R version 3.6.3 (2020-02-29) -- "Holding the Windsock"
Copyright (C) 2020 The R Foundation for Statistical Computing
Platform: x86_64-w64-mingw32/x64 (64-bit)
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Type 'contributors()' for more information and
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> ############################################################################
> # MLwiN User Manual
> #
> # 11 Fitting an Ordered Category Response Model . . . . . . . . . . . . 161
> #
> # Rasbash, J., Steele, F., Browne, W. J. and Goldstein, H. (2012).
> # A User's Guide to MLwiN, v2.26. Centre for Multilevel Modelling,
> # University of Bristol.
> ############################################################################
> # R script to replicate all analyses using R2MLwiN
> #
> # Zhang, Z., Charlton, C., Parker, R, Leckie, G., and Browne, W.J.
> # Centre for Multilevel Modelling, 2012
> # http://www.bristol.ac.uk/cmm/software/R2MLwiN/
> ############################################################################
>
> library(R2MLwiN)
R2MLwiN: A package to run models implemented in MLwiN from R
Copyright 2013-2017 Zhengzheng Zhang, Christopher M. J. Charlton, Richard M. A. Parker, William J. Browne and George Leckie
Support provided by the Economic and Social Research Council (ESRC)
(Grants RES-149-25-1084, RES-576-25-0032 and ES/K007246/1)
To cite R2MLwiN in publications use:
Zhengzheng Zhang, Richard M. A. Parker, Christopher M. J. Charlton,
George Leckie, William J. Browne (2016). R2MLwiN: A Package to Run
MLwiN from within R. Journal of Statistical Software, 72(10), 1-43.
doi:10.18637/jss.v072.i10
A BibTeX entry for LaTeX users is
@Article{,
title = {{R2MLwiN}: A Package to Run {MLwiN} from within {R}},
author = {Zhengzheng Zhang and Richard M. A. Parker and Christopher M. J. Charlton and George Leckie and William J. Browne},
journal = {Journal of Statistical Software},
year = {2016},
volume = {72},
number = {10},
pages = {1--43},
doi = {10.18637/jss.v072.i10},
}
The MLwiN_path option is currently set to C:/Program Files/MLwiN v3.05/
To change this use: options(MLwiN_path="")
> # MLwiN folder
> mlwin <- getOption("MLwiN_path")
> while (!file.access(mlwin, mode = 1) == 0) {
+ cat("Please specify the root MLwiN folder or the full path to the MLwiN executable:\n")
+ mlwin <- scan(what = character(0), sep = "\n")
+ mlwin <- gsub("\\", "/", mlwin, fixed = TRUE)
+ }
> options(MLwiN_path = mlwin)
>
>
> # 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . .161
>
> data(alevchem, package = "R2MLwiN")
> summary(alevchem)
lea estab pupil a_point gcse_tot
Min. :203.0 Min. :4001 Min. : 1650 F:429 Min. :22.00
1st Qu.:802.0 1st Qu.:4259 1st Qu.: 66172 E:289 1st Qu.:47.00
Median :903.0 Median :5423 Median :112453 D:311 Median :54.00
Mean :777.1 Mean :5974 Mean :106870 C:367 Mean :54.42
3rd Qu.:919.0 3rd Qu.:8001 3rd Qu.:145998 B:407 3rd Qu.:62.00
Max. :938.0 Max. :8603 Max. :194909 A:363 Max. :92.00
gcse_no cons gender
Min. : 5.000 Min. :1 male :1223
1st Qu.: 8.000 1st Qu.:1 female: 943
Median : 9.000 Median :1
Mean : 8.808 Mean :1
3rd Qu.: 9.000 3rd Qu.:1
Max. :12.000 Max. :1
>
> # 11.2 An analysis using the traditional approach . . . . . . . . . . . .162
>
> if (!require(lattice)) {
+ warning("package lattice required to run this example")
+ } else {
+ histogram(as.integer(alevchem$a_point))
+ }
Loading required package: lattice
>
> a_point_rank <- rank(alevchem$a_point)
> a_point_uniform <- (a_point_rank - 0.5)/length(a_point_rank)
>
> alevchem$alevelnormal <- qnorm(a_point_uniform)
>
> (mymodel1 <- runMLwiN(alevelnormal ~ 1 + (1 | pupil), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence achieved
TOLE 2
MAXI 20
NEXT
iteration 2
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Normal)
Estimation algorithm: IGLS Elapsed time : 0.03s
Number of obs: 2166 (from total 2166) The model converged after 3 iterations.
