mvtb: Fitting a Multivariate Tree Boosting Model
In mvtboost: Tree Boosting for Multivariate Outcomes
Description
Usage
Arguments
Details
Value
Functions
References
See Also
Examples
Description
Builds on gbm (Ridgeway 2013; Friedman, 2001) to fit a univariate tree model for each outcome, selecting predictors at each iteration that explain (co)variance in the outcomes. The number of trees included in the model can be chosen by minimizing the multivariate mean squared error using cross validation or a test set.
Usage
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mvtb(Y, X,
n.trees = 100,
shrinkage = 0.01,
interaction.depth = 1,
distribution="gaussian",
train.fraction = 1,
bag.fraction = 1,
cv.folds = 1,
s = NULL,
seednum = NULL,
compress = FALSE,
save.cv = FALSE,
iter.details = TRUE,
verbose=FALSE,
mc.cores = 1, ...)
mvtb.fit(Y,X,
n.trees=100,
shrinkage=.01,
interaction.depth=1,
bag.fraction=1,
s=1:nrow(X),
seednum=NULL,...)
Arguments
Y
vector, matrix, or data.frame for outcome variables with no missing values. To easily compare influences across outcomes and for numerical stability, outcome variables should be scaled to have unit variance.
X
vector, matrix, or data.frame of predictors. For best performance, continuous predictors should be scaled to have unit variance. Categorical variables should converted to factors.
n.trees
maximum number of trees to be included in the model. Each individual tree is grown until a minimum number observations in each node is reached.
shrinkage
a constant multiplier for the predictions from each tree to ensure a slow learning rate. Default is .01. Small shrinkage values may require a large number of trees to provide adequate fit.
interaction.depth
fixed depth of trees to be included in the model. A tree depth of 1 corresponds to fitting stumps (main effects only), higher tree depths capture higher order interactions (e.g. 2 implies a model with up to 2-way interactions)
distribution
Character vector specifying the distribution of all outcomes. Default is "gaussian" see ?gbm for further details.
train.fraction
proportion of the sample used for training the multivariate additive model. If both cv.folds and train.fraction are specified, the CV is carried out within the training set.
bag.fraction
proportion of the training sample used to fit univariate trees for each response at each iteration. Default: 1
cv.folds
number of cross validation folds. Default: 1. Runs k + 1 models, where the k models are run in parallel and the final model is run on the entire sample. If larger than 1, the number of trees that minimize the multivariate MSE averaged over k-folds is reported in object$best.trees
s
vector of indices denoting observations to be used for the training sample. If s is given, train.fraction is ignored.
seednum
integer passed to set.seed
compress
TRUE/FALSE. Compress output results list using bzip2 (approx 10% of original size). Default is FALSE.
save.cv
TRUE/FALSE. Save all k-fold cross-validation models. Default is FALSE.
iter.details
TRUE/FALSE. Return training, test, and cross-validation error at each iteration. Default is FALSE.
verbose
If TRUE, will print out progress and performance indicators for each model. Default is FALSE.
mc.cores
Number of cores for cross validation.
...
additional arguments passed to gbm. These include distribution, weights, var.monotone, n.minobsinnode, keep.data, verbose, class.stratify.cv. Note that other distribution arguments have not been tested.
Details
This function selects predictors that explain covariance in multivariate outcomes.
This is done efficiently by fitting separate gbm models for each outcome (contained in $models).
(Relative) influences can be retrieved using summary or mvtb.ri, which are the usual reductions in SSE due to splitting on each predictor.
The covariance explained in pairs of outcomes by each predictor can be computed using mvtb.covex.
Partial dependence plots can be obtained from mvtb.plot.
The model is tuned jointly by selecting the number of trees that minimize multivariate mean squared error in a test set (by setting train.fraction) or averaged over k folds in k-fold cross-validation (by setting cv.folds > 1).
The best number of trees is available via $best.trees.
If both cv.folds and train.fraction is specified, cross-validation is carried out within the training set.
If s is specified, train.fraction is ignored but cross-validation will be carried out for observations in s.
Cross-validation models are usually discarded but can be saved by setting save.cv = TRUE. CV models can be accessed from $ocv of the
output object. Observations can be specifically set for inclusion in the training set by passing a vector of integers indexing the rows to include to s.
