snp.lhs.estimates: Logistic regression with SNP genotypes as dependent variable
In snpStats: SnpMatrix and XSnpMatrix classes and methods
Description
Usage
Arguments
Details
Value
Note
Author(s)
See Also
Examples
Description
Under the assumption of Hardy-Weinberg equilibrium, a SNP genotype is
a binomial variate with two trials for an autosomal SNP or with one or
two trials (depending on sex) for a SNP on the X chromosome.
With each SNP in an input
"SnpMatrix" as dependent variable, this function fits a
logistic regression model. The Hardy-Weinberg
assumption can be relaxed by use of a "robust" option.
Usage
1
2
3
snp.lhs.estimates(snp.data, base.formula, add.formula, subset, snp.subset,
data = sys.parent(), robust = FALSE, uncertain = FALSE,
control=glm.test.control())
Arguments
snp.data
The SNP data, as an object of class
"SnpMatrix" or "XSnpMatrix"
base.formula
A formula object describing a base model
containing those terms which are to be fitted but for which
parameter estimates are not required
(the dependent variable is omitted from the model formula)
add.formula
A formula object describing the additional
terms in the model for which parameter estimates are required (again,
the dependent variable is omitted)
subset
An array describing the subset of observations to be
considered
snp.subset
An array describing the subset of SNPs to be
considered. Default action is to test all SNPs.
data
The data frame in which base.formula,
add.formula and subset are to be evaluated
robust
If TRUE, Hardy-Weinberg equilibrium will is not
assumed in calculating the variance-covariance matrix of parameter
estimates
uncertain
If TRUE, uncertain genotypes are used and
scored by their posterior expectations. Otherwise they are treated
as missing. If set, this option forces robust variance estimates
control
An object giving parameters for the IRLS algorithm
fitting of the base model and for the acceptable aliasing amongst
new terms to be tested. See glm.test.control
Details
The model fitted is the union of the base.formula and
add.formula models, although parameter estimates (and their
variance-covariance matrix) are only
generated for the parameters of the latter.
The "robust" option causes a Huber-White "sandwich" estimate of the
variance-covariance matrix to be used in place of the usual inverse
second derivative matrix of the log-likelihood (which assumes
Hardy-Weinberg equilibrium).
If a data argument is supplied, the snp.data and
data objects are aligned by rowname. Otherwise all variables in
the model formulae are assumed to be stored in the same order as the
columns of the snp.data object.
Value
An object of class GlmEstimates
Note
A factor (or
several factors) may be included as arguments to the function
strata(...) in the base.formula. This fits all
interactions of the factors so included, but leads to faster
computation than fitting these in the normal way. Additionally, a
cluster(...) call may be included in the base model
formula. This identifies clusters of potentially correlated
observations (e.g. for members of the same family); in this case, an
appropriate robust estimate of the variance-covariance matrix of
parameter estimates is calculated. No more than one
strata() call may be used, and neither strata(...) or
cluster(...) calls may appear in the add.formula.
If uncertain genotypes (e.g. as a result of imputation) are used, the
interpretation of the regression coefficients is questionable.
A known bug is that the function fails when no data argument is
supplied and the base model formula contains no variables
(~1). A work-round is to create a data frame to hold the
variables in the models and pass this as data=.
