[R-sig-ME] update to previous message about false positives

John Kingston jkingston at linguist.umass.edu
Mon May 26 06:29:13 CEST 2014


This message follows my earlier one regarding possible false positives.

The test:

relgrad <- with(sfHSxRtCxRtR at optinfo$derivs, solve(Hessian, gradient))
max(abs(relgrad))

yielded a small value, too: 0.0003628809

And a further test:

xx <- update(sfHSxRtCxRtR,devFunOnly=TRUE)
params <- unlist(getME(sfHSxRtCxRtR, c("theta", "beta")))
grad(xx,params)

yielded:

[1] -0.0033705847  0.0114374278 -0.0088389651 -0.0013375443  
-0.0112697898  0.0011420500  0.0024532777  0.0023931444  0.0109466237  
-0.0007213523 -0.0006562741 -0.0004396474  0.0039678684
[14] -0.0001146848  0.0044656719  0.0150139408 -0.0049835953   
0.0106851591  0.0022508263 -0.0031896368  0.0085055924 -0.0020030117   
0.0117194911

which differs relatively little from gg, calculated earlier:

  [1] -3.368978e-03  1.132823e-02 -8.620318e-03 -1.396875e-03  
-1.111574e-02 -5.324182e-05  2.831584e-03  3.310606e-03  1.246932e-02  
-1.287135e-03 -7.301514e-04 -2.738943e-04  3.954865e-03
[14] -2.018623e-04  4.035155e-04  1.503184e-02 -4.957783e-03   
1.072177e-02  2.304259e-03 -3.187470e-03  2.128822e-01 -9.298437e-03   
1.459412e-02

grad(xx, params) - gg =

  [1] -1.607096e-06  1.091984e-04 -2.186470e-04  5.933041e-05  
-1.540546e-04  1.195292e-03 -3.783067e-04 -9.174618e-04 -1.522694e-03   
5.657828e-04  7.387734e-05 -1.657531e-04  1.300342e-05
[14]  8.717753e-05  4.062156e-03 -1.789655e-05 -2.581237e-05  
-3.661019e-05 -5.343309e-05 -2.167105e-06 -2.043766e-01  7.295426e-03  
-2.874625e-03

Doing the same comparison for the Hessian yields:

> hessian(xx, params)