Multivariate mean squared training, test, and cv error are available from $trainerr, $testerr, $cverr from the output object
when iter.details = TRUE.
Since the output objects can be large, automatic compression is available by setting compress=TRUE.
All methods that use the mvtb object automatically uncompress this object if necessary.
The function mvtb.uncomp is available to manually decompress the object.
Note that trees are grown until a minimum number of observations in each node is reached.
If the number of training samples*bag.fraction is less the minimum number of observations, (which can occur with small data sets), this will cause an error.
Adjust the n.minobsinnode, train.fraction, or bag.fraction.
Cross-validation can be parallelized by setting mc.cores > 1. Parallel cross-validation is carried out using parallel::mclapply, which makes mc.cores copies of the original environment.
For models with many trees (> 100K), memory limits can be reached rapidly. mc.cores will not work on Windows.
Value
Fitted model. This is a list containing the following elements:
-
models - list of gbm models for each outcome. Functions from the gbm package (e.g. to compute relative influence, print trees, obtain predictions, etc) can be directly applied to each of these models
-
best.trees - A list containing the number of trees that minimize the multivariate MSE in a test set or by CV, and n.trees.
Many of the functions in the package default to using the minimum value of the three.
-
params - arguments to mvtb
-
trainerr - multivariate training error at each tree (If iter.details = TRUE)
-
testerr - multivariate test error at each tree (if train.fraction < 1 and iter.details = TRUE)
-
cverr - multivariate cv error at each tree (if cv.folds > 1 and iter.details = TRUE)
-
ocv - the CV models if save.cv=TRUE
-
s - indices of training sample
-
n - number of observations
-
xnames
-
ynames
Functions
-
mvtb.fit:
References
Miller P.J., Lubke G.H, McArtor D.B., Bergeman C.S. (Accepted) Finding structure in data with multivariate tree boosting.
Ridgeway, G., Southworth, M. H., & RUnit, S. (2013). Package 'gbm'. Viitattu, 10, 2013.
Elith, J., Leathwick, J. R., & Hastie, T. (2008). A working guide to boosted regression trees. Journal of Animal Ecology, 77(4), 802-813.
Friedman, J. H. (2001). Greedy function approximation: a gradient boosting machine. Annals of statistics, 1189-1232.
See Also
mvtb.covex to estimate the covariance explained in pairs of outcomes by predictors
mvtb.nonlin to help detect nonlinear effects or interactions
plot.mvtb, mvtb.perspec for partial dependence plots
mvtb.uncomp to uncompress a compressed output object
Examples
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data(wellbeing)
Y <- wellbeing[,21:26]
X <- wellbeing[,1:20]
Ys <- scale(Y)
cont.id <- unlist(lapply(X,is.numeric))
Xs <- scale(X[,cont.id])
## Fit the model
res <- mvtb(Y=Ys,X=Xs)
## Interpret the model
summary(res)
covex <- mvtb.covex(res, Y=Ys, X=Xs)
plot(res,predictor.no = 8)
predict(res,newdata=Xs)
mvtb.cluster(covex)
mvtb.heat(t(mvtb.ri(res)),cexRow=.8,cexCol=1,dec=0)
Example output
$best.trees
[1] 100
$relative.influence
autonomy envmast prsgrwth posrel prpsnlf slfaccpt
age 0.00 0.00 0.00 0.00 0.00 0.00
chrhlth 0.00 0.00 0.00 0.00 0.00 0.00
somhlth 0.00 0.00 0.00 0.00 0.00 0.00
slfhlth 0.00 0.00 0.00 0.00 0.00 0.00
posaff 0.00 0.60 0.00 0.00 10.84 14.83
negaff 0.00 16.69 0.00 0.00 0.00 16.95
pscntrl 0.00 2.79 2.86 2.22 1.22 4.17
cistot 86.26 25.68 46.90 0.00 10.87 9.92
comit 2.00 0.00 14.72 0.00 23.41 12.47
cntrl 7.34 0.00 2.11 0.00 2.07 0.00