Author(s)
David Clayton dc208@cam.ac.uk
See Also
GlmEstimates-class, snp.lhs.tests
Examples
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
data(testdata)
test1 <-
snp.lhs.estimates(Autosomes[,1:10], ~cc, ~region, data=subject.data)
test2 <-
snp.lhs.estimates(Autosomes[,1:10], ~strata(region), ~cc,
data=subject.data)
test3 <-
snp.lhs.estimates(Autosomes[,1:10], ~cc, ~region, data=subject.data, robust=TRUE)
test4 <-
snp.lhs.estimates(Autosomes[,1:10], ~strata(region), ~cc,
data=subject.data, robust=TRUE)
test5 <- snp.lhs.estimates(Autosomes[,1:10], ~region+sex, ~cc, data=subject.data, robust=TRUE)
print(test1)
print(test2)
print(test3)
print(test4)
print(test5)
Example output
Loading required package: survival
Loading required package: Matrix
Warning message:
In snp.lhs.estimates(Autosomes[, 1:10], ~cc, ~region, data = subject.data) :
Monomorphic SNP: 6
There were 13 warnings (use warnings() to see them)
Warning message:
In snp.lhs.estimates(Autosomes[, 1:10], ~cc, ~region, data = subject.data, :
Monomorphic SNP: 6
There were 13 warnings (use warnings() to see them)
Warning messages:
1: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
Variable(s) in the base model were aliased and have been dropped
2: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
Monomorphic SNP: 6
3: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
Failure to converge while fitting model for SNP 7
4: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
No estimable parameters for test 7
Model Y-variable Parameter Estimate S.E. z-value
----------------------------------------------------------------------------
173760 173760 regionE & W Ridings 0.39201 7274.9 0.000
regionNorth Midlands 0.26996 6752.7 0.000
regionEastern 0.40499 6467.9 0.000
regionSouth-East -0.55677 9853.1 -0.000
regionSouthern 0.10589 8060.8 0.000
regionSouth-West 0.32633 6696.7 0.000
regionMidlands 0.50665 6824.2 0.000
regionLondon 0.11718 7453.4 0.000
regionNorth-West 16.621 6289.6 0.003
----------------------------------------------------------------------------
173761 173761 regionE & W Ridings -0.63382 0.60277 -1.052
regionNorth Midlands -0.69774 0.5563 -1.254
regionEastern -1.0848 0.534 -2.032
regionSouth-East -1.0587 0.76127 -1.391
regionSouthern -1.031 0.66732 -1.545
regionSouth-West -0.75518 0.5518 -1.369
regionMidlands -1.3374 0.57142 -2.340
regionLondon -1.1751 0.61997 -1.895
regionNorth-West -1.1277 0.54836 -2.057
----------------------------------------------------------------------------
173762 173762 regionE & W Ridings -0.63809 0.60296 -1.058
regionNorth Midlands -0.74302 0.55662 -1.335
regionEastern -1.0894 0.53417 -2.039
regionSouth-East -1.0531 0.76141 -1.383
regionSouthern -1.0327 0.66751 -1.547
regionSouth-West -0.72386 0.55241 -1.310
regionMidlands -1.3689 0.5735 -2.387
regionLondon -1.177 0.62014 -1.898
regionNorth-West -1.1317 0.54854 -2.063
----------------------------------------------------------------------------
173767 173767 regionE & W Ridings 0.20983 0.60937 0.344
regionNorth Midlands 0.06599 0.54673 0.121
regionEastern -0.14769 0.52102 -0.283
regionSouth-East 0.82081 0.83625 0.982
regionSouthern -0.62109 0.66515 -0.934
regionSouth-West -0.03987 0.54178 -0.074
regionMidlands -0.32735 0.55513 -0.590
regionLondon -0.78515 0.60617 -1.295
regionNorth-West 0.27804 0.53877 0.516
----------------------------------------------------------------------------
173769 173769 regionE & W Ridings 4.5881 7.5594 0.607
regionNorth Midlands -0.34476 1.0102 -0.341
regionEastern -0.91347 0.78971 -1.157
regionSouth-East -1.3439 1.2662 -1.061
regionSouthern 4.6814 10.011 0.468
regionSouth-West -0.60396 0.92292 -0.654
regionMidlands 4.5527 5.5668 0.818
regionLondon 4.6776 7.9665 0.587
----------------------------------------------------------------------------
173770 - No estimates available
----------------------------------------------------------------------------
173772 173772 regionE & W Ridings 0.51442 4684.7 0.000
regionNorth Midlands -15.513 3882.2 -0.004
regionEastern 0.51587 4029.5 0.000
regionSouth-East -0.47471 6572.8 -0.000
regionSouthern 0.13355 5040.4 0.000
regionSouth-West 0.45914 4198.5 0.000
regionMidlands 0.71392 4368.7 0.000
regionLondon 0.14812 4650.3 0.000
regionNorth-West 0.42546 4143.4 0.000
----------------------------------------------------------------------------
173774 173774 regionE & W Ridings -0.58188 0.85382 -0.681
regionNorth Midlands 0.13666 0.82751 0.165
regionEastern -0.31416 0.77684 -0.404