Log likelihood: -2816.9
Deviance statistic: 5633.7
---------------------------------------------------------------------------------------------------
The model formula:
alevelnormal ~ 1 + (1 | pupil)
Level 1: pupil
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept 0.00279 0.01909 0.15 0.8838 -0.03462 0.04020
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the pupil level:
Coef. Std. Err.
var_Intercept 0.78907 0.02398
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> alevchem$gcseav <- alevchem$gcse_tot/alevchem$gcse_no
>
> gcseav_rank <- rank(alevchem$gcseav)
> gcseav_uniform <- (gcseav_rank - 0.5)/length(gcseav_rank)
>
> alevchem$gcseavnormal <- qnorm(gcseav_uniform)
>
> (mymodel2 <- runMLwiN(alevelnormal ~ 1 + gender + gcseavnormal + I(gcseavnormal^2) + I(gcseavnormal^3) + (1 | pupil),
+ data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence achieved
TOLE 2
MAXI 20
NEXT
iteration 2
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Normal)
Estimation algorithm: IGLS Elapsed time : 0.05s
Number of obs: 2166 (from total 2166) The model converged after 3 iterations.
Log likelihood: -1984.4
Deviance statistic: 3968.9
---------------------------------------------------------------------------------------------------
The model formula:
alevelnormal ~ 1 + gender + gcseavnormal + I(gcseavnormal^2) +
I(gcseavnormal^3) + (1 | pupil)
Level 1: pupil
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept 0.07748 0.01979 3.92 9.01e-05 *** 0.03870 0.11626
genderfemale -0.24626 0.02665 -9.24 2.47e-20 *** -0.29849 -0.19402
gcseavnormal 0.78683 0.02126 37.01 7.168e-300 *** 0.74516 0.82849
I(gcseavnormal^2) 0.03250 0.00928 3.50 0.0004627 *** 0.01431 0.05069
I(gcseavnormal^3) -0.04562 0.00558 -8.17 3e-16 *** -0.05656 -0.03468
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the pupil level:
Coef. Std. Err.
var_Intercept 0.36585 0.01112
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> (mymodel3 <- runMLwiN(alevelnormal ~ 1 + gender + gcseavnormal + I(gcseavnormal^2) + (1 | pupil), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence achieved
TOLE 2
MAXI 20
NEXT
iteration 2
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Normal)
Estimation algorithm: IGLS Elapsed time : 0.05s
Number of obs: 2166 (from total 2166) The model converged after 3 iterations.
Log likelihood: -2017.3
Deviance statistic: 4034.7
---------------------------------------------------------------------------------------------------
The model formula:
alevelnormal ~ 1 + gender + gcseavnormal + I(gcseavnormal^2) +
(1 | pupil)
Level 1: pupil
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept 0.07142 0.02008 3.56 0.0003744 *** 0.03207 0.11076
genderfemale -0.23551 0.02703 -8.71 2.93e-18 *** -0.28849 -0.18254
gcseavnormal 0.65070 0.01341 48.51 0 *** 0.62441 0.67700
I(gcseavnormal^2) 0.03407 0.00942 3.62 0.0002985 *** 0.01561 0.05254
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the pupil level:
Coef. Std. Err.
var_Intercept 0.37713 0.01146
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> (mymodel4 <- runMLwiN(alevelnormal ~ 1 + gender + (1 | pupil), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence achieved
TOLE 2
MAXI 20
NEXT
iteration 2
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Normal)
Estimation algorithm: IGLS Elapsed time : 0.04s
Number of obs: 2166 (from total 2166) The model converged after 3 iterations.
Log likelihood: -2816.8
Deviance statistic: 5633.7
---------------------------------------------------------------------------------------------------
The model formula:
alevelnormal ~ 1 + gender + (1 | pupil)
Level 1: pupil
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept 0.00647 0.02540 0.25 0.7989 -0.04331 0.05625
genderfemale -0.00846 0.03850 -0.22 0.8262 -0.08391 0.06699
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the pupil level:
Coef. Std. Err.
var_Intercept 0.78905 0.02398
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> (mymodel5 <- runMLwiN(gcseavnormal ~ 1 + gender + (1 | pupil), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence achieved
TOLE 2
MAXI 20
NEXT
iteration 2
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Normal)
Estimation algorithm: IGLS Elapsed time : 0.03s
Number of obs: 2166 (from total 2166) The model converged after 3 iterations.