chlng 0.00 0.00 0.00 0.00 0.00 0.00
egores 0.00 0.00 31.37 0.00 0.00 0.00
pssfrnd 0.00 0.00 0.00 14.46 0.00 0.00
pssfam 0.00 0.00 0.00 0.00 0.00 0.00
pssprob 4.39 39.61 2.05 0.00 39.66 32.80
pssemot 0.00 8.69 0.00 0.00 0.00 0.59
lonlnes 0.00 5.94 0.00 83.32 11.92 8.26
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[129,] 0.3630535826 0.253531856 0.2314105624 0.394592680 0.3236559575
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lonlnes cistot pssprob egores pssfrnd cntrl
posrel-autonomy 0.1500630 0.1609527 0.0087822 0.0000000 0.0166512 0.0136198
posrel-prsgrwth 0.1988106 0.1090084 0.0048551 0.0671922 0.0373774 0.0047043
posrel-posrel 0.3271528 0.0000000 0.0000000 0.0000000 0.0567931 0.0000000
slfaccpt-posrel 0.3175304 0.0191384 0.0219874 0.0000000 0.0345187 0.0000000
posrel-envmast 0.3124335 0.0739475 0.1108084 0.0000000 0.0343328 0.0000000
prpsnlf-posrel 0.2917310 0.0319066 0.1053673 0.0000000 0.0393666 0.0052305
envmast-autonomy 0.0114136 0.2182412 0.0985397 0.0000000 0.0000000 0.0167812
prpsnlf-autonomy 0.0059311 0.2149187 0.0935203 0.0000000 0.0000000 0.0217504
autonomy-autonomy 0.0000000 0.1523852 0.0077588 0.0000000 0.0000000 0.0129740
prsgrwth-autonomy 0.0000000 0.2363931 0.0131975 0.0517955 0.0000000 0.0188996
slfaccpt-autonomy 0.0130292 0.2069042 0.0294062 0.0000000 0.0000000 0.0156899
prsgrwth-prsgrwth 0.0000000 0.1235166 0.0053958 0.0826232 0.0000000 0.0055445
slfaccpt-prsgrwth 0.0181652 0.1334014 0.0281987 0.0710779 0.0000000 0.0056648
prsgrwth-envmast 0.0152155 0.1579355 0.1138150 0.0708789 0.0000000 0.0060480
prpsnlf-prsgrwth 0.0078616 0.1530701 0.1080856 0.0763362 0.0000000 0.0119409
slfaccpt-prpsnlf 0.0663284 0.0606621 0.1625828 0.0000000 0.0000000 0.0063604
prpsnlf-prpsnlf 0.0400963 0.0365598 0.1333789 0.0000000 0.0000000 0.0069552
slfaccpt-slfaccpt 0.0296138 0.0355623 0.1175842 0.0000000 0.0000000 0.0000000
prpsnlf-envmast 0.0312365 0.1229600 0.2803111 0.0000000 0.0000000 0.0067220
envmast-envmast 0.0224058 0.0968988 0.1494423 0.0000000 0.0000000 0.0000000
slfaccpt-envmast 0.0483188 0.1144805 0.1720837 0.0000000 0.0000000 0.0000000
pssfam chlng slfhlth somhlth age chrhlth pscntrl pssemot
posrel-autonomy 0 0 0 0 0 0 0.0054332 0.0000000
posrel-prsgrwth 0 0 0 0 0 0 0.0159315 0.0000000
posrel-posrel 0 0 0 0 0 0 0.0087024 0.0000000
slfaccpt-posrel 0 0 0 0 0 0 0.0213405 0.0013529
posrel-envmast 0 0 0 0 0 0 0.0175503 0.0199349
prpsnlf-posrel 0 0 0 0 0 0 0.0120992 0.0000000
envmast-autonomy 0 0 0 0 0 0 0.0062431 0.0143088
prpsnlf-autonomy 0 0 0 0 0 0 0.0025681 0.0000000
autonomy-autonomy 0 0 0 0 0 0 0.0000000 0.0000000
prsgrwth-autonomy 0 0 0 0 0 0 0.0052156 0.0000000
slfaccpt-autonomy 0 0 0 0 0 0 0.0086623 0.0009469
prsgrwth-prsgrwth 0 0 0 0 0 0 0.0075280 0.0000000
slfaccpt-prsgrwth 0 0 0 0 0 0 0.0196357 0.0010564
prsgrwth-envmast 0 0 0 0 0 0 0.0161767 0.0155210
prpsnlf-prsgrwth 0 0 0 0 0 0 0.0115092 0.0000000
slfaccpt-prpsnlf 0 0 0 0 0 0 0.0182933 0.0017735
prpsnlf-prpsnlf 0 0 0 0 0 0 0.0040881 0.0000000
slfaccpt-slfaccpt 0 0 0 0 0 0 0.0149670 0.0021049
prpsnlf-envmast 0 0 0 0 0 0 0.0138561 0.0259223
envmast-envmast 0 0 0 0 0 0 0.0105174 0.0328002
slfaccpt-envmast 0 0 0 0 0 0 0.0247809 0.0331110
comit posaff negaff
posrel-autonomy 0.0040131 0.0000000 0.0000000
posrel-prsgrwth 0.0345209 0.0000000 0.0000000
posrel-posrel 0.0000000 0.0000000 0.0000000
slfaccpt-posrel 0.0244094 0.0314579 0.0426163
posrel-envmast 0.0000000 0.0015582 0.0433062
prpsnlf-posrel 0.0620896 0.0270613 0.0000000
envmast-autonomy 0.0049442 0.0013532 0.0351424
prpsnlf-autonomy 0.0550739 0.0218678 0.0000000