regionSouth-East 13.126 322.33 0.041
regionSouthern -0.0071896 0.97631 -0.007
regionSouth-West 0.08923 0.81648 0.109
regionMidlands -0.14467 0.82405 -0.176
regionLondon -0.13347 0.89696 -0.149
regionNorth-West -0.35987 0.79362 -0.453
----------------------------------------------------------------------------
173775 173775 regionE & W Ridings -0.66611 0.72745 -0.916
regionNorth Midlands -0.15507 0.62869 -0.247
regionEastern -0.37129 0.60146 -0.617
regionSouth-East -13.82 275.34 -0.050
regionSouthern -1.2929 0.93791 -1.378
regionSouth-West -0.57642 0.63565 -0.907
regionMidlands -0.50419 0.65354 -0.771
regionLondon -1.0341 0.78327 -1.320
regionNorth-West -0.33239 0.61948 -0.537
----------------------------------------------------------------------------
173776 173776 regionE & W Ridings 0.17345 0.61225 0.283
regionNorth Midlands 0.27629 0.45841 0.603
regionEastern 0.23642 0.37815 0.625
regionSouth-East -3.9329 3.9715 -0.990
regionSouthern 0.4868 0.69274 0.703
regionSouth-West 0.65519 0.41428 1.582
regionMidlands 0.076408 0.50534 0.151
regionLondon -0.45808 0.79158 -0.579
----------------------------------------------------------------------------
Model Y-variable Parameter Estimate S.E. z-value
-----------------------------------------------------------------
173760 - No estimates available
-----------------------------------------------------------------
173761 173761 cccase 0.17833 0.14735 1.210
-----------------------------------------------------------------
173762 173762 cccase 0.20456 0.1479 1.383
-----------------------------------------------------------------
173767 173767 cccase -0.12877 0.14882 -0.865
-----------------------------------------------------------------
173769 - No estimates available
-----------------------------------------------------------------
173770 - No estimates available
-----------------------------------------------------------------
173772 - No estimates available
-----------------------------------------------------------------
173774 - No estimates available
-----------------------------------------------------------------
173775 - No estimates available
-----------------------------------------------------------------
173776 - No estimates available
-----------------------------------------------------------------
Model Y-variable Parameter Estimate S.E. z-value
----------------------------------------------------------------------------
173760 173760 regionE & W Ridings 0.39201 1.0066 0.389
regionNorth Midlands 0.26996 1.0026 0.269
regionEastern 0.40499 1.001 0.405
regionSouth-East -0.55677 1.0111 -0.551
regionSouthern 0.10589 1.0095 0.105
regionSouth-West 0.32633 1.0024 0.326
regionMidlands 0.50665 1.0038 0.505
regionLondon 0.11718 1.006 0.116
regionNorth-West 16.621 1.0133 16.403
----------------------------------------------------------------------------
173761 173761 regionE & W Ridings -0.63382 0.63125 -1.004
regionNorth Midlands -0.69774 0.3544 -1.969
regionEastern -1.0848 0.4292 -2.528
regionSouth-East -1.0587 0.70062 -1.511
regionSouthern -1.031 0.77971 -1.322
regionSouth-West -0.75518 0.40639 -1.858
regionMidlands -1.3374 0.54592 -2.450
regionLondon -1.1751 0.37585 -3.127
regionNorth-West -1.1277 0.63813 -1.767
----------------------------------------------------------------------------
173762 173762 regionE & W Ridings -0.63809 0.62765 -1.017
regionNorth Midlands -0.74302 0.34879 -2.130
regionEastern -1.0894 0.42326 -2.574
regionSouth-East -1.0531 0.69589 -1.513
regionSouthern -1.0327 0.76743 -1.346
regionSouth-West -0.72386 0.40092 -1.805
regionMidlands -1.3689 0.5499 -2.489
regionLondon -1.177 0.37644 -3.127
regionNorth-West -1.1317 0.637 -1.777
----------------------------------------------------------------------------
173767 173767 regionE & W Ridings 0.20983 0.62144 0.338
regionNorth Midlands 0.06599 0.30591 0.216
regionEastern -0.14769 0.44357 -0.333
regionSouth-East 0.82081 0.64343 1.276
regionSouthern -0.62109 0.74606 -0.833
regionSouth-West -0.03987 0.46223 -0.086
regionMidlands -0.32735 0.61056 -0.536
regionLondon -0.78515 0.42325 -1.855
regionNorth-West 0.27804 0.48999 0.567
----------------------------------------------------------------------------
173769 173769 regionE & W Ridings 4.5881 NaN NaN
regionNorth Midlands -0.34476 0.77714 -0.444
regionEastern -0.91347 0.52824 -1.729
regionSouth-East -1.3439 1.081 -1.243
regionSouthern 4.6814 0.45549 10.278
regionSouth-West -0.60396 0.9026 -0.669