Log likelihood: -3037.8
Deviance statistic: 6075.7
---------------------------------------------------------------------------------------------------
The model formula:
gcseavnormal ~ 1 + gender + (1 | pupil)
Level 1: pupil
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept -0.15269 0.02813 -5.43 5.695e-08 *** -0.20782 -0.09756
genderfemale 0.35037 0.04263 8.22 2.056e-16 *** 0.26682 0.43393
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the pupil level:
Coef. Std. Err.
var_Intercept 0.96767 0.02940
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> # 11.3 A single-level model with an ordered categorical response variable 166
>
> (mymodel6 <- runMLwiN(logit(a_point, cons, 6) ~ 1, D = "Ordered Multinomial", data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
Estimation algorithm: IGLS MQL1 Elapsed time : 0.31s
Number of obs: 2166 (from total 2166) The model converged after 4 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1
Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -1.39844 0.05377 -26.01 4.274e-149 *** -1.50383 -1.29304
Intercept_E -0.70147 0.04564 -15.37 2.671e-53 *** -0.79093 -0.61201
Intercept_D -0.09981 0.04303 -2.32 0.02036 * -0.18414 -0.01547
Intercept_C 0.59498 0.04489 13.25 4.258e-40 *** 0.50699 0.68296
Intercept_B 1.60280 0.05743 27.91 2.075e-171 *** 1.49024 1.71535
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> # 11.4 A two-level model . . . . . . . . . . . . . . . . . . . . . . . . 171
>
> # Note: Establishment codes on their own do not uniquely identify schools. Schools are instead uniquely
> # identified by LEA code, establishment ID combination. Thus, here we generated a unique school ID.
>
> alevchem$school <- as.numeric(factor(paste0(alevchem$lea, alevchem$estab)))
>
> (mymodel7 <- runMLwiN(logit(a_point, cons, 6) ~ 1 + (1[1:5] | school), D = "Ordered Multinomial", data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
N min mean max N_complete min_complete mean_complete max_complete
school 220 1 9.845455 94 220 1 9.845455 94
Estimation algorithm: IGLS MQL1 Elapsed time : 0.31s
Number of obs: 2166 (from total 2166) The model converged after 5 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1 + (1[1:5] | school)
Level 2: school Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -1.09382 0.08266 -13.23 5.646e-40 *** -1.25582 -0.93181
Intercept_E -0.41014 0.07938 -5.17 2.385e-07 *** -0.56573 -0.25455
Intercept_D 0.17955 0.07898 2.27 0.02301 * 0.02475 0.33435
Intercept_C 0.86226 0.08118 10.62 2.357e-26 *** 0.70316 1.02136
Intercept_B 1.85928 0.09128 20.37 3.173e-92 *** 1.68037 2.03819
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the school level:
Coef. Std. Err.
var_Intercept_12345 0.73827 0.11549
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> (mymodel8 <- runMLwiN(logit(a_point, cons, 6) ~ 1 + (1[1:5] | school), D = "Ordered Multinomial", estoptions = list(nonlinear = c(N = 1,
+ M = 2)), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
N min mean max N_complete min_complete mean_complete max_complete
school 220 1 9.845455 94 220 1 9.845455 94
Estimation algorithm: IGLS PQL2 Elapsed time : 0.7s
Number of obs: 2166 (from total 2166) The model converged after 8 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1 + (1[1:5] | school)
Level 2: school Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -1.37227 0.10317 -13.30 2.279e-40 *** -1.57448 -1.17007
Intercept_E -0.48099 0.09828 -4.89 9.88e-07 *** -0.67362 -0.28836
Intercept_D 0.29402 0.09767 3.01 0.002609 ** 0.10259 0.48545
Intercept_C 1.17129 0.10013 11.70 1.309e-31 *** 0.97504 1.36755
Intercept_B 2.39154 0.10993 21.76 6.109e-105 *** 2.17609 2.60700
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the school level:
Coef. Std. Err.
var_Intercept_12345 1.32989 0.17842
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> (mymodel9 <- runMLwiN(logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + (1[1:5] | school), D = "Ordered Multinomial",
+ estoptions = list(nonlinear = c(N = 1, M = 2)), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9
iteration 10
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
N min mean max N_complete min_complete mean_complete max_complete
school 220 1 9.845455 94 220 1 9.845455 94
Estimation algorithm: IGLS PQL2 Elapsed time : 1.01s
Number of obs: 2166 (from total 2166) The model converged after 11 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + (1[1:5] | school)
Level 2: school Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -2.29255 0.10028 -22.86 1.148e-115 *** -2.48910 -2.09600
Intercept_E -1.09169 0.08956 -12.19 3.556e-34 *** -1.26723 -0.91615
Intercept_D -0.01945 0.08639 -0.23 0.8219 -0.18877 0.14987
Intercept_C 1.21316 0.08994 13.49 1.826e-41 *** 1.03688 1.38944
Intercept_B 2.94351 0.10771 27.33 1.943e-164 *** 2.73241 3.15462
gcseavnormal_12345 -2.03916 0.06507 -31.34 1.493e-215 *** -2.16670 -1.91162
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the school level:
Coef. Std. Err.