autonomy-autonomy 0.0035393 0.0000000 0.0000000
prsgrwth-autonomy 0.0340730 0.0000000 0.0000000
slfaccpt-autonomy 0.0252421 0.0262331 0.0345362
prsgrwth-prsgrwth 0.0387790 0.0000000 0.0000000
slfaccpt-prsgrwth 0.0702610 0.0303868 0.0288549
prsgrwth-envmast 0.0432242 0.0016060 0.0296175
prpsnlf-prsgrwth 0.1092188 0.0263008 0.0000000
slfaccpt-prpsnlf 0.1093046 0.0799714 0.0525868
prpsnlf-prpsnlf 0.0787325 0.0364654 0.0000000
slfaccpt-slfaccpt 0.0447211 0.0531802 0.0607648
prpsnlf-envmast 0.0773693 0.0392566 0.0531692
envmast-envmast 0.0000000 0.0022456 0.0629844
slfaccpt-envmast 0.0302699 0.0457603 0.1231494
mvtboost documentation built on May 2, 2019, 2:14 p.m.
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Description Usage Arguments Details Value Functions References See Also Examples
Description
Builds on gbm (Ridgeway 2013; Friedman, 2001) to fit a univariate tree model for each outcome, selecting predictors at each iteration that explain (co)variance in the outcomes. The number of trees included in the model can be chosen by minimizing the multivariate mean squared error using cross validation or a test set.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 | mvtb(Y, X,
n.trees = 100,
shrinkage = 0.01,
interaction.depth = 1,
distribution="gaussian",
train.fraction = 1,
bag.fraction = 1,
cv.folds = 1,
s = NULL,
seednum = NULL,
compress = FALSE,
save.cv = FALSE,
iter.details = TRUE,
verbose=FALSE,
mc.cores = 1, ...)
mvtb.fit(Y,X,
n.trees=100,
shrinkage=.01,
interaction.depth=1,
bag.fraction=1,
s=1:nrow(X),
seednum=NULL,...)
|
Arguments
Y |
vector, matrix, or data.frame for outcome variables with no missing values. To easily compare influences across outcomes and for numerical stability, outcome variables should be scaled to have unit variance. |
X |
vector, matrix, or data.frame of predictors. For best performance, continuous predictors should be scaled to have unit variance. Categorical variables should converted to factors. |
n.trees |
maximum number of trees to be included in the model. Each individual tree is grown until a minimum number observations in each node is reached. |
shrinkage |
a constant multiplier for the predictions from each tree to ensure a slow learning rate. Default is .01. Small shrinkage values may require a large number of trees to provide adequate fit. |
interaction.depth |
fixed depth of trees to be included in the model. A tree depth of 1 corresponds to fitting stumps (main effects only), higher tree depths capture higher order interactions (e.g. 2 implies a model with up to 2-way interactions) |
distribution |
Character vector specifying the distribution of all outcomes. Default is "gaussian" see ?gbm for further details. |
train.fraction |
proportion of the sample used for training the multivariate additive model. If both |
bag.fraction |
proportion of the training sample used to fit univariate trees for each response at each iteration. Default: 1 |
cv.folds |
number of cross validation folds. Default: 1. Runs k + 1 models, where the k models are run in parallel and the final model is run on the entire sample. If larger than 1, the number of trees that minimize the multivariate MSE averaged over k-folds is reported in |
s |
vector of indices denoting observations to be used for the training sample. If |
seednum |
integer passed to |
compress |
|
save.cv |
|
iter.details |
|
verbose |
If |
mc.cores |
Number of cores for cross validation. |
... |
additional arguments passed to |
Details
This function selects predictors that explain covariance in multivariate outcomes.