regionMidlands 4.5527 0.7114 6.400
regionLondon 4.6776 0.7111 6.578
----------------------------------------------------------------------------
173770 - No estimates available
----------------------------------------------------------------------------
173772 173772 regionE & W Ridings 0.51442 1.0059 0.511
regionNorth Midlands -15.513 1.0002 -15.511
regionEastern 0.51587 0.059151 8.721
regionSouth-East -0.47471 0.36987 -1.283
regionSouthern 0.13355 0.16895 0.790
regionSouth-West 0.45914 0.083373 5.507
regionMidlands 0.71392 0.095051 7.511
regionLondon 0.14812 0.14406 1.028
regionNorth-West 0.42546 0.22185 1.918
----------------------------------------------------------------------------
173774 173774 regionE & W Ridings -0.58188 0.56282 -1.034
regionNorth Midlands 0.13666 0.35524 0.385
regionEastern -0.31416 0.32302 -0.973
regionSouth-East 13.126 NaN NaN
regionSouthern -0.0071896 0.68956 -0.010
regionSouth-West 0.08923 0.4062 0.220
regionMidlands -0.14467 0.56319 -0.257
regionLondon -0.13347 0.60599 -0.220
regionNorth-West -0.35987 0.7519 -0.479
----------------------------------------------------------------------------
173775 173775 regionE & W Ridings -0.66611 0.58238 -1.144
regionNorth Midlands -0.15507 0.28296 -0.548
regionEastern -0.37129 0.30948 -1.200
regionSouth-East -13.82 66.939 -0.206
regionSouthern -1.2929 0.82212 -1.573
regionSouth-West -0.57642 0.35407 -1.628
regionMidlands -0.50419 0.45256 -1.114
regionLondon -1.0341 0.53978 -1.916
regionNorth-West -0.33239 0.69552 -0.478
----------------------------------------------------------------------------
173776 173776 regionE & W Ridings 0.17345 0.59392 0.292
regionNorth Midlands 0.27629 0.35001 0.789
regionEastern 0.23642 0.31759 0.744
regionSouth-East -3.9329 0.32562 -12.078
regionSouthern 0.4868 0.73901 0.659
regionSouth-West 0.65519 0.3645 1.798
regionMidlands 0.076408 0.46793 0.163
regionLondon -0.45808 0.76845 -0.596
----------------------------------------------------------------------------
Warning messages:
1: In sqrt(x$Var.beta[ii]) : NaNs produced
2: In sqrt(x$Var.beta[ii]) : NaNs produced
Model Y-variable Parameter Estimate S.E. z-value
-----------------------------------------------------------------
173760 - No estimates available
-----------------------------------------------------------------
173761 173761 cccase 0.17833 0.14592 1.222
-----------------------------------------------------------------
173762 173762 cccase 0.20456 0.14603 1.401
-----------------------------------------------------------------
173767 173767 cccase -0.12877 0.14544 -0.885
-----------------------------------------------------------------
173769 - No estimates available
-----------------------------------------------------------------
173770 - No estimates available
-----------------------------------------------------------------
173772 - No estimates available
-----------------------------------------------------------------
173774 - No estimates available
-----------------------------------------------------------------
173775 - No estimates available
-----------------------------------------------------------------
173776 - No estimates available
-----------------------------------------------------------------
Model Y-variable Parameter Estimate S.E. z-value
-----------------------------------------------------------------
173760 173760 cccase -13.467 1.0027 -13.432
-----------------------------------------------------------------
173761 173761 cccase 0.18763 0.14553 1.289
-----------------------------------------------------------------
173762 173762 cccase 0.21178 0.14568 1.454
-----------------------------------------------------------------
173767 173767 cccase -0.1287 0.14571 -0.883
-----------------------------------------------------------------
173769 173769 cccase 0.8949 0.53343 1.678
-----------------------------------------------------------------
173770 - No estimates available
-----------------------------------------------------------------
173772 - No estimates available
-----------------------------------------------------------------
173774 173774 cccase 0.17924 0.2148 0.834
-----------------------------------------------------------------
173775 173775 cccase -0.188 0.19069 -0.986
-----------------------------------------------------------------
173776 173776 cccase 0.071589 0.23134 0.309
-----------------------------------------------------------------
snpStats documentation built on Nov. 8, 2020, 10:59 p.m.
