Example L7 Binary response (survival) model (filled and lapsed)

These examples are from a study that provides the first estimates of the determinants of employer search in the UK using duration modelling techniques. It involves modelling a job vacancy duration until either it is successfully filled or withdrawn from the market. For further detail see http://www.lancs.ac.uk/staff/ecasb/papers/vacdur_economica.pdf.

We treat the 'filled' and 'lapsed' datasets as if they were independent, both data sets have 390,432 binary observations (at the weekly level) on 12,840 vacancies. For the first risk ('filled') the final response for each vacancy is 1 at the point where the vacancy fills, and similarly for the ('lapsed') risk. At all other weeks the responses are zero. There are 7,234 filled vacancies and 5,606 lapsed vacancies.

For each type of risk we used a 26-piece non-parametric baseline hazard with 55 covariates.

Filled durations

The first few lines and columns of vac4-filled.dat look like

Sabre commands (filled analysis)

out filled.log

trace filled.trace

data ij provider vacnum dayrel appren inhouse sic0 sic1 sic2 sic3 sic4 &

written noemps1 noemps2 noemps3 noemps4 year d n dn n1_d lnwd1_n &

lnwdn lnpopden lnrelstaff nonman skilled english maths eng_maths &

science othersub olderapp year2 year3 year4 year5 year6 year7 year8 &

month1 month2 month3 month4 month5 month6 month7 month8 month9 &

month10 month11 month12 j lnu18 lnvj y d_1 d_2 d_3 d_4 d_5 d_6 d_7 &

d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 d_17 d_18 d_19 d_20 d_21 &

d_22 d_23 d_24 d_25 d_26 type

case vacnum

yvar y

fit d_1 d_2 d_3 d_4 d_5 d_6 d_7 d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 &

d_17 d_18 d_19 d_20 d_21 d_22 d_23 d_24 d_25 d_26 noemps2 noemps3 &

noemps4 sic0 sic1 sic2 sic3 sic4 sic5 sic7 sic8 sic9 centre provider &

lnwd1_n dn lnwdn n1_d nonman skilled inhouse dayrel appren grade2 &

written lnu18 lnvj lnpopden lnrelstaff year2 year3 year4 year5 year6 &

year7 year8 month1 month2 month3 month4 month6 month7 month8 month9 &

month10 month11 month12

dis m

dis e

stop

Sabre log file

<S> trace filled.trace

<S> data ij provider vacnum dayrel appren inhouse sic0 sic1 sic2 sic3 sic4 &

<S>      written noemps1 noemps2 noemps3 noemps4 year d n dn n1_d lnwd1_n &

<S>      lnwdn lnpopden lnrelstaff nonman skilled english maths eng_maths &

<S>      science othersub olderapp year2 year3 year4 year5 year6 year7 year8 &

<S>      month1 month2 month3 month4 month5 month6 month7 month8 month9 &

<S>      month10 month11 month12 j lnu18 lnvj y d_1 d_2 d_3 d_4 d_5 d_6 d_7 &

<S>      d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 d_17 d_18 d_19 d_20 d_21 &

<S>      d_22 d_23 d_24 d_25 d_26 type

390432 observations in dataset

<S> case vacnum

<S> yvar y

<S> fit d_1 d_2 d_3 d_4 d_5 d_6 d_7 d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 &

<S>     d_17 d_18 d_19 d_20 d_21 d_22 d_23 d_24 d_25 d_26 noemps2 noemps3 &

<S>     noemps4 sic0 sic1 sic2 sic3 sic4 sic5 sic7 sic8 sic9 centre provider &

<S>     lnwd1_n dn lnwdn n1_d nonman skilled inhouse dayrel appren grade2 &

<S>     written lnu18 lnvj lnpopden lnrelstaff year2 year3 year4 year5 year6 &

<S>     year7 year8 month1 month2 month3 month4 month6 month7 month8 month9 &

<S>     month10 month11 month12

Initial Homogeneous Fit:

Iteration       Log. lik.       Difference

__________________________________________

1          -386516.06

2          -84780.650       0.3017E+06

3          -45785.228       0.3900E+05

4          -35969.984        9815.

5          -33826.874        2143.