This is done efficiently by fitting separate gbm models for each outcome (contained in $models).
(Relative) influences can be retrieved using summary or mvtb.ri, which are the usual reductions in SSE due to splitting on each predictor.
The covariance explained in pairs of outcomes by each predictor can be computed using mvtb.covex.
Partial dependence plots can be obtained from mvtb.plot.
The model is tuned jointly by selecting the number of trees that minimize multivariate mean squared error in a test set (by setting train.fraction) or averaged over k folds in k-fold cross-validation (by setting cv.folds > 1).
The best number of trees is available via $best.trees.
If both cv.folds and train.fraction is specified, cross-validation is carried out within the training set.
If s is specified, train.fraction is ignored but cross-validation will be carried out for observations in s.
Cross-validation models are usually discarded but can be saved by setting save.cv = TRUE. CV models can be accessed from $ocv of the
output object. Observations can be specifically set for inclusion in the training set by passing a vector of integers indexing the rows to include to s.
Multivariate mean squared training, test, and cv error are available from $trainerr, $testerr, $cverr from the output object
when iter.details = TRUE.
Since the output objects can be large, automatic compression is available by setting compress=TRUE.
All methods that use the mvtb object automatically uncompress this object if necessary.
The function mvtb.uncomp is available to manually decompress the object.
Note that trees are grown until a minimum number of observations in each node is reached.
If the number of training samples*bag.fraction is less the minimum number of observations, (which can occur with small data sets), this will cause an error.
Adjust the n.minobsinnode, train.fraction, or bag.fraction.
Cross-validation can be parallelized by setting mc.cores > 1. Parallel cross-validation is carried out using parallel::mclapply, which makes mc.cores copies of the original environment.
For models with many trees (> 100K), memory limits can be reached rapidly. mc.cores will not work on Windows.
Value
Fitted model. This is a list containing the following elements:
-
models- list of gbm models for each outcome. Functions from the gbm package (e.g. to compute relative influence, print trees, obtain predictions, etc) can be directly applied to each of these models -
best.trees- A list containing the number of trees that minimize the multivariate MSE in a test set or by CV, andn.trees. Many of the functions in the package default to using the minimum value of the three. -
params- arguments to mvtb -
trainerr- multivariate training error at each tree (Ifiter.details = TRUE) -
testerr- multivariate test error at each tree (iftrain.fraction < 1anditer.details = TRUE) -
cverr- multivariate cv error at each tree (ifcv.folds > 1anditer.details = TRUE) -
ocv- the CV models ifsave.cv=TRUE -
s- indices of training sample -
n- number of observations -
xnames -
ynames
Functions
-
mvtb.fit:
References
Miller P.J., Lubke G.H, McArtor D.B., Bergeman C.S. (Accepted) Finding structure in data with multivariate tree boosting.
Ridgeway, G., Southworth, M. H., & RUnit, S. (2013). Package 'gbm'. Viitattu, 10, 2013.
Elith, J., Leathwick, J. R., & Hastie, T. (2008). A working guide to boosted regression trees. Journal of Animal Ecology, 77(4), 802-813.
Friedman, J. H. (2001). Greedy function approximation: a gradient boosting machine. Annals of statistics, 1189-1232.