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Description Usage Arguments Details Value Note Author(s) See Also Examples
Description
Under the assumption of Hardy-Weinberg equilibrium, a SNP genotype is
a binomial variate with two trials for an autosomal SNP or with one or
two trials (depending on sex) for a SNP on the X chromosome.
With each SNP in an input
"SnpMatrix" as dependent variable, this function fits a
logistic regression model. The Hardy-Weinberg
assumption can be relaxed by use of a "robust" option.
Usage
1 2 3 | snp.lhs.estimates(snp.data, base.formula, add.formula, subset, snp.subset,
data = sys.parent(), robust = FALSE, uncertain = FALSE,
control=glm.test.control())
|
Arguments
snp.data |
The SNP data, as an object of class
|
base.formula |
A |
add.formula |
A |
subset |
An array describing the subset of observations to be considered |
snp.subset |
An array describing the subset of SNPs to be considered. Default action is to test all SNPs. |
data |
The data frame in which |
robust |
If |
uncertain |
If |
control |
An object giving parameters for the IRLS algorithm
fitting of the base model and for the acceptable aliasing amongst
new terms to be tested. See |
Details
The model fitted is the union of the base.formula and
add.formula models, although parameter estimates (and their
variance-covariance matrix) are only
generated for the parameters of the latter.
The "robust" option causes a Huber-White "sandwich" estimate of the
variance-covariance matrix to be used in place of the usual inverse
second derivative matrix of the log-likelihood (which assumes
Hardy-Weinberg equilibrium).
If a data argument is supplied, the snp.data and
data objects are aligned by rowname. Otherwise all variables in
the model formulae are assumed to be stored in the same order as the
columns of the snp.data object.
Value
An object of class GlmEstimates
Note
A factor (or
several factors) may be included as arguments to the function
strata(...) in the base.formula. This fits all
interactions of the factors so included, but leads to faster
computation than fitting these in the normal way. Additionally, a
cluster(...) call may be included in the base model
formula. This identifies clusters of potentially correlated
observations (e.g. for members of the same family); in this case, an
appropriate robust estimate of the variance-covariance matrix of
parameter estimates is calculated. No more than one
strata() call may be used, and neither strata(...) or
cluster(...) calls may appear in the add.formula.
If uncertain genotypes (e.g. as a result of imputation) are used, the interpretation of the regression coefficients is questionable.
A known bug is that the function fails when no data argument is
supplied and the base model formula contains no variables
(~1). A work-round is to create a data frame to hold the
variables in the models and pass this as data=.
Author(s)
David Clayton dc208@cam.ac.uk
See Also
GlmEstimates-class, snp.lhs.tests
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 | data(testdata)
test1 <-
snp.lhs.estimates(Autosomes[,1:10], ~cc, ~region, data=subject.data)
test2 <-
snp.lhs.estimates(Autosomes[,1:10], ~strata(region), ~cc,
data=subject.data)
test3 <-
snp.lhs.estimates(Autosomes[,1:10], ~cc, ~region, data=subject.data, robust=TRUE)
test4 <-
snp.lhs.estimates(Autosomes[,1:10], ~strata(region), ~cc,
data=subject.data, robust=TRUE)
test5 <- snp.lhs.estimates(Autosomes[,1:10], ~region+sex, ~cc, data=subject.data, robust=TRUE)
print(test1)
print(test2)
print(test3)
print(test4)
print(test5)
|
Example output
Loading required package: survival
Loading required package: Matrix
Warning message:
In snp.lhs.estimates(Autosomes[, 1:10], ~cc, ~region, data = subject.data) :
Monomorphic SNP: 6
There were 13 warnings (use warnings() to see them)
Warning message:
In snp.lhs.estimates(Autosomes[, 1:10], ~cc, ~region, data = subject.data, :
Monomorphic SNP: 6
There were 13 warnings (use warnings() to see them)
Warning messages:
1: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