6          -33489.729        337.1

7          -33465.995        23.73

8          -33465.694       0.3004

9          -33465.694       0.1636E-03

10          -33465.694       0.1433E-08

Iteration       Log. lik.         Step      End-points     Orthogonality

length    0          1      criterion

________________________________________________________________________

1          -33757.916        1.0000    fixed  fixed       67.679

2          -33711.882        0.5000    fixed  fixed       15.600

3          -33495.120        1.0000    fixed  fixed       6.5731

4          -33481.845        1.0000    fixed  fixed       4.8202

5          -33469.033        0.5000    fixed  fixed       1130.8

6          -33430.503        1.0000    fixed  fixed       7.3092

7          -33424.272        1.0000    fixed  fixed       2.7345

8          -33424.160        1.0000    fixed  fixed       1.9924

9          -33424.160        1.0000    fixed  fixed       2.1109

10          -33424.160        1.0000    fixed  fixed

<S> dis m

X-vars            Y-var             Case-var

________________________________________________

d_1               y                 vacnum

d_2

d_3

d_4

d_5

d_6

d_7

d_8

d_9

d_10

d_11

d_12

d_13

d_14

d_15

d_16

d_17

d_18

d_19

d_20

d_21

d_22

d_23

d_24

d_25

d_26

noemps2

noemps3

noemps4

sic0

sic1

sic2

sic3

sic4

sic5

sic7

sic8

sic9

centre

provider

lnwd1_n

dn

lnwdn

n1_d

nonman

skilled

inhouse

dayrel

appren

english

maths

eng_maths

science

othersub

olderapp

written

lnu18

lnvj

lnpopden

lnrelstaff

year2

year3

year4

year5

year6

year7

year8

month1

month2

month3

month4

month6

month7

month8

month9

month10

month11

month12

Univariate model

Standard complementary log-log

Gaussian random effects

Number of observations             =  390432

Number of cases                    =   12840

X-var df           =    81

Scale df           =     1

Log likelihood =     -33424.160     on  390350 residual degrees of freedom

<S> dis e

Parameter              Estimate         Std. Err.

