240 -0.01324968 0.27265011 0.62805010
Function Value
[1] 55.59936
Gradient:
[1] -0.1476295 0.1533271 11.9219868 2.3001185 -2.7752158
iteration = 13
Step:
[1] -2.161574e-04 -3.363418e-04 1.464905e-05 8.474317e-04 1.161466e-03
Parameter:
[1] 0.01367804 1.15567605 -0.01323503 0.27349754 0.62921156
Function Value
[1] 55.59845
Gradient:
[1] 0.001112454 0.211353186 20.419473287 2.309517370 -2.476852991
iteration = 14
Step:
[1] -2.088932e-04 -4.252463e-04 1.953791e-05 6.764875e-04 1.927817e-03
Parameter:
[1] 0.01346914 1.15525081 -0.01321549 0.27417403 0.63113938
Function Value
[1] 55.5961
Gradient:
[1] 0.2404947 0.3153472 33.7968048 2.3118226 -1.9823419
iteration = 15
Step:
[1] 3.369304e-05 -3.592887e-04 1.987934e-05 -7.174267e-04 3.127760e-03
Parameter:
[1] 0.01350284 1.15489152 -0.01319561 0.27345660 0.63426714
Function Value
[1] 55.59023
Gradient:
[1] 0.6095535 0.5025264 53.6679393 2.2831436 -1.1823416
iteration = 16
Step:
[1] 9.517540e-04 2.484439e-04 2.110652e-06 -5.483508e-03 4.790299e-03
Parameter:
[1] 0.01445459 1.15513996 -0.01319350 0.26797309 0.63905744
Function Value
[1] 55.57644
Gradient:
[1] 1.12710099 0.83201768 79.66540174 2.16314918 0.03686374
iteration = 17
Step:
[1] 3.276493e-03 2.152326e-03 -6.180635e-05 -1.703339e-02 6.065806e-03
Parameter:
[1] 0.01773108 1.15729229 -0.01325531 0.25093971 0.64512324
Function Value
[1] 55.54862
Gradient:
[1] 1.680746 1.348176 102.947639 1.841034 1.573250
iteration = 18
Step:
[1] 0.0067836239 0.0054898838 -0.0001817005 -0.0337960053 0.0042469873
Parameter:
[1] 0.02451471 1.16278217 -0.01343701 0.21714370 0.64937023
Function Value
[1] 55.50832
Gradient:
[1] 1.903909 1.949905 101.515793 1.243283 2.667115
iteration = 19
Step:
[1] 0.0074591773 0.0068599564 -0.0002434808 -0.0359910848 -0.0019551940
Parameter:
[1] 0.03197388 1.16964213 -0.01368049 0.18115262 0.64741504
Function Value
[1] 55.47725
Gradient:
[1] 1.4808321 2.2839731 63.6782829 0.6107532 2.2529371
iteration = 20
Step:
[1] 0.0028906328 0.0032049549 -0.0001284514 -0.0131711102 -0.0051624919
Parameter:
[1] 0.03486452 1.17284708 -0.01380894 0.16798151 0.64225255
Function Value
[1] 55.46738
Gradient:
[1] 0.7967717 2.1623817 20.4515645 0.3685095 1.0282386
iteration = 21
Step:
[1] -2.784684e-04 7.698159e-05 -1.399989e-05 1.816475e-03 -2.620404e-03
Parameter:
[1] 0.03458605 1.17292407 -0.01382294 0.16979798 0.63963214
Function Value
[1] 55.46605
Gradient:
[1] 0.4379634 1.9641385 1.3430362 0.3986591 0.3972916
iteration = 22
Step:
[1] -3.270487e-04 -2.478646e-04 6.965651e-06 1.653009e-03 -3.538327e-04
Parameter:
[1] 0.03425900 1.17267620 -0.01381598 0.17145099 0.63927831
Function Value
[1] 55.46599
Gradient:
[1] 0.3932840 1.9176692 -0.4484865 0.4286262 0.3127178
iteration = 23
Step:
[1] -4.784184e-05 -4.278825e-05 1.572686e-06 2.324103e-04 -1.091682e-05
Parameter:
[1] 0.03421116 1.17263341 -0.01381440 0.17168340 0.63926739
Function Value
[1] 55.46598
Gradient:
[1] 0.3960711 1.9156881 -0.2012953 0.4328866 0.3102883
iteration = 24
Step:
[1] -1.406266e-04 -1.321138e-04 4.869115e-06 6.735665e-04 -2.933668e-05
Parameter:
[1] 0.03407053 1.17250130 -0.01380953 0.17235697 0.63923806
Function Value
[1] 55.46596
Gradient:
[1] 0.4076997 1.9113822 0.7141092 0.4452625 0.3038118
iteration = 25
Step:
[1] -1.815508e-04 -1.840437e-04 6.479897e-06 8.490960e-04 -3.921052e-05
Parameter:
[1] 0.03388898 1.17231726 -0.01380305 0.17320606 0.63919885
Function Value
[1] 55.46591
Gradient:
[1] 0.4236033 1.9053465 1.9495757 0.4609188 0.2951103
iteration = 26
Step:
[1] -3.225709e-04 -3.642812e-04 1.191606e-05 1.451990e-03 -7.162228e-05
Parameter:
[1] 0.03356641 1.17195297 -0.01379114 0.17465805 0.63912722
Function Value
[1] 55.46578
Gradient:
[1] 0.4517300 1.8917948 4.1526063 0.4878503 0.2791383
iteration = 27
Step:
[1] -5.038233e-04 -6.636859e-04 1.958371e-05 2.123960e-03 -1.157051e-04
Parameter:
[1] 0.03306259 1.17128929 -0.01377155 0.17678201 0.63901152
Function Value
[1] 55.46544
Gradient:
[1] 0.4943032 1.8628450 7.5580409 0.5276727 0.2531846
iteration = 28
Step:
[1] -8.114959e-04 -1.314954e-03 3.404951e-05 3.047291e-03 -1.959979e-04
Parameter:
[1] 0.03225109 1.16997433 -0.01373750 0.17982930 0.63881552
Function Value
[1] 55.46459
Gradient:
[1] 0.5588927 1.7957351 12.9263366 0.5860254 0.2089235
iteration = 29
Step:
[1] -1.217899e-03 -2.598422e-03 5.747866e-05 3.623872e-03 -3.192569e-04
Parameter:
[1] 0.03103319 1.16737591 -0.01368003 0.18345317 0.63849626
Function Value
[1] 55.46253
Gradient:
[1] 0.6454119 1.6428073 20.6703392 0.6589926 0.1363922
iteration = 30
Step:
[1] -1.577059e-03 -4.933296e-03 9.050034e-05 2.309101e-03 -4.794377e-04
Parameter:
[1] 0.02945613 1.16244262 -0.01358953 0.18576227 0.63801683
Function Value
[1] 55.45794
Gradient:
[1] 0.73090743 1.31355169 29.89105404 0.71690174 0.02728338
iteration = 31
Step:
[1] -0.0012317179 -0.0077383457 0.0001106893 -0.0041004734 -0.0005461381
Parameter:
[1] 0.02822441 1.15470427 -0.01347884 0.18166180 0.63747069
Function Value
[1] 55.44984
Gradient:
[1] 0.73299201 0.73221144 35.14431806 0.67059315 -0.09679972
iteration = 32
Step:
[1] 5.698054e-04 -7.445375e-03 6.254506e-05 -1.485675e-02 -2.392295e-04
Parameter:
[1] 0.02879422 1.14725889 -0.01341629 0.16680505 0.63723146
Function Value
[1] 55.44095
Gradient:
[1] 0.55641337 0.08627239 27.60362614 0.42842279 -0.15516839
iteration = 33
Step:
[1] 2.159426e-03 -1.776175e-03 -3.622574e-05 -1.612610e-02 3.043072e-04
Parameter:
[1] 0.03095365 1.14548272 -0.01345252 0.15067895 0.63753577
Function Value
[1] 55.43664
Gradient:
[1] 0.30839294 -0.16767397 11.28189554 0.14077256 -0.09577193
iteration = 34
Step:
[1] 1.329174e-03 1.693987e-03 -5.186797e-05 -5.691026e-03 3.438891e-04
Parameter:
[1] 0.03228282 1.14717671 -0.01350439 0.14498793 0.63787965
Function Value
[1] 55.43592
Gradient:
[1] 0.18565946 -0.10103569 1.74549687 0.03155287 -0.01987298
iteration = 35
Step:
[1] 2.406597e-04 8.303781e-04 -1.505240e-05 -2.357704e-04 8.198753e-05
Parameter:
[1] 0.03252348 1.14800709 -0.01351944 0.14475216 0.63796164