Variable(s) in the base model were aliased and have been dropped
2: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
Monomorphic SNP: 6
3: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
Failure to converge while fitting model for SNP 7
4: In snp.lhs.estimates(Autosomes[, 1:10], ~region + sex, ~cc, data = subject.data, :
No estimable parameters for test 7
Model Y-variable Parameter Estimate S.E. z-value
----------------------------------------------------------------------------
173760 173760 regionE & W Ridings 0.39201 7274.9 0.000
regionNorth Midlands 0.26996 6752.7 0.000
regionEastern 0.40499 6467.9 0.000
regionSouth-East -0.55677 9853.1 -0.000
regionSouthern 0.10589 8060.8 0.000
regionSouth-West 0.32633 6696.7 0.000
regionMidlands 0.50665 6824.2 0.000
regionLondon 0.11718 7453.4 0.000
regionNorth-West 16.621 6289.6 0.003
----------------------------------------------------------------------------
173761 173761 regionE & W Ridings -0.63382 0.60277 -1.052
regionNorth Midlands -0.69774 0.5563 -1.254
regionEastern -1.0848 0.534 -2.032
regionSouth-East -1.0587 0.76127 -1.391
regionSouthern -1.031 0.66732 -1.545
regionSouth-West -0.75518 0.5518 -1.369
regionMidlands -1.3374 0.57142 -2.340
regionLondon -1.1751 0.61997 -1.895
regionNorth-West -1.1277 0.54836 -2.057
----------------------------------------------------------------------------
173762 173762 regionE & W Ridings -0.63809 0.60296 -1.058
regionNorth Midlands -0.74302 0.55662 -1.335
regionEastern -1.0894 0.53417 -2.039
regionSouth-East -1.0531 0.76141 -1.383
regionSouthern -1.0327 0.66751 -1.547
regionSouth-West -0.72386 0.55241 -1.310
regionMidlands -1.3689 0.5735 -2.387
regionLondon -1.177 0.62014 -1.898
regionNorth-West -1.1317 0.54854 -2.063
----------------------------------------------------------------------------
173767 173767 regionE & W Ridings 0.20983 0.60937 0.344
regionNorth Midlands 0.06599 0.54673 0.121
regionEastern -0.14769 0.52102 -0.283
regionSouth-East 0.82081 0.83625 0.982
regionSouthern -0.62109 0.66515 -0.934
regionSouth-West -0.03987 0.54178 -0.074
regionMidlands -0.32735 0.55513 -0.590
regionLondon -0.78515 0.60617 -1.295
regionNorth-West 0.27804 0.53877 0.516
----------------------------------------------------------------------------
173769 173769 regionE & W Ridings 4.5881 7.5594 0.607
regionNorth Midlands -0.34476 1.0102 -0.341
regionEastern -0.91347 0.78971 -1.157
regionSouth-East -1.3439 1.2662 -1.061
regionSouthern 4.6814 10.011 0.468
regionSouth-West -0.60396 0.92292 -0.654
regionMidlands 4.5527 5.5668 0.818
regionLondon 4.6776 7.9665 0.587
----------------------------------------------------------------------------
173770 - No estimates available
----------------------------------------------------------------------------
173772 173772 regionE & W Ridings 0.51442 4684.7 0.000
regionNorth Midlands -15.513 3882.2 -0.004
regionEastern 0.51587 4029.5 0.000
regionSouth-East -0.47471 6572.8 -0.000
regionSouthern 0.13355 5040.4 0.000
regionSouth-West 0.45914 4198.5 0.000
regionMidlands 0.71392 4368.7 0.000
regionLondon 0.14812 4650.3 0.000
regionNorth-West 0.42546 4143.4 0.000
----------------------------------------------------------------------------
173774 173774 regionE & W Ridings -0.58188 0.85382 -0.681
regionNorth Midlands 0.13666 0.82751 0.165
regionEastern -0.31416 0.77684 -0.404
regionSouth-East 13.126 322.33 0.041
regionSouthern -0.0071896 0.97631 -0.007
regionSouth-West 0.08923 0.81648 0.109
regionMidlands -0.14467 0.82405 -0.176
regionLondon -0.13347 0.89696 -0.149
regionNorth-West -0.35987 0.79362 -0.453
----------------------------------------------------------------------------
173775 173775 regionE & W Ridings -0.66611 0.72745 -0.916
regionNorth Midlands -0.15507 0.62869 -0.247
regionEastern -0.37129 0.60146 -0.617
regionSouth-East -13.82 275.34 -0.050
regionSouthern -1.2929 0.93791 -1.378
regionSouth-West -0.57642 0.63565 -0.907
regionMidlands -0.50419 0.65354 -0.771
regionLondon -1.0341 0.78327 -1.320
regionNorth-West -0.33239 0.61948 -0.537
----------------------------------------------------------------------------