                [,1]         [,2]          [,3]         [,4]           
[,5]         [,6]         [,7]        [,8]          [,9]         [,10]  
        [,11]        [,12]       [,13]        [,14]
  [1,]   120.1740592   105.442861  -107.5745280    52.670499     
822.582502    -7.504852    -1.506024    1.358660    -6.3002315  
-8.502787e+00    1.0206522     5.367529   -2.984625     4.145573
  [2,]   105.4428611  8002.527882 -2457.2221203  -102.419212   
-2312.601923   369.489001    35.510026   17.399144   118.7589983  
-1.505657e+01    5.7026516    32.342155  -18.621484     5.162396
  [3,]  -107.5745280 -2457.222120  4577.1322564  -276.573290     
346.906019    16.382111   -38.982669   -2.432062    -0.7133908  
-7.764190e+01   -5.3027926     5.844216    3.691355    21.479957
  [4,]    52.6704989  -102.419212  -276.5732902   737.922041    
1300.431563    10.459564    -1.764205   10.622713    16.2841119  
-2.731945e+01    1.0064528    -4.795930   -1.518830    39.934229
  [5,]   822.5825016 -2312.601923   346.9060192  1300.431563   
19098.452236    33.916906     7.832260   19.364769    35.5692713  
-1.012937e+02    3.5862966    58.764282  -41.774123    28.094613
  [6,]    -7.5048522   369.489001    16.3821110    10.459564      
33.916906 13986.671883 -2236.417643 -106.713739 -2273.5207699  
-1.669204e+01   41.5750859     5.155602   -2.023642    11.201909
  [7,]    -1.5060244    35.510026   -38.9826685    -1.764205       
7.832260 -2236.417643  4413.504625 -266.587541   332.9324243  
-8.312557e+01  -39.2883785   -37.440896  -41.408529   -31.265860
  [8,]     1.3586601    17.399144    -2.4320616    10.622713      
19.364769  -106.713739  -266.587541  749.607763  1364.0263240  
-4.925123e+01   -8.7128203    21.746147   25.574510    44.477344
  [9,]    -6.3002315   118.758998    -0.7133908    16.284112      
35.569271 -2273.520770   332.932424 1364.026324 19104.3149051  
-1.046625e+02   16.1393701   308.306118   32.406834   117.265865
[10,]    -8.5027867   -15.056572   -77.6419036   -27.319448    
-101.293680   -16.692040   -83.125575  -49.251226  -104.6624698   
8.228576e+03 -339.0694670   282.233599  -43.532856     9.178118
[11,]     1.0206522     5.702652    -5.3027926     1.006453       
3.586297    41.575086   -39.288379   -8.712820    16.1393701  
-3.390695e+02  710.6842938  1240.305931   -5.786735   -60.986719
[12,]     5.3675294    32.342155     5.8442155    -4.795930      
58.764282     5.155602   -37.440896   21.746147   308.3061177   
2.822336e+02 1240.3059308 18444.354308  -93.130339   -87.987859
[13,]    -2.9846245   -18.621484     3.6913547    -1.518830     
-41.774123    -2.023642   -41.408529   25.574510    32.4068336  
-4.353286e+01   -5.7867350   -93.130339 1090.460202   778.296730
[14,]     4.1455734     5.162396    21.4799567    39.934229      
28.094613    11.201909   -31.265860   44.477344   117.2658650   
9.178118e+00  -60.9867194   -87.987859  778.296730 15541.250246
[15,]    -3.3266306  -202.993511    19.9748010    96.184231     
482.812590  -206.702930    54.502400   67.653255   451.8587709  
-6.693112e+01  -38.1608720   -29.873503 -292.912538 -3764.642188
[16,]     0.2912339    -9.349129    -2.4009252     3.349133      
12.877780    -4.025141     4.372661   -3.911761   -32.6386647  
-2.411221e+00   -0.4705178    -3.584774   -2.357494    -4.436009
[17,]   -14.0198211    89.356392   -13.3961674    -4.616096     
-67.199087  -454.832736    61.714665    7.017614    48.7781235  
-1.033230e+02   13.6842720    72.066398  -31.391468    44.439705
[18,]    10.9251160   -84.749391   -25.1606425    89.013582     
434.877479    64.788609    27.690336  -97.933405  -750.7025742   
9.253063e-02  -30.1165345  -176.577184  -47.932266  -132.656737
[19,]    -2.5757481    -5.377063    12.6585955   -16.815331     
-41.860866    86.888308  -112.384214   20.561753    23.2548131  
-6.523163e+01  -11.3970316   -48.690053   -2.417331    29.048922