var_Intercept_12345 0.71686 0.11787
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> (mymodel10 <- runMLwiN(logit(a_point, cons, 6) ~ 1 + gcseavnormal + (1[1:5] | school), D = "Ordered Multinomial",
+ estoptions = list(nonlinear = c(N = 1, M = 2)), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
V has gone -ve definite for block 0 - reconstruction used
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V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 137 - reconstruction used
V has gone -ve definite for block 139 - reconstruction used
V has gone -ve definite for block 145 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 162 - reconstruction used
V has gone -ve definite for block 168 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 184 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 200 - reconstruction used
V has gone -ve definite for block 207 - reconstruction used
V has gone -ve definite for block 219 - reconstruction used
V has gone -ve definite for block 0 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 14 - reconstruction used
V has gone -ve definite for block 17 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 31 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 35 - reconstruction used
V has gone -ve definite for block 36 - reconstruction used
V has gone -ve definite for block 40 - reconstruction used
V has gone -ve definite for block 44 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 50 - reconstruction used
V has gone -ve definite for block 53 - reconstruction used
V has gone -ve definite for block 65 - reconstruction used
V has gone -ve definite for block 69 - reconstruction used
V has gone -ve definite for block 72 - reconstruction used
V has gone -ve definite for block 73 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 99 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 137 - reconstruction used
V has gone -ve definite for block 139 - reconstruction used
V has gone -ve definite for block 145 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 162 - reconstruction used
V has gone -ve definite for block 168 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 184 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 200 - reconstruction used
V has gone -ve definite for block 207 - reconstruction used
V has gone -ve definite for block 219 - reconstruction used
V has gone -ve definite for block 0 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 14 - reconstruction used
V has gone -ve definite for block 17 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 31 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 35 - reconstruction used
V has gone -ve definite for block 36 - reconstruction used
V has gone -ve definite for block 40 - reconstruction used
V has gone -ve definite for block 44 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 50 - reconstruction used
V has gone -ve definite for block 53 - reconstruction used
V has gone -ve definite for block 65 - reconstruction used
V has gone -ve definite for block 69 - reconstruction used
V has gone -ve definite for block 72 - reconstruction used
V has gone -ve definite for block 73 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 99 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 137 - reconstruction used
V has gone -ve definite for block 139 - reconstruction used
V has gone -ve definite for block 145 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 162 - reconstruction used
V has gone -ve definite for block 168 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 184 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 200 - reconstruction used
V has gone -ve definite for block 207 - reconstruction used
V has gone -ve definite for block 219 - reconstruction used
V has gone -ve definite for block 0 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 14 - reconstruction used
V has gone -ve definite for block 17 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 31 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 35 - reconstruction used
V has gone -ve definite for block 36 - reconstruction used
V has gone -ve definite for block 40 - reconstruction used
V has gone -ve definite for block 44 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 50 - reconstruction used
V has gone -ve definite for block 53 - reconstruction used
V has gone -ve definite for block 65 - reconstruction used
V has gone -ve definite for block 69 - reconstruction used
V has gone -ve definite for block 72 - reconstruction used
V has gone -ve definite for block 73 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 99 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 137 - reconstruction used
V has gone -ve definite for block 139 - reconstruction used
V has gone -ve definite for block 145 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 162 - reconstruction used
V has gone -ve definite for block 168 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 184 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 200 - reconstruction used
V has gone -ve definite for block 207 - reconstruction used
V has gone -ve definite for block 219 - reconstruction used
Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
V has gone -ve definite for block 0 - reconstruction used
V has gone -ve definite for block 8 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 14 - reconstruction used
V has gone -ve definite for block 17 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 24 - reconstruction used