Function Value
[1] 55.43588
Gradient:
[1] 0.166314294 -0.048618401 -0.034773834 0.024763821 -0.000102375
iteration = 36
Step:
[1] 2.176200e-06 9.103215e-05 -1.007243e-06 1.235977e-04 -6.863360e-07
Parameter:
[1] 0.03252566 1.14809812 -0.01352044 0.14487575 0.63796096
Function Value
[1] 55.43588
Gradient:
[1] 1.671713e-01 -4.137046e-02 -2.856078e-02 2.674685e-02 -4.596501e-05
iteration = 37
Step:
[1] -1.453098e-06 5.199941e-06 -6.803913e-09 1.576172e-05 -1.088528e-06
Parameter:
[1] 0.03252420 1.14810332 -0.01352045 0.14489152 0.63795987
Function Value
[1] 55.43588
Gradient:
[1] 0.1675834369 -0.0407589183 -0.0060234129 0.0270183165 -0.0002847145
iteration = 38
Step:
[1] -7.018031e-06 2.132072e-05 5.795043e-09 6.557846e-05 -4.917844e-06
Parameter:
[1] 0.03251718 1.14812464 -0.01352045 0.14495709 0.63795495
Function Value
[1] 55.43588
Gradient:
[1] 0.169520021 -0.038109858 0.100900948 0.028149842 -0.001373564
iteration = 39
Step:
[1] -1.025201e-05 2.604498e-05 4.079207e-08 7.848309e-05 -6.020541e-06
Parameter:
[1] 0.03250693 1.14815068 -0.01352040 0.14503558 0.63794893
Function Value
[1] 55.43588
Gradient:
[1] 0.171911353 -0.034856335 0.234380977 0.029505991 -0.002709768
iteration = 40
Step:
[1] -2.379585e-05 4.832576e-05 1.612808e-07 1.416707e-04 -1.099602e-05
Parameter:
[1] 0.03248314 1.14819901 -0.01352024 0.14517725 0.63793793
Function Value
[1] 55.43588
Gradient:
[1] 0.176225797 -0.028884274 0.479667349 0.031960639 -0.005153083
iteration = 41
Step:
[1] -4.975047e-05 7.664985e-05 4.670112e-07 2.152422e-04 -1.693579e-05
Parameter:
[1] 0.03243339 1.14827566 -0.01351978 0.14539249 0.63792100
Function Value
[1] 55.43588
Gradient:
[1] 0.182681902 -0.019620962 0.858509395 0.035707693 -0.008920978
iteration = 42
Step:
[1] -1.155539e-04 1.304495e-04 1.336277e-06 3.422457e-04 -2.750061e-05
Parameter:
[1] 0.03231783 1.14840611 -0.01351844 0.14573474 0.63789350
Function Value
[1] 55.43587
Gradient:
[1] 0.19263973 -0.00441388 1.47517113 0.04171345 -0.01505077
iteration = 43
Step:
[1] -2.700496e-04 2.181017e-04 3.580838e-06 5.123954e-04 -4.267814e-05
Parameter:
[1] 0.03204778 1.14862421 -0.01351486 0.14624713 0.63785082
Function Value
[1] 55.43585
Gradient:
[1] 0.20670809 0.01961264 2.43536878 0.05083264 -0.02459187
iteration = 44
Step:
[1] -6.375624e-04 3.638714e-04 9.251417e-06 7.092973e-04 -6.317613e-05
Parameter:
[1] 0.03141022 1.14898808 -0.01350561 0.14695643 0.63778764
Function Value
[1] 55.43579
Gradient:
[1] 0.22388539 0.05628653 3.86427760 0.06380475 -0.03878446
iteration = 45
Step:
[1] -1.427347e-03 5.666489e-04 2.202241e-05 7.662118e-04 -7.978570e-05
Parameter:
[1] 0.02998287 1.14955473 -0.01348359 0.14772264 0.63770786
Function Value
[1] 55.43566
Gradient:
[1] 0.23598767 0.10546101 5.68621928 0.07880081 -0.05686896
iteration = 46
Step:
[1] -2.735302e-03 7.121201e-04 4.418494e-05 2.288645e-04 -6.016317e-05
Parameter:
[1] 0.02724757 1.15026685 -0.01343940 0.14795151 0.63764769
Function Value
[1] 55.43541
Gradient:
[1] 0.21945948 0.15005929 7.10202634 0.08636999 -0.07088492
iteration = 47
Step:
[1] -3.608464e-03 4.539553e-04 6.087765e-05 -1.309925e-03 4.062775e-05
Parameter:
[1] 0.02363911 1.15072081 -0.01337852 0.14664158 0.63768832
Function Value
[1] 55.43509
Gradient:
[1] 0.14641570 0.14459199 6.29046136 0.06882706 -0.06266988
iteration = 48
Step:
[1] -2.169158e-03 -2.347575e-04 3.930104e-05 -2.473445e-03 1.497573e-04
Parameter:
[1] 0.02146995 1.15048605 -0.01333922 0.14416813 0.63783808
Function Value
[1] 55.43489
Gradient:
[1] 0.04942878 0.07431887 3.02524417 0.02943145 -0.02998014
iteration = 49
Step:
[1] 5.557258e-05 -4.539996e-04 1.416156e-06 -1.461011e-03 1.104264e-04
Parameter:
[1] 0.02152552 1.15003205 -0.01333781 0.14270712 0.63794850
Function Value
[1] 55.43484
Gradient:
[1] 0.003353335 0.015154033 0.567880448 0.004341068 -0.005494222
iteration = 50
Step:
[1] 3.836532e-04 -1.617514e-04 -5.891470e-06 -2.342879e-04 2.407737e-05
Parameter:
[1] 0.02190918 1.14987030 -0.01334370 0.14247284 0.63797258
Function Value
[1] 55.43484
Gradient:
[1] -1.228557e-03 4.846942e-04 8.041553e-03 -1.853309e-04 -2.093969e-05
iteration = 51
Step:
[1] -4.062326e-04 -1.327259e-05 8.100931e-06 -1.626987e-05 1.338393e-07
Parameter:
[1] 0.02150294 1.14985702 -0.01333560 0.14245657 0.63797272
Function Value
[1] 55.43484
Gradient:
[1] 2.118476e-05 2.484121e-04 -2.034779e-02 3.547563e-04 -1.413970e-04
iteration = 52
Step:
[1] -2.230488e-05 -3.600743e-06 4.673192e-07 -2.107057e-05 7.438154e-07
Parameter:
[1] 0.02148064 1.14985342 -0.01333513 0.14243550 0.63797346
Function Value
[1] 55.43484
Gradient:
[1] -3.952927e-05 -2.804369e-05 -1.970639e-03 2.897963e-05 1.439702e-06
iteration = 53
Step:
[1] -7.615441e-08 2.402892e-08 2.612985e-09 -1.534459e-06 1.329647e-08
Parameter:
[1] 0.02148056 1.14985345 -0.01333513 0.14243396 0.63797347
Function Value
[1] 55.43484
Gradient:
[1] -9.626717e-06 -6.582133e-06 -4.536789e-04 1.316529e-06 1.798171e-06
iteration = 54
Step:
[1] 5.077235e-08 1.172134e-08 -6.731285e-10 -6.724250e-08 -5.737773e-09
Parameter:
[1] 0.02148061 1.14985346 -0.01333513 0.14243389 0.63797347
Function Value
[1] 55.43484
Gradient:
[1] -1.126423e-06 -6.620630e-07 -5.630881e-05 -4.806822e-08 2.609468e-07
iteration = 55
Parameter:
[1] 0.02148062 1.14985346 -0.01333513 0.14243390 0.63797347
Function Value
[1] 55.43484
Gradient:
[1] -3.829825e-08 -1.476881e-08 -2.150529e-06 -1.111999e-08 1.193712e-08
Successive iterates within tolerance.
Current iterate is probably solution.
difFGLS:
[1] 9.821324e-12 9.881451e-11 3.340536e-12
******************************************
*** GOOD convergence indicated by FGLS ***
******************************************
Warning message:
In polygenic(height ~ sex + age, kin = gkin, ge03d2.clean) :
some eigenvalues close/less than 1e-8, setting them to 1e-8
you can also try option llfun='polylik' instead
[1] 0.1424339
Warning message:
In mmscore(h2ht, data = ge03d2.clean) : Lambda estimated < 1, set to 1
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.