[20,]     2.9369754    -7.413088   -12.5884897    38.095891      
88.441659     4.104393    20.001128  -47.375002  -102.5932378  
-8.267404e+00  -12.1042232   -27.950744   -7.499306   -66.464994
[21,] -1140.1100054  8677.326772 -2094.5772787 -3292.407408  
-47965.509870 -1906.108077  1508.941003 -164.753978 -6475.7960985  
-2.840359e+03   15.8131613  4192.604414 -694.771182  -469.902347
[22,]  -302.8082321   990.009194 -1388.5931994  -272.781461   
-5756.551118 -1110.695682 -1293.057165  161.812331   748.1841020   
1.588311e+03 -382.3264838 -3456.696864  252.860935  1383.021534
[23,]   -17.0974103    31.132358     6.7955401  -156.860690    
-285.905857   -36.209011    -2.910781 -170.972637   -66.8478459  
-1.881380e+02  127.4555154   468.018755  -31.070752   493.226459
              [,15]        [,16]        [,17]         [,18]         
[,19]        [,20]         [,21]        [,22]         [,23]
  [1,]    -3.326631    0.2912339   -14.019821  1.092512e+01     
-2.575748     2.936975   -1140.11001    -302.8082    -17.097410
  [2,]  -202.993511   -9.3491287    89.356392 -8.474939e+01     
-5.377063    -7.413088    8677.32677     990.0092     31.132358
  [3,]    19.974801   -2.4009252   -13.396167 -2.516064e+01     
12.658596   -12.588490   -2094.57728   -1388.5932      6.795540
  [4,]    96.184231    3.3491332    -4.616096  8.901358e+01    
-16.815331    38.095891   -3292.40741    -272.7815   -156.860690
  [5,]   482.812590   12.8777796   -67.199087  4.348775e+02    
-41.860866    88.441659  -47965.50987   -5756.5511   -285.905857
  [6,]  -206.702930   -4.0251414  -454.832736  6.478861e+01     
86.888308     4.104393   -1906.10808   -1110.6957    -36.209011
  [7,]    54.502400    4.3726609    61.714665  2.769034e+01   
-112.384214    20.001128    1508.94100   -1293.0572     -2.910781
  [8,]    67.653255   -3.9117609     7.017614 -9.793341e+01     
20.561753   -47.375002    -164.75398     161.8123   -170.972637
  [9,]   451.858771  -32.6386647    48.778124 -7.507026e+02     
23.254813  -102.593238   -6475.79610     748.1841    -66.847846
[10,]   -66.931125   -2.4112213  -103.323010  9.253063e-02    
-65.231628    -8.267404   -2840.35931    1588.3113   -188.138017
[11,]   -38.160872   -0.4705178    13.684272 -3.011653e+01    
-11.397032   -12.104223      15.81316    -382.3265    127.455515
[12,]   -29.873503   -3.5847738    72.066398 -1.765772e+02    
-48.690053   -27.950744    4192.60441   -3456.6969    468.018755
[13,]  -292.912538   -2.3574936   -31.391468 -4.793227e+01     
-2.417331    -7.499306    -694.77118     252.8609    -31.070752
[14,] -3764.642188   -4.4360095    44.439705 -1.326567e+02     
29.048922   -66.464994    -469.90235    1383.0215    493.226459
[15,] 32619.378440  -19.1405337  -191.118547 -3.797848e+02     
12.457206   -67.412229   -3534.26399   -4364.0650   -213.676684
[16,]   -19.140534   83.3564695    99.644738  8.638272e+02   
-113.919302    57.787450     568.33498    -256.6745     95.290072
[17,]  -191.118547   99.6447377  8321.518528 -2.336166e+03  
-2504.879964  -116.069782   23410.78444   -7737.2818   -413.061830
[18,]  -379.784795  863.8272298 -2336.166492  2.031025e+04    
327.923878  1449.493218    5210.53272    -331.5682   2365.347580
[19,]    12.457206 -113.9193021 -2504.879964  3.279239e+02   
4729.120058  -302.478304   -8249.67578    9321.4641   -513.296202
[20,]   -67.412229   57.7874499  -116.069782  1.449493e+03   
-302.478304   798.715340    -120.24179   -1027.9713   1229.253152
[21,] -3534.263989  568.3349771 23410.784438  5.210533e+03  
-8249.675776  -120.241792 5103138.59345 -532580.1167 -21433.406503
[22,] -4364.064956 -256.6744716 -7737.281789 -3.315682e+02   
9321.464107 -1027.971291 -532580.11673 2448665.3906  -4467.482967
[23,]  -213.676684   95.2900719  -413.061830  2.365348e+03   
-513.296202  1229.253152  -21433.40650   -4467.4830  95608.545859