V has gone -ve definite for block 31 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 35 - reconstruction used
V has gone -ve definite for block 36 - reconstruction used
V has gone -ve definite for block 40 - reconstruction used
V has gone -ve definite for block 44 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 50 - reconstruction used
V has gone -ve definite for block 53 - reconstruction used
V has gone -ve definite for block 65 - reconstruction used
V has gone -ve definite for block 69 - reconstruction used
V has gone -ve definite for block 70 - reconstruction used
V has gone -ve definite for block 72 - reconstruction used
V has gone -ve definite for block 73 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 99 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 133 - reconstruction used
V has gone -ve definite for block 137 - reconstruction used
V has gone -ve definite for block 138 - reconstruction used
V has gone -ve definite for block 138 - reconstruction used
V has gone -ve definite for block 139 - reconstruction used
V has gone -ve definite for block 145 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 156 - reconstruction used
V has gone -ve definite for block 162 - reconstruction used
V has gone -ve definite for block 166 - reconstruction used
V has gone -ve definite for block 168 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 181 - reconstruction used
V has gone -ve definite for block 184 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 189 - reconstruction used
V has gone -ve definite for block 199 - reconstruction used
V has gone -ve definite for block 200 - reconstruction used
V has gone -ve definite for block 207 - reconstruction used
V has gone -ve definite for block 218 - reconstruction used
V has gone -ve definite for block 219 - reconstruction used
V has gone -ve definite for block 0 - reconstruction used
V has gone -ve definite for block 8 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 14 - reconstruction used
V has gone -ve definite for block 17 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 24 - reconstruction used
V has gone -ve definite for block 31 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 35 - reconstruction used
V has gone -ve definite for block 36 - reconstruction used
V has gone -ve definite for block 40 - reconstruction used
V has gone -ve definite for block 44 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 50 - reconstruction used
V has gone -ve definite for block 53 - reconstruction used
V has gone -ve definite for block 65 - reconstruction used
V has gone -ve definite for block 69 - reconstruction used
V has gone -ve definite for block 70 - reconstruction used
V has gone -ve definite for block 72 - reconstruction used
V has gone -ve definite for block 73 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 99 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 133 - reconstruction used
V has gone -ve definite for block 137 - reconstruction used
V has gone -ve definite for block 138 - reconstruction used
V has gone -ve definite for block 138 - reconstruction used
V has gone -ve definite for block 139 - reconstruction used
V has gone -ve definite for block 145 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 156 - reconstruction used
V has gone -ve definite for block 162 - reconstruction used
V has gone -ve definite for block 166 - reconstruction used
V has gone -ve definite for block 168 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 181 - reconstruction used
V has gone -ve definite for block 184 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 189 - reconstruction used
V has gone -ve definite for block 199 - reconstruction used
V has gone -ve definite for block 200 - reconstruction used
V has gone -ve definite for block 207 - reconstruction used
V has gone -ve definite for block 218 - reconstruction used
V has gone -ve definite for block 219 - reconstruction used
V has gone -ve definite for block 0 - reconstruction used
V has gone -ve definite for block 8 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 14 - reconstruction used
V has gone -ve definite for block 17 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 24 - reconstruction used
V has gone -ve definite for block 31 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 35 - reconstruction used
V has gone -ve definite for block 36 - reconstruction used
V has gone -ve definite for block 40 - reconstruction used
V has gone -ve definite for block 44 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 50 - reconstruction used
V has gone -ve definite for block 53 - reconstruction used
V has gone -ve definite for block 65 - reconstruction used
V has gone -ve definite for block 69 - reconstruction used
V has gone -ve definite for block 70 - reconstruction used
V has gone -ve definite for block 72 - reconstruction used
V has gone -ve definite for block 73 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 99 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 126 - reconstruction used
V has gone -ve definite for block 133 - reconstruction used
V has gone -ve definite for block 137 - reconstruction used
V has gone -ve definite for block 138 - reconstruction used
V has gone -ve definite for block 138 - reconstruction used
V has gone -ve definite for block 139 - reconstruction used
V has gone -ve definite for block 145 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 152 - reconstruction used
V has gone -ve definite for block 156 - reconstruction used
V has gone -ve definite for block 162 - reconstruction used
V has gone -ve definite for block 166 - reconstruction used