See Also
mvtb.covex to estimate the covariance explained in pairs of outcomes by predictors
mvtb.nonlin to help detect nonlinear effects or interactions
plot.mvtb, mvtb.perspec for partial dependence plots
mvtb.uncomp to uncompress a compressed output object
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | data(wellbeing)
Y <- wellbeing[,21:26]
X <- wellbeing[,1:20]
Ys <- scale(Y)
cont.id <- unlist(lapply(X,is.numeric))
Xs <- scale(X[,cont.id])
## Fit the model
res <- mvtb(Y=Ys,X=Xs)
## Interpret the model
summary(res)
covex <- mvtb.covex(res, Y=Ys, X=Xs)
plot(res,predictor.no = 8)
predict(res,newdata=Xs)
mvtb.cluster(covex)
mvtb.heat(t(mvtb.ri(res)),cexRow=.8,cexCol=1,dec=0)
|
Example output
$best.trees
[1] 100
$relative.influence
autonomy envmast prsgrwth posrel prpsnlf slfaccpt
age 0.00 0.00 0.00 0.00 0.00 0.00
chrhlth 0.00 0.00 0.00 0.00 0.00 0.00
somhlth 0.00 0.00 0.00 0.00 0.00 0.00
slfhlth 0.00 0.00 0.00 0.00 0.00 0.00
posaff 0.00 0.60 0.00 0.00 10.84 14.83
negaff 0.00 16.69 0.00 0.00 0.00 16.95
pscntrl 0.00 2.79 2.86 2.22 1.22 4.17
cistot 86.26 25.68 46.90 0.00 10.87 9.92
comit 2.00 0.00 14.72 0.00 23.41 12.47
cntrl 7.34 0.00 2.11 0.00 2.07 0.00
chlng 0.00 0.00 0.00 0.00 0.00 0.00
egores 0.00 0.00 31.37 0.00 0.00 0.00
pssfrnd 0.00 0.00 0.00 14.46 0.00 0.00
pssfam 0.00 0.00 0.00 0.00 0.00 0.00
pssprob 4.39 39.61 2.05 0.00 39.66 32.80
pssemot 0.00 8.69 0.00 0.00 0.00 0.59
lonlnes 0.00 5.94 0.00 83.32 11.92 8.26
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[187,] 0.0764435770 0.242899259 0.2888506292 0.126300479 0.2619287123
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[759,] 0.1049988178
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[767,] 0.0986625312
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[769,] 0.2520201466
[770,] -0.1183737534
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[772,] 0.1855971272
[773,] 0.3029991677
[774,] -0.0693125244
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[778,] 0.1946338518
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[787,] -0.4178059409
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[790,] 0.2281511162
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[794,] 0.3029991677
[795,] 0.0885995176
[796,] 0.0526278188
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[798,] -0.1892181418
[799,] 0.0979105878
[800,] 0.2192711947
[801,] -0.4792885714
[802,] 0.2520201466
[803,] 0.2520201466
[804,] -0.2796205089
[805,] -0.0033664981
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[808,] -0.2643568384
[809,] 0.2266498941
[810,] -0.0045035524
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[812,] -0.0618898472
[813,] -0.0169340520
[814,] 0.1620341951
[815,] -0.1766135340
[816,] -0.3992294611
[817,] -0.6345197073
[818,] -0.2227201871
[819,] 0.3029991677
[820,] 0.3029991677
[821,] 0.2185181013
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[823,] 0.2520201466
[824,] 0.3029991677
[825,] 0.0971765282
[826,] 0.3029991677
[827,] -0.0100084375
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[829,] 0.3029991677
[830,] 0.3029991677
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[832,] 0.0124686160
[833,] 0.3029991677
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[835,] 0.2270274976
[836,] 0.0479246076
[837,] 0.3029991677
[838,] -0.6345197073
[839,] 0.0912838317
[840,] 0.0320937047
[841,] -0.3086132950
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[843,] 0.2465152614