173776 173776 regionE & W Ridings 0.17345 0.61225 0.283
regionNorth Midlands 0.27629 0.45841 0.603
regionEastern 0.23642 0.37815 0.625
regionSouth-East -3.9329 3.9715 -0.990
regionSouthern 0.4868 0.69274 0.703
regionSouth-West 0.65519 0.41428 1.582
regionMidlands 0.076408 0.50534 0.151
regionLondon -0.45808 0.79158 -0.579
----------------------------------------------------------------------------
Model Y-variable Parameter Estimate S.E. z-value
-----------------------------------------------------------------
173760 - No estimates available
-----------------------------------------------------------------
173761 173761 cccase 0.17833 0.14735 1.210
-----------------------------------------------------------------
173762 173762 cccase 0.20456 0.1479 1.383
-----------------------------------------------------------------
173767 173767 cccase -0.12877 0.14882 -0.865
-----------------------------------------------------------------
173769 - No estimates available
-----------------------------------------------------------------
173770 - No estimates available
-----------------------------------------------------------------
173772 - No estimates available
-----------------------------------------------------------------
173774 - No estimates available
-----------------------------------------------------------------
173775 - No estimates available
-----------------------------------------------------------------
173776 - No estimates available
-----------------------------------------------------------------
Model Y-variable Parameter Estimate S.E. z-value
----------------------------------------------------------------------------
173760 173760 regionE & W Ridings 0.39201 1.0066 0.389
regionNorth Midlands 0.26996 1.0026 0.269
regionEastern 0.40499 1.001 0.405
regionSouth-East -0.55677 1.0111 -0.551
regionSouthern 0.10589 1.0095 0.105
regionSouth-West 0.32633 1.0024 0.326
regionMidlands 0.50665 1.0038 0.505
regionLondon 0.11718 1.006 0.116
regionNorth-West 16.621 1.0133 16.403
----------------------------------------------------------------------------
173761 173761 regionE & W Ridings -0.63382 0.63125 -1.004
regionNorth Midlands -0.69774 0.3544 -1.969
regionEastern -1.0848 0.4292 -2.528
regionSouth-East -1.0587 0.70062 -1.511
regionSouthern -1.031 0.77971 -1.322
regionSouth-West -0.75518 0.40639 -1.858
regionMidlands -1.3374 0.54592 -2.450
regionLondon -1.1751 0.37585 -3.127
regionNorth-West -1.1277 0.63813 -1.767
----------------------------------------------------------------------------
173762 173762 regionE & W Ridings -0.63809 0.62765 -1.017
regionNorth Midlands -0.74302 0.34879 -2.130
regionEastern -1.0894 0.42326 -2.574
regionSouth-East -1.0531 0.69589 -1.513
regionSouthern -1.0327 0.76743 -1.346
regionSouth-West -0.72386 0.40092 -1.805
regionMidlands -1.3689 0.5499 -2.489
regionLondon -1.177 0.37644 -3.127
regionNorth-West -1.1317 0.637 -1.777
----------------------------------------------------------------------------
173767 173767 regionE & W Ridings 0.20983 0.62144 0.338
regionNorth Midlands 0.06599 0.30591 0.216
regionEastern -0.14769 0.44357 -0.333
regionSouth-East 0.82081 0.64343 1.276
regionSouthern -0.62109 0.74606 -0.833
regionSouth-West -0.03987 0.46223 -0.086
regionMidlands -0.32735 0.61056 -0.536
regionLondon -0.78515 0.42325 -1.855
regionNorth-West 0.27804 0.48999 0.567
----------------------------------------------------------------------------
173769 173769 regionE & W Ridings 4.5881 NaN NaN
regionNorth Midlands -0.34476 0.77714 -0.444
regionEastern -0.91347 0.52824 -1.729
regionSouth-East -1.3439 1.081 -1.243
regionSouthern 4.6814 0.45549 10.278
regionSouth-West -0.60396 0.9026 -0.669
regionMidlands 4.5527 0.7114 6.400
regionLondon 4.6776 0.7111 6.578
----------------------------------------------------------------------------
173770 - No estimates available
----------------------------------------------------------------------------
173772 173772 regionE & W Ridings 0.51442 1.0059 0.511
regionNorth Midlands -15.513 1.0002 -15.511
regionEastern 0.51587 0.059151 8.721