V has gone -ve definite for block 168 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 175 - reconstruction used
V has gone -ve definite for block 181 - reconstruction used
V has gone -ve definite for block 184 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 187 - reconstruction used
V has gone -ve definite for block 189 - reconstruction used
V has gone -ve definite for block 199 - reconstruction used
V has gone -ve definite for block 200 - reconstruction used
V has gone -ve definite for block 207 - reconstruction used
V has gone -ve definite for block 218 - reconstruction used
V has gone -ve definite for block 219 - reconstruction used
V has gone -ve definite for block 0 - reconstruction used
V has gone -ve definite for block 8 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 9 - reconstruction used
V has gone -ve definite for block 14 - reconstruction used
V has gone -ve definite for block 17 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 20 - reconstruction used
V has gone -ve definite for block 24 - reconstruction used
V has gone -ve definite for block 31 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 34 - reconstruction used
V has gone -ve definite for block 35 - reconstruction used
V has gone -ve definite for block 36 - reconstruction used
V has gone -ve definite for block 40 - reconstruction used
V has gone -ve definite for block 44 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 45 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 47 - reconstruction used
V has gone -ve definite for block 50 - reconstruction used
V has gone -ve definite for block 53 - reconstruction used
V has gone -ve definite for block 65 - reconstruction used
V has gone -ve definite for block 69 - reconstruction used
V has gone -ve definite for block 70 - reconstruction used
V has gone -ve definite for block 72 - reconstruction used
V has gone -ve definite for block 73 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 78 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 80 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 84 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 87 - reconstruction used
V has gone -ve definite for block 99 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 101 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 105 - reconstruction used
V has gone -ve definite for block 107 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 111 - reconstruction used
V has gone -ve definite for block 114 - reconstruction used
V has gone -ve definite for block 118 - reconstruction used
V has gone -ve definite for block 122 - reconstruction used
V has gone -ve definite for block 123 - reconstruction used
V has gone -ve definite for block 124 - reconstruction used
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iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9
iteration 10
iteration 11
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
N min mean max N_complete min_complete mean_complete max_complete
school 220 1 9.845455 94 220 1 9.845455 94
Estimation algorithm: IGLS PQL2 Elapsed time : 1.33s
Number of obs: 2166 (from total 2166) The model converged after 12 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1 + gcseavnormal + (1[1:5] | school)
Level 2: school Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -2.23672 0.11609 -19.27 1.007e-82 *** -2.46425 -2.00919
Intercept_E -1.05371 0.09340 -11.28 1.62e-29 *** -1.23677 -0.87064
Intercept_D 0.01038 0.08695 0.12 0.9049 -0.16003 0.18080
Intercept_C 1.25125 0.09404 13.31 2.146e-40 *** 1.06694 1.43556
Intercept_B 3.20018 0.14390 22.24 1.45e-109 *** 2.91813 3.48222
gcseavnormal_F -1.94226 0.10273 -18.91 1.011e-79 *** -2.14361 -1.74092
gcseavnormal_E -1.94537 0.09040 -21.52 1.015e-102 *** -2.12255 -1.76819
gcseavnormal_D -1.92940 0.08652 -22.30 3.692e-110 *** -2.09898 -1.75983
gcseavnormal_C -2.02321 0.09188 -22.02 1.891e-107 *** -2.20330 -1.84312
gcseavnormal_B -2.34177 0.12349 -18.96 3.432e-80 *** -2.58380 -2.09973
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the school level:
Coef. Std. Err.
var_Intercept_12345 0.70920 0.11707
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> (mymodel11 <- runMLwiN(logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + gender[1:5] + I(gcseavnormal^2)[1:5] + (1[1:5] | school),
+ D = "Ordered Multinomial", estoptions = list(nonlinear = c(N = 1, M = 2)), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence not achieved
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
N min mean max N_complete min_complete mean_complete max_complete
school 220 1 9.845455 94 220 1 9.845455 94
Estimation algorithm: IGLS PQL2 Elapsed time : 1.03s
Number of obs: 2166 (from total 2166) The model converged after 10 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + gender[1:5] +
I(gcseavnormal^2)[1:5] + (1[1:5] | school)
Level 2: school Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -2.49152 0.11563 -21.55 5.647e-103 *** -2.71815 -2.26489
Intercept_E -1.30849 0.10357 -12.63 1.372e-36 *** -1.51148 -1.10550
Intercept_D -0.23061 0.09920 -2.32 0.02008 * -0.42503 -0.03619
Intercept_C 1.03769 0.10241 10.13 3.969e-24 *** 0.83696 1.23842
Intercept_B 2.87813 0.12466 23.09 6.243e-118 *** 2.63379 3.12247
gcseavnormal_12345 -2.18918 0.06891 -31.77 1.73e-221 *** -2.32424 -2.05412
genderfemale_12345 0.74277 0.09417 7.89 3.084e-15 *** 0.55820 0.92735
I(gcseavnormal^2)_12345 -0.23764 0.04455 -5.33 9.596e-08 *** -0.32496 -0.15032
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the school level:
Coef. Std. Err.