[844,] 0.3029991677
[845,] -0.3723518486
[846,] 0.3029991677
[847,] -0.5399006074
[848,] 0.1872551523
[849,] 0.2520201466
[850,] -0.4059319083
[851,] -0.5821487084
[852,] -0.1043395373
[853,] 0.1074698237
[854,] -0.6345197073
[855,] 0.0912838317
[856,] -0.6345197073
[857,] 0.2956204682
[858,] 0.3029991677
[859,] -0.3213728276
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[862,] 0.3029991677
[863,] 0.2520201466
[864,] -0.1128688683
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[866,] 0.1685675972
[867,] -0.4766072516
[868,] -0.4002579780
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[870,] -0.5050463414
[871,] -0.6345197073
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[874,] -0.5399006074
[875,] 0.2506281687
[876,] 0.3029991677
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[878,] 0.1422628528
[879,] 0.0464754687
[880,] 0.0761854787
[881,] -0.3383845419
[882,] -0.5638476521
[883,] -0.4072245383
[884,] -0.0455382266
[885,] 0.2520201466
[886,] 0.2520201466
[887,] 0.0761128497
[888,] 0.2580068681
[889,] -0.1892181418
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[891,] -0.3071137257
[892,] 0.1946338518
[893,] -0.0272371703
[894,] 0.3029991677
[895,] 0.0909844849
[896,] 0.2956204682
[897,] 0.2580068681
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[900,] 0.0931576460
[901,] 0.2266498941
[902,] 0.3029991677
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[905,] 0.1381499456
[906,] 0.3029991677
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[909,] 0.0311931792
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[911,] 0.0660628745
[912,] -0.6345197073
[913,] -0.6345197073
[914,] 0.2185181013
[915,] -0.6345197073
[916,] -0.6345197073
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[919,] 0.1421688277
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[921,] -0.0832314872
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[924,] 0.1496415522
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[931,] 0.1909532277
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[937,] 0.2520201466
[938,] -0.6175079930
[939,] 0.2266498941
[940,] 0.1109058788
[941,] 0.2580068681
[942,] -0.5302675925
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[945,] 0.3029991677
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[948,] 0.2520201466
[949,] 0.0508152262
[950,] -0.2561347046
[951,] -0.5018436383
[952,] -0.6101292936
[953,] -0.1165494923
[954,] -0.2062745415
[955,] -0.3093692637
[956,] 0.1756708730
[957,] 0.3029991677
[958,] -0.3260089703
[959,] 0.2520201466
[960,] -0.2008860746
[961,] 0.3029991677
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[963,] -0.5472793068
[964,] 0.0941044028
[965,] 0.3029991677
[966,] -0.6345197073
[967,] -0.2861362425
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[969,] -0.2497209336
[970,] -0.5399006074
[971,] -0.4293350281
[972,] -0.2833769084
[973,] -0.2961548646
[974,] 0.3029991677
[975,] -0.4692285521
[976,] 0.0391208245
[977,] 0.1496415522
[978,] -0.0481356432
[979,] 0.3029991677
[980,] 0.0177551292
[981,] -0.4086165162
[982,] 0.1436548307
[983,] 0.2070278471
[984,] -0.3967422624
lonlnes cistot pssprob egores pssfrnd cntrl
posrel-autonomy 0.1500630 0.1609527 0.0087822 0.0000000 0.0166512 0.0136198
posrel-prsgrwth 0.1988106 0.1090084 0.0048551 0.0671922 0.0373774 0.0047043
posrel-posrel 0.3271528 0.0000000 0.0000000 0.0000000 0.0567931 0.0000000
slfaccpt-posrel 0.3175304 0.0191384 0.0219874 0.0000000 0.0345187 0.0000000