regionSouth-East -0.47471 0.36987 -1.283
regionSouthern 0.13355 0.16895 0.790
regionSouth-West 0.45914 0.083373 5.507
regionMidlands 0.71392 0.095051 7.511
regionLondon 0.14812 0.14406 1.028
regionNorth-West 0.42546 0.22185 1.918
----------------------------------------------------------------------------
173774 173774 regionE & W Ridings -0.58188 0.56282 -1.034
regionNorth Midlands 0.13666 0.35524 0.385
regionEastern -0.31416 0.32302 -0.973
regionSouth-East 13.126 NaN NaN
regionSouthern -0.0071896 0.68956 -0.010
regionSouth-West 0.08923 0.4062 0.220
regionMidlands -0.14467 0.56319 -0.257
regionLondon -0.13347 0.60599 -0.220
regionNorth-West -0.35987 0.7519 -0.479
----------------------------------------------------------------------------
173775 173775 regionE & W Ridings -0.66611 0.58238 -1.144
regionNorth Midlands -0.15507 0.28296 -0.548
regionEastern -0.37129 0.30948 -1.200
regionSouth-East -13.82 66.939 -0.206
regionSouthern -1.2929 0.82212 -1.573
regionSouth-West -0.57642 0.35407 -1.628
regionMidlands -0.50419 0.45256 -1.114
regionLondon -1.0341 0.53978 -1.916
regionNorth-West -0.33239 0.69552 -0.478
----------------------------------------------------------------------------
173776 173776 regionE & W Ridings 0.17345 0.59392 0.292
regionNorth Midlands 0.27629 0.35001 0.789
regionEastern 0.23642 0.31759 0.744
regionSouth-East -3.9329 0.32562 -12.078
regionSouthern 0.4868 0.73901 0.659
regionSouth-West 0.65519 0.3645 1.798
regionMidlands 0.076408 0.46793 0.163
regionLondon -0.45808 0.76845 -0.596
----------------------------------------------------------------------------
Warning messages:
1: In sqrt(x$Var.beta[ii]) : NaNs produced
2: In sqrt(x$Var.beta[ii]) : NaNs produced
Model Y-variable Parameter Estimate S.E. z-value
-----------------------------------------------------------------
173760 - No estimates available
-----------------------------------------------------------------
173761 173761 cccase 0.17833 0.14592 1.222
-----------------------------------------------------------------
173762 173762 cccase 0.20456 0.14603 1.401
-----------------------------------------------------------------
173767 173767 cccase -0.12877 0.14544 -0.885
-----------------------------------------------------------------
173769 - No estimates available
-----------------------------------------------------------------
173770 - No estimates available
-----------------------------------------------------------------
173772 - No estimates available
-----------------------------------------------------------------
173774 - No estimates available
-----------------------------------------------------------------
173775 - No estimates available
-----------------------------------------------------------------
173776 - No estimates available
-----------------------------------------------------------------
Model Y-variable Parameter Estimate S.E. z-value
-----------------------------------------------------------------
173760 173760 cccase -13.467 1.0027 -13.432
-----------------------------------------------------------------
173761 173761 cccase 0.18763 0.14553 1.289
-----------------------------------------------------------------
173762 173762 cccase 0.21178 0.14568 1.454
-----------------------------------------------------------------
173767 173767 cccase -0.1287 0.14571 -0.883
-----------------------------------------------------------------
173769 173769 cccase 0.8949 0.53343 1.678
-----------------------------------------------------------------
173770 - No estimates available
-----------------------------------------------------------------
173772 - No estimates available
-----------------------------------------------------------------
173774 173774 cccase 0.17924 0.2148 0.834
-----------------------------------------------------------------
173775 173775 cccase -0.188 0.19069 -0.986
-----------------------------------------------------------------
173776 173776 cccase 0.071589 0.23134 0.309
-----------------------------------------------------------------
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