var_Intercept_12345 0.66699 0.11193
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
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>
> (mymodel12 <- runMLwiN(logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + gender[1:5] + I(gcseavnormal^2)[1:5] + (1[1:5] + gcseavnormal[1:5] | school),
+ D = "Ordered Multinomial", estoptions = list(nonlinear = c(N = 1, M = 2), startval = list(FP.b = mymodel11@FP,
+ FP.v = mymodel11@FP.cov, RP.b = mymodel11@RP, RP.v = mymodel11@RP.cov)), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence not achieved
JOIN -2.49151925200167 -1.30849192175647 -0.230609423177079 1.03768941461926 2.87813064357528 -2.1891800057869 0.742772829383256 -0.237639010072097 '_FP_b'
JOIN 0.0133707010561911 0.0100698577745065 0.0107265952217868 0.00839131118415635 0.0087341721539345 0.00983985017345386 0.0071852995861948 0.00748383076869353 0.00827932240845671 0.0104884834999581 0.00630409197455969 0.00669449341409377 0.0075224552317277 0.00937568467156292 0.0155411415776731 0.00297305854607278 0.00207500667194473 0.00111091252755147 -0.000169283447524993 -0.00211037259961808 0.0047484619179859 -0.00483199686410059 -0.00447884434570599 -0.00413101773913304 -0.00370753196355913 -0.00312771228775965 -0.00186411948860604 0.00886827297617633 -0.00146161062352187 -0.00116883010273691 -0.0011170391665958 -0.001365584856497 -0.00225034379756666 0.000572375824357903 -5.27967327380932e-05 0.00198469620694617 '_FP_v'
JOIN 0 0 0.66698959266933 1 '_RP_b'
JOIN 0 0 0 0 0 0.0125276541154032 0 0 0 0 '_RP_v'
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9
iteration 10
iteration 11
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
N min mean max N_complete min_complete mean_complete max_complete
school 220 1 9.845455 94 220 1 9.845455 94
Estimation algorithm: IGLS PQL2 Elapsed time : 1.52s
Number of obs: 2166 (from total 2166) The model converged after 12 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + gender[1:5] +
I(gcseavnormal^2)[1:5] + (1[1:5] + gcseavnormal[1:5] | school)
Level 2: school Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -2.53796 0.11735 -21.63 1e-103 *** -2.76796 -2.30795
Intercept_E -1.32396 0.10459 -12.66 9.969e-37 *** -1.52894 -1.11897
Intercept_D -0.22828 0.10002 -2.28 0.02248 * -0.42432 -0.03224
Intercept_C 1.05673 0.10336 10.22 1.55e-24 *** 0.85415 1.25931
Intercept_B 2.93800 0.12704 23.13 2.512e-118 *** 2.68901 3.18700
gcseavnormal_12345 -2.25166 0.08253 -27.28 7.016e-164 *** -2.41342 -2.08989
genderfemale_12345 0.74573 0.09535 7.82 5.235e-15 *** 0.55885 0.93261
I(gcseavnormal^2)_12345 -0.22513 0.04912 -4.58 4.578e-06 *** -0.32140 -0.12886
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the school level:
Coef. Std. Err.
var_gcseavnormal_12345 0.21431 0.07950
cov_gcseavnormal_12345_Intercept_12345 0.05428 0.06761
var_Intercept_12345 0.65859 0.11630
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
> invlogit <- function(x) exp(x)/(1 + exp(x))
>
> invlogit(mymodel12@FP["FP_Intercept_F"])
FP_Intercept_F
0.07323982
>
> invlogit(mymodel12@FP["FP_Intercept_E"])
FP_Intercept_E
0.2101608
>
> invlogit(mymodel12@FP["FP_Intercept_D"])
FP_Intercept_D
0.4431776
>
> invlogit(mymodel12@FP["FP_Intercept_C"])
FP_Intercept_C
0.7420651
>
> invlogit(mymodel12@FP["FP_Intercept_B"])
FP_Intercept_B
0.9496935
>
> invlogit(mymodel12@FP["FP_Intercept_F"] + mymodel12@FP["FP_gcseavnormal_12345"])
FP_Intercept_F
0.008247098
>
> invlogit(mymodel12@FP["FP_Intercept_E"] + mymodel12@FP["FP_gcseavnormal_12345"])
FP_Intercept_E
0.02723569
>
> invlogit(mymodel12@FP["FP_Intercept_D"] + mymodel12@FP["FP_gcseavnormal_12345"])
FP_Intercept_D
0.077277
>
> invlogit(mymodel12@FP["FP_Intercept_C"] + mymodel12@FP["FP_gcseavnormal_12345"])
FP_Intercept_C
0.2323789
>
> invlogit(mymodel12@FP["FP_Intercept_B"] + mymodel12@FP["FP_gcseavnormal_12345"])
FP_Intercept_B
0.6651539
>
> (mymodel13 <- runMLwiN(logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + gender[1:5] + I(gcseavnormal^2)[1:5] + (1[1:5] + gcseavnormal[1:5] + gender[1:5] | school),