posrel-envmast 0.3124335 0.0739475 0.1108084 0.0000000 0.0343328 0.0000000
prpsnlf-posrel 0.2917310 0.0319066 0.1053673 0.0000000 0.0393666 0.0052305
envmast-autonomy 0.0114136 0.2182412 0.0985397 0.0000000 0.0000000 0.0167812
prpsnlf-autonomy 0.0059311 0.2149187 0.0935203 0.0000000 0.0000000 0.0217504
autonomy-autonomy 0.0000000 0.1523852 0.0077588 0.0000000 0.0000000 0.0129740
prsgrwth-autonomy 0.0000000 0.2363931 0.0131975 0.0517955 0.0000000 0.0188996
slfaccpt-autonomy 0.0130292 0.2069042 0.0294062 0.0000000 0.0000000 0.0156899
prsgrwth-prsgrwth 0.0000000 0.1235166 0.0053958 0.0826232 0.0000000 0.0055445
slfaccpt-prsgrwth 0.0181652 0.1334014 0.0281987 0.0710779 0.0000000 0.0056648
prsgrwth-envmast 0.0152155 0.1579355 0.1138150 0.0708789 0.0000000 0.0060480
prpsnlf-prsgrwth 0.0078616 0.1530701 0.1080856 0.0763362 0.0000000 0.0119409
slfaccpt-prpsnlf 0.0663284 0.0606621 0.1625828 0.0000000 0.0000000 0.0063604
prpsnlf-prpsnlf 0.0400963 0.0365598 0.1333789 0.0000000 0.0000000 0.0069552
slfaccpt-slfaccpt 0.0296138 0.0355623 0.1175842 0.0000000 0.0000000 0.0000000
prpsnlf-envmast 0.0312365 0.1229600 0.2803111 0.0000000 0.0000000 0.0067220
envmast-envmast 0.0224058 0.0968988 0.1494423 0.0000000 0.0000000 0.0000000
slfaccpt-envmast 0.0483188 0.1144805 0.1720837 0.0000000 0.0000000 0.0000000
pssfam chlng slfhlth somhlth age chrhlth pscntrl pssemot
posrel-autonomy 0 0 0 0 0 0 0.0054332 0.0000000
posrel-prsgrwth 0 0 0 0 0 0 0.0159315 0.0000000
posrel-posrel 0 0 0 0 0 0 0.0087024 0.0000000
slfaccpt-posrel 0 0 0 0 0 0 0.0213405 0.0013529
posrel-envmast 0 0 0 0 0 0 0.0175503 0.0199349
prpsnlf-posrel 0 0 0 0 0 0 0.0120992 0.0000000
envmast-autonomy 0 0 0 0 0 0 0.0062431 0.0143088
prpsnlf-autonomy 0 0 0 0 0 0 0.0025681 0.0000000
autonomy-autonomy 0 0 0 0 0 0 0.0000000 0.0000000
prsgrwth-autonomy 0 0 0 0 0 0 0.0052156 0.0000000
slfaccpt-autonomy 0 0 0 0 0 0 0.0086623 0.0009469
prsgrwth-prsgrwth 0 0 0 0 0 0 0.0075280 0.0000000
slfaccpt-prsgrwth 0 0 0 0 0 0 0.0196357 0.0010564
prsgrwth-envmast 0 0 0 0 0 0 0.0161767 0.0155210
prpsnlf-prsgrwth 0 0 0 0 0 0 0.0115092 0.0000000
slfaccpt-prpsnlf 0 0 0 0 0 0 0.0182933 0.0017735
prpsnlf-prpsnlf 0 0 0 0 0 0 0.0040881 0.0000000
slfaccpt-slfaccpt 0 0 0 0 0 0 0.0149670 0.0021049
prpsnlf-envmast 0 0 0 0 0 0 0.0138561 0.0259223
envmast-envmast 0 0 0 0 0 0 0.0105174 0.0328002
slfaccpt-envmast 0 0 0 0 0 0 0.0247809 0.0331110
comit posaff negaff
posrel-autonomy 0.0040131 0.0000000 0.0000000
posrel-prsgrwth 0.0345209 0.0000000 0.0000000
posrel-posrel 0.0000000 0.0000000 0.0000000
slfaccpt-posrel 0.0244094 0.0314579 0.0426163
posrel-envmast 0.0000000 0.0015582 0.0433062
prpsnlf-posrel 0.0620896 0.0270613 0.0000000
envmast-autonomy 0.0049442 0.0013532 0.0351424
prpsnlf-autonomy 0.0550739 0.0218678 0.0000000
autonomy-autonomy 0.0035393 0.0000000 0.0000000
prsgrwth-autonomy 0.0340730 0.0000000 0.0000000
slfaccpt-autonomy 0.0252421 0.0262331 0.0345362
prsgrwth-prsgrwth 0.0387790 0.0000000 0.0000000
slfaccpt-prsgrwth 0.0702610 0.0303868 0.0288549
prsgrwth-envmast 0.0432242 0.0016060 0.0296175
prpsnlf-prsgrwth 0.1092188 0.0263008 0.0000000
slfaccpt-prpsnlf 0.1093046 0.0799714 0.0525868
prpsnlf-prpsnlf 0.0787325 0.0364654 0.0000000
slfaccpt-slfaccpt 0.0447211 0.0531802 0.0607648
prpsnlf-envmast 0.0773693 0.0392566 0.0531692
envmast-envmast 0.0000000 0.0022456 0.0629844
slfaccpt-envmast 0.0302699 0.0457603 0.1231494
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