> hessian(xx, params) - hh

                [,1]          [,2]          [,3]          [,4]          
  [,5]          [,6]          [,7]          [,8]          [,9]          
[,10]         [,11]         [,12]         [,13]
  [1,] -2.174154e-02  2.675581e-03  0.0045735202 -5.465446e-03  
-1.116520e-03  0.0031433803  0.0044736188  0.0012992506 -1.952712e-03  
-0.0028477402  5.027177e-03  0.0037599058  0.0052436214
  [2,]  2.675581e-03  5.381220e-04 -0.0030651423 -6.248245e-03   
4.339480e-03 -0.0073984082  0.0005657110 -0.0017347483 -4.856674e-03   
0.0053176302  5.080799e-03 -0.0034874581 -0.0074703357
  [3,]  4.573520e-03 -3.065142e-03  0.0126275109 -2.306296e-03   
3.553370e-03  0.0002750179 -0.0003687140  0.0017763164  1.201199e-02   
0.0031159288  1.528691e-03 -0.0187605446  0.0019015601
  [4,] -5.465446e-03 -6.248245e-03 -0.0023062958  1.725601e-02  
-7.753215e-05  0.0003357576 -0.0040729665 -0.0152260468 -8.856897e-03  
-0.0067041255  4.409771e-05 -0.0242620770 -0.0010689367
  [5,] -1.116520e-03  4.339480e-03  0.0035533701 -7.753215e-05  
-1.529336e-02 -0.0064341321  0.0030975296  0.0094225420 -2.017720e-03   
0.0008753729 -6.537866e-03 -0.0041504293  0.0076763089
  [6,]  3.143380e-03 -7.398408e-03  0.0002750179  3.357576e-04  
-6.434132e-03 -0.0412513715  0.0050258520  0.0099552340  8.588000e-03  
-0.0046618529  5.627845e-03  0.0007554417  0.0008332370
  [7,]  4.473619e-03  5.657110e-04 -0.0003687140 -4.072967e-03   
3.097530e-03  0.0050258520 -0.0310195782  0.0072467573  3.347200e-03  
-0.0022839282 -5.785742e-03 -0.0013209058 -0.0014243946
  [8,]  1.299251e-03 -1.734748e-03  0.0017763164 -1.522605e-02   
9.422542e-03  0.0099552340  0.0072467573 -0.0213878149  1.971016e-03  
-0.0025075191 -2.432119e-03 -0.0101399815 -0.0033095579
  [9,] -1.952712e-03 -4.856674e-03  0.0120119931 -8.856897e-03  
-2.017720e-03  0.0085880000  0.0033472002  0.0019710163 -4.430788e-03  
-0.0054263026 -8.276628e-04 -0.0089457676 -0.0060692192
[10,] -2.847740e-03  5.317630e-03  0.0031159288 -6.704125e-03   
8.753729e-04 -0.0046618529 -0.0022839282 -0.0025075191 -5.426303e-03  
-0.0300369404 -4.362219e-04 -0.0041943211  0.0041312709
[11,]  5.027177e-03  5.080799e-03  0.0015286913  4.409771e-05  
-6.537866e-03  0.0056278445 -0.0057857419 -0.0024321188 -8.276628e-04  
-0.0004362219 -2.078431e-02 -0.0077289030 -0.0001138733
[12,]  3.759906e-03 -3.487458e-03 -0.0187605446 -2.426208e-02  
-4.150429e-03  0.0007554417 -0.0013209058 -0.0101399815 -8.945768e-03  
-0.0041943211 -7.728903e-03  0.0667107794 -0.0011886298
[13,]  5.243621e-03 -7.470336e-03  0.0019015601 -1.068937e-03   
7.676309e-03  0.0008332370 -0.0014243946 -0.0033095579 -6.069219e-03   
0.0041312709 -1.138733e-04 -0.0011886298 -0.0102566466
[14,] -4.512078e-03  6.329052e-03  0.0043097096 -6.262132e-03   
7.271405e-03  0.0032390754 -0.0017607563  0.0091437088  1.208078e-02   
0.0055714542  7.360190e-03 -0.0105033416 -0.0000836716