+ D = "Ordered Multinomial", estoptions = list(nonlinear = c(N = 1, M = 2), startval = list(FP.b = mymodel12@FP,
+ FP.v = mymodel12@FP.cov, RP.b = mymodel12@RP, RP.v = mymodel12@RP.cov)), data = alevchem))
/nogui option ignored
ECHO 0
Echoing is ON
BATC 1
Batch mode is ON
MAXI 2
STAR
iteration 0
iteration 1
Convergence not achieved
JOIN -2.53795553500274 -1.32395655329939 -0.228275659802407 1.0567297585535 2.93800450506876 -2.25165706108741 0.745730259422644 -0.225128517155073 '_FP_b'
JOIN 0.0137712684238937 0.010274934809184 0.0109381695657136 0.00852223560994445 0.00887282091108815 0.0100045125829718 0.00725957561565565 0.00757891198662552 0.00840195665731901 0.0106830074697652 0.00632080740084703 0.00674936413029105 0.00762344900804181 0.009565390378012 0.0161394544301811 0.00359869129595539 0.0025954990334822 0.00156177324557199 0.00021611593535914 -0.00185784350270411 0.00681185303114811 -0.00499637635269901 -0.00462058811561032 -0.00424841163226089 -0.00379194525260463 -0.00317194544142362 -0.0019549248668753 0.00909126095985585 -0.00150715941698443 -0.00119453551650622 -0.00113534561851497 -0.00138837349729907 -0.00234928348848111 0.000758478349031761 -6.11669980052443e-05 0.00241276891133626 '_FP_v'
JOIN 0.21431231793329 0 0 0.0542846980620451 0 0.658585070354844 1 '_RP_b'
JOIN 0.00632099137726559 0 0 0 0 0 0.000908897126394028 0 0 0.00457114733694438 0 0 0 0 0 -0.000676925584474623 0 0 0.0013046242517152 0 0.0135245379670239 0 0 0 0 0 0 0 '_RP_v'
TOLE 2
MAXI 20
NEXT
iteration 2
iteration 3
iteration 4
iteration 5
iteration 6
iteration 7
iteration 8
iteration 9
iteration 10
iteration 11
iteration 12
iteration 13
iteration 14
iteration 15
Convergence achieved
ECHO 0
Execution completed
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
MLwiN (version: 3.05) multilevel model (Multinomial)
N min mean max N_complete min_complete mean_complete max_complete
school 220 1 9.845455 94 220 1 9.845455 94
Estimation algorithm: IGLS PQL2 Elapsed time : 2.55s
Number of obs: 2166 (from total 2166) The model converged after 16 iterations.
Log likelihood: NA
Deviance statistic: NA
---------------------------------------------------------------------------------------------------
The model formula:
logit(a_point, cons, 6) ~ 1 + gcseavnormal[1:5] + gender[1:5] +
I(gcseavnormal^2)[1:5] + (1[1:5] + gcseavnormal[1:5] + gender[1:5] |
school)
Level 2: school Level 1: l1id
---------------------------------------------------------------------------------------------------
The fixed part estimates:
Coef. Std. Err. z Pr(>|z|) [95% Conf. Interval]
Intercept_F -2.59698 0.11997 -21.65 6.406e-104 *** -2.83211 -2.36185
Intercept_E -1.35979 0.10665 -12.75 3.101e-37 *** -1.56881 -1.15076
Intercept_D -0.24515 0.10183 -2.41 0.01607 * -0.44473 -0.04556
Intercept_C 1.05910 0.10518 10.07 7.564e-24 *** 0.85294 1.26525
Intercept_B 2.96077 0.12936 22.89 6.111e-116 *** 2.70723 3.21431
gcseavnormal_12345 -2.28492 0.08205 -27.85 1.092e-170 *** -2.44573 -2.12411
genderfemale_12345 0.78262 0.11088 7.06 1.687e-12 *** 0.56530 0.99994
I(gcseavnormal^2)_12345 -0.22776 0.04930 -4.62 3.848e-06 *** -0.32439 -0.13112
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
---------------------------------------------------------------------------------------------------
The random part estimates at the school level:
Coef. Std. Err.
var_gcseavnormal_12345 0.18135 0.07811
cov_gcseavnormal_12345_genderfemale_12345 0.03744 0.08646
var_genderfemale_12345 0.32472 0.18658
cov_gcseavnormal_12345_Intercept_12345 0.01474 0.07523
cov_genderfemale_12345_Intercept_12345 -0.05144 0.12776
var_Intercept_12345 0.66330 0.14500
---------------------------------------------------------------------------------------------------
The random part estimates at the l1id level:
Coef. Std. Err.
bcons_1 1.00000 0.00000
-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-
>
>
> # Chapter learning outcomes . . . . . . . . . . . . . . . . . . . . . . .180
>
> ############################################################################
>
> proc.time()
user system elapsed
4.48 0.73 16.43