___________________________________________________

d_1                    -6.4338          0.51637

d_2                    -7.0011          0.50937

d_3                    -7.7040          0.50843

d_4                    -7.6598          0.50658

d_5                    -7.5495          0.50456

d_6                    -7.4617          0.50267

d_7                    -7.1142          0.49965

d_8                    -6.8503          0.49690

d_9                    -7.1359          0.49626

d_10                   -7.3896          0.49655

d_11                   -7.2214          0.49481

d_12                   -7.1999          0.49399

d_13                   -7.1767          0.49322

d_14                   -7.0299          0.49177

d_15                   -7.0685          0.48377

d_16                   -7.0656          0.48028

d_17                   -7.1705          0.47878

d_18                   -7.2494          0.47836

d_19                   -7.4207          0.47943

d_20                   -7.5001          0.48069

d_21                   -7.5973          0.47503

d_22                   -7.6094          0.47796

d_23                   -7.6917          0.48535

d_24                   -7.8672          0.50320

d_25                   -7.7771          0.51840

d_26                   -7.3596          0.49844

noemps2                0.70217E-01      0.41816E-01

noemps3                0.15315          0.50666E-01

noemps4                0.18331          0.59021E-01

sic0                  -0.34010          0.14881

sic1                  -0.27980          0.31320

sic2                   0.11162          0.14420

sic3                   0.10681          0.55326E-01

sic4                  -0.37340E-01      0.48817E-01

sic5                   0.17095          0.68950E-01

sic7                   0.10590          0.13050

sic8                   0.15159          0.62793E-01

sic9                  -0.85747E-02      0.56799E-01

centre                 0.27273          0.37251E-01

provider              -0.14480          0.36248E-01

lnwd1_n                0.36398E-01      0.73249E-01

dn                    -0.28776          0.98936E-01

lnwdn                  0.60535E-01      0.24654

n1_d                   0.34671E-01      0.45849E-01

nonman                -0.38460          0.58816E-01

skilled                0.14399          0.59189E-01

inhouse                0.89923E-02      0.69330E-01

dayrel                -0.33592          0.59014E-01

appren                -0.46354          0.78031E-01

english               -0.11540E-01      0.79475E-01

maths                  0.20110          0.10759

eng_maths             -0.10601E-01      0.10886

science               -0.27547E-01      0.83063E-01

othersub               0.21354E-01      0.10592

olderapp              -0.36379          0.46444E-01

written                -1.0805          0.68038E-01

lnu18                  0.28837          0.32527E-01

lnvj                   0.49958E-01      0.24144E-01

lnpopden               0.10854E-01      0.25346E-01

lnrelstaff            -0.18725          0.44184E-01

year2                  0.15567E-01      0.99046E-01

year3                 -0.49198E-02      0.99675E-01

year4                  0.97943E-01      0.10327

year5                  0.24163          0.11629

year6                  0.37347          0.11839

year7                  0.63728          0.11703

year8                  0.54556          0.13589

month1                 0.38008          0.78627E-01

month2                -0.25102E-01      0.78237E-01

month3                -0.62243E-01      0.74242E-01

month4                -0.44664E-01      0.73326E-01

month6                 0.40476          0.72406E-01

month7                 0.35940          0.79140E-01

month8                 0.30456          0.74459E-01

month9                 0.25623          0.73212E-01

month10                0.43678          0.76507E-01

month11                0.35861          0.82962E-01

month12                0.23984          0.99498E-01

scale                  0.94838          0.95319E-01

<S> stop

Lapsed durations

The first few lines and columns of vac4-lapsed.dat look like

Sabre commands (lapsed)

out lapsed.log

trace lapsed.trace

data ij provider vacnum dayrel appren inhouse sic0 sic1 sic2 sic3 sic4 &

written noemps1 noemps2 noemps3 noemps4 year d n dn n1_d lnwd1_n &

lnwdn lnpopden lnrelstaff nonman skilled english maths eng_maths &

science othersub olderapp year2 year3 year4 year5 year6 year7 year8 &

month1 month2 month3 month4 month5 month6 month7 month8 month9 &

month10 month11 month12 j lnu18 lnvj y d_1 d_2 d_3 d_4 d_5 d_6 d_7 &

d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 d_17 d_18 d_19 d_20 d_21 &

d_22 d_23 d_24 d_25 d_26 type

case vacnum

yvar y

fit d_1 d_2 d_3 d_4 d_5 d_6 d_7 d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 &

d_17 d_18 d_19 d_20 d_21 d_22 d_23 d_24 d_25 d_26 noemps2 noemps3 &

noemps4 sic0 sic1 sic2 sic3 sic4 sic5 sic7 sic8 sic9 centre provider &

lnwd1_n dn lnwdn n1_d nonman skilled inhouse dayrel appren grade2 &

written lnu18 lnvj lnpopden lnrelstaff year2 year3 year4 year5 year6 &

year7 year8 month1 month2 month3 month4 month6 month7 month8 month9 &

month10 month11 month12

dis m

dis e

stop

Sabre log file (lapsed)

<S> trace lapsed.trace

<S> data ij provider vacnum dayrel appren inhouse sic0 sic1 sic2 sic3 sic4 &

<S>      written noemps1 noemps2 noemps3 noemps4 year d n dn n1_d lnwd1_n &

<S>      lnwdn lnpopden lnrelstaff nonman skilled english maths eng_maths &

<S>      science othersub olderapp year2 year3 year4 year5 year6 year7 year8 &

<S>      month1 month2 month3 month4 month5 month6 month7 month8 month9 &

<S>      month10 month11 month12 j lnu18 lnvj y d_1 d_2 d_3 d_4 d_5 d_6 d_7 &

<S>      d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 d_17 d_18 d_19 d_20 d_21 &

<S>      d_22 d_23 d_24 d_25 d_26 type

390432 observations in dataset

<S> case vacnum

<S> yvar y

<S> fit d_1 d_2 d_3 d_4 d_5 d_6 d_7 d_8 d_9 d_10 d_11 d_12 d_13 d_14 d_15 d_16 &

<S>     d_17 d_18 d_19 d_20 d_21 d_22 d_23 d_24 d_25 d_26 noemps2 noemps3 &

<S>     noemps4 sic0 sic1 sic2 sic3 sic4 sic5 sic7 sic8 sic9 centre provider &

<S>     lnwd1_n dn lnwdn n1_d nonman skilled inhouse dayrel appren grade2 &

<S>     written lnu18 lnvj lnpopden lnrelstaff year2 year3 year4 year5 year6 &

<S>     year7 year8 month1 month2 month3 month4 month6 month7 month8 month9 &

<S>     month10 month11 month12

Initial Homogeneous Fit:

Iteration       Log. lik.       Difference

__________________________________________

1          -387397.33

2          -81669.171       0.3057E+06

3          -41369.595       0.4030E+05

4          -31094.274       0.1028E+05

5          -29032.908        2061.