[15,]  3.813757e-03 -2.971857e-03  0.0139855283  5.886356e-03  
-1.626739e-02  0.0019036593  0.0049630113 -0.0010414008 -1.031374e-03  
-0.0023530046  1.014852e-02  0.0016194862  0.0033557662
[16,] -5.519030e-03  5.346496e-05 -0.0009618441 -4.931706e-03  
-3.079761e-03  0.0026905827 -0.0031935818 -0.0015436450  8.369026e-03   
0.0008270508  1.242832e-04 -0.0002401364  0.0061538743
[17,]  4.776049e-03 -1.151523e-03  0.0066035479 -1.135960e-02   
6.968132e-03  0.0021026348 -0.0006667256  0.0016224097  1.695299e-03  
-0.0024531098 -2.556583e-03  0.0004799392 -0.0061534164
[18,]  6.129375e-06  1.891128e-03 -0.0112895132 -9.184442e-03   
1.181774e-02  0.0067484503 -0.0035722955  0.0026908638  6.118690e-04  
-0.0021959342 -3.924641e-03 -0.0034539168  0.0029756813
[19,] -6.748987e-04 -2.306801e-03 -0.0031476283  5.164174e-03  
-4.481530e-03 -0.0026219509 -0.0023168610  0.0014504421 -9.241644e-04   
0.0012215803  5.373212e-03 -0.0041398000 -0.0054653719
[20,]  1.855820e-03  2.683495e-03 -0.0062143107  1.239519e-02  
-3.653245e-03  0.0107655543 -0.0091255232  0.0009132156 -9.818685e-05  
-0.0029384774  7.410119e-03 -0.0029292879 -0.0066907956
[21,]  6.937942e-03  6.023135e-02 -0.0059286185 -5.185891e-03   
8.235450e-02 -0.5279987913  0.1448606613  0.0017593525 -4.176498e-02  
-0.0161059468  6.337541e-03 -0.0459771204  0.0046360941
[22,]  7.807939e-03 -1.137521e-02  0.0180066118 -4.385140e-02   
1.412810e-02  0.0402804010 -0.0241446273 -0.0131691950 -6.235801e-02  
-0.0082738265  1.342096e-02 -0.1189830478  0.0044892077
[23,] -1.585136e-03 -3.327251e-04  0.0068438419 -2.395877e-02  
-5.226395e-04 -0.0033223756  0.0043186677 -0.0182913958 -2.185717e-02   
0.0018760011  4.373088e-04 -0.0308054882 -0.0041019134
               [,14]         [,15]         [,16]         [,17]          
[,18]         [,19]         [,20]         [,21]        [,22]          
[,23]
  [1,] -0.0045120783  0.0038137571 -5.519030e-03  0.0047760491   
6.129375e-06 -0.0006748987  1.855820e-03  0.0069379417  0.007807939  
-0.0015851357
  [2,]  0.0063290515 -0.0029718566  5.346496e-05 -0.0011515230   
1.891128e-03 -0.0023068005  2.683495e-03  0.0602313476 -0.011375205  
-0.0003327251
  [3,]  0.0043097096  0.0139855283 -9.618441e-04  0.0066035479  
-1.128951e-02 -0.0031476283 -6.214311e-03 -0.0059286185  0.018006612   
0.0068438419
  [4,] -0.0062621325  0.0058863563 -4.931706e-03 -0.0113595996  
-9.184442e-03  0.0051641741  1.239519e-02 -0.0051858913 -0.043851395  
-0.0239587711
  [5,]  0.0072714047 -0.0162673916 -3.079761e-03  0.0069681318   
1.181774e-02 -0.0044815295 -3.653245e-03  0.0823544982  0.014128099  
-0.0005226395
  [6,]  0.0032390754  0.0019036593  2.690583e-03  0.0021026348   
6.748450e-03 -0.0026219509  1.076555e-02 -0.5279987913  0.040280401  
-0.0033223756
  [7,] -0.0017607563  0.0049630113 -3.193582e-03 -0.0006667256  
-3.572295e-03 -0.0023168610 -9.125523e-03  0.1448606613 -0.024144627   
0.0043186677
