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) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. Natural language support but running in an English locale R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > ############################################################################ > # 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 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 - 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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 - 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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 - 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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 - 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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 - 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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 84 - 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 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 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 152 - reconstruction used V has gone -ve definite for block 162 - reconstruction used V has gone -ve definite for block 175 - 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 31 - reconstruction used V has gone -ve definite for block 35 - 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 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 80 - reconstruction used V has gone -ve definite for block 84 - 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 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 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 152 - reconstruction used V has gone -ve definite for block 162 - reconstruction used V has gone -ve definite for block 175 - 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 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 -*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*-*- > > (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