  [8,]  0.0091437088 -0.0010414008 -1.543645e-03  0.0016224097   
2.690864e-03  0.0014504421  9.132156e-04  0.0017593525 -0.013169195  
-0.0182913958
  [9,]  0.0120807757 -0.0010313741  8.369026e-03  0.0016952993   
6.118690e-04 -0.0009241644 -9.818685e-05 -0.0417649796 -0.062358010  
-0.0218571699
[10,]  0.0055714542 -0.0023530046  8.270508e-04 -0.0024531098  
-2.195934e-03  0.0012215803 -2.938477e-03 -0.0161059468 -0.008273826   
0.0018760011
[11,]  0.0073601903  0.0101485229  1.242832e-04 -0.0025565827  
-3.924641e-03  0.0053732115  7.410119e-03  0.0063375408  0.013420956   
0.0004373088
[12,] -0.0105033416  0.0016194862 -2.401364e-04  0.0004799392  
-3.453917e-03 -0.0041398000 -2.929288e-03 -0.0459771204 -0.118983048  
-0.0308054882
[13,] -0.0000836716  0.0033557662  6.153874e-03 -0.0061534164   
2.975681e-03 -0.0054653719 -6.690796e-03  0.0046360941  0.004489208  
-0.0041019134
[14,]  0.0175798113  0.0902339108 -2.659874e-03  0.0020223468   
6.166098e-03  0.0079064466  1.558615e-03 -0.0389437950 -0.001049385   
0.0140569129
[15,]  0.0902339108 -0.1323017313 -5.801023e-04 -0.0026411842   
1.452162e-02  0.0078649448 -5.490748e-03  0.1736938980  0.022812160  
-0.0005974097
[16,] -0.0026598737 -0.0005801023 -1.340357e-02 -0.0022349675   
4.598005e-03  0.0028781256  7.908915e-03  0.0009316806 -0.006869086  
-0.0039344365
[17,]  0.0020223468 -0.0026411842 -2.234967e-03  0.0136455855   
2.514638e-03  0.0013840837  2.861133e-04  0.0897969890 -0.010487408   
0.0070791040
[18,]  0.0061660984  0.0145216196  4.598005e-03  0.0025146382  
-5.823754e-03 -0.0022082184 -2.570122e-03 -0.0021295272  0.009604257  
-0.0039216392
[19,]  0.0079064466  0.0078649448  2.878126e-03  0.0013840837  
-2.208218e-03 -0.0027442362 -3.267145e-03 -0.0297189825 -0.008732238   
0.0011612826
[20,]  0.0015586155 -0.0054907482  7.908915e-03  0.0002861133  
-2.570122e-03 -0.0032671450 -3.148659e-02 -0.0018014206 -0.002723892  
-0.0032563813
[21,] -0.0389437950  0.1736938980  9.316806e-04  0.0897969890  
-2.129527e-03 -0.0297189825 -1.801421e-03  3.0560996104 -0.281465531  
-0.0451748433
[22,] -0.0010493852  0.0228121604 -6.869086e-03 -0.0104874083   
9.604257e-03 -0.0087322380 -2.723892e-03 -0.2814655309  1.216295037  
-0.1057700633
[23,]  0.0140569129 -0.0005974097 -3.934436e-03  0.0070791040  
-3.921639e-03  0.0011612826 -3.256381e-03 -0.0451748433 -0.105770063   
0.0580663878

The maximum absolute value of this difference is 3.0561, which appears  
in [21,21]; no other difference is within an order of magnitude of  
that size. A histogram of the log transforms of the absolute values of  
these differences is attached.

John Kingston
--------------------------------
Professor and Head
Linguistics Department
University of Massachusetts
150 Hicks Way, 226 South College
Amherst, MA 01003-9274
1-413-545-6837, fax -2792
jkingston at linguist.umass.edu
https://blogs.umass.edu/jkingstn/
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