6          -28805.631        227.3

7          -28797.933        7.697

8          -28797.909       0.2438E-01

9          -28797.909       0.1894E-05

Iteration       Log. lik.         Step      End-points     Orthogonality

length    0          1      criterion

________________________________________________________________________

1          -29123.205        1.0000    fixed  fixed       63.037

2          -28786.404        0.5000    fixed  fixed       6.4499

3          -28763.431        1.0000    fixed  fixed       42.781

4          -28738.614        1.0000    fixed  fixed       5.7802

5          -28733.881        1.0000    fixed  fixed       4.2273

6          -28732.825        1.0000    fixed  fixed       19.024

7          -28732.365        1.0000    fixed  fixed       3.1079

8          -28732.364        1.0000    fixed  fixed       2.3861

9          -28732.364        1.0000    fixed  fixed

<S> dis m

X-vars            Y-var             Case-var

________________________________________________

d_1               y                 vacnum

d_2

d_3

d_4

d_5

d_6

d_7

d_8

d_9

d_10

d_11

d_12

d_13

d_14

d_15

d_16

d_17

d_18

d_19

d_20

d_21

d_22

d_23

d_24

d_25

d_26

noemps2

noemps3

noemps4

sic0

sic1

sic2

sic3

sic4

sic5

sic7

sic8

sic9

centre

provider

lnwd1_n

dn

lnwdn

n1_d

nonman

skilled

inhouse

dayrel

appren

english

maths

eng_maths

science

othersub

olderapp

written

lnu18

lnvj

lnpopden

lnrelstaff

year2

year3

year4

year5

year6

year7

year8

month1

month2

month3

month4

month6

month7

month8

month9

month10

month11

month12

Univariate model

Standard complementary log-log

Gaussian random effects

Number of observations             =  390432

Number of cases                    =   12840

X-var df           =    81

Scale df           =     1

Log likelihood =     -28732.364     on  390350 residual degrees of freedom

<S> dis e

Parameter              Estimate         Std. Err.

___________________________________________________

d_1                    -6.2753          0.71370

d_2                    -5.5053          0.70308

d_3                    -5.7993          0.70015

d_4                    -5.6606          0.69655

d_5                    -5.5133          0.69322

d_6                    -5.5197          0.69138

d_7                    -4.9215          0.68608

d_8                    -4.6562          0.68255

d_9                    -4.7441          0.68087

d_10                   -5.0326          0.68126

d_11                   -4.8632          0.67944

d_12                   -4.9539          0.67948

d_13                   -4.9710          0.67927

d_14                   -4.6571          0.67672

d_15                   -4.3932          0.66775

d_16                   -4.1717          0.66477

d_17                   -3.9009          0.66382

d_18                   -3.7389          0.66404

d_19                   -3.6462          0.66520

d_20                   -3.5632          0.66663

d_21                   -3.2793          0.66695

d_22                   -3.0628          0.67443

d_23                   -2.5167          0.68349

d_24                   -2.3234          0.69633

d_25                   -2.3937          0.71225

d_26                   -1.6268          0.71566

noemps2               -0.14824          0.60436E-01

noemps3               -0.15179          0.71504E-01

noemps4               -0.94087E-01      0.79157E-01

sic0                  -0.90116E-01      0.19364

sic1                   -1.1694          0.41520

sic2                   0.81021E-01      0.19616

sic3                  -0.10651          0.80658E-01

sic4                  -0.12826          0.70356E-01

sic5                  -0.28963E-01      0.99968E-01

sic7                  -0.48313          0.19964

sic8                  -0.25867          0.89602E-01

sic9                  -0.12623          0.76814E-01

centre                -0.74097E-01      0.51199E-01

provider              -0.96176E-01      0.50017E-01

lnwd1_n                0.25999          0.99911E-01

dn                    -0.18580          0.13668

lnwdn                  0.38198          0.31999

n1_d                  -0.13178E-01      0.63886E-01

nonman                 0.15326          0.77426E-01

skilled               -0.59179E-01      0.78718E-01

inhouse                0.69393E-02      0.95665E-01

dayrel                -0.57654          0.83008E-01

appren                -0.39845          0.10741

english               -0.97608E-01      0.10583

maths                 -0.39740          0.15147

eng_maths             -0.34409          0.15392

science               -0.29147          0.11269

othersub              -0.39185          0.14714

olderapp               0.94213E-01      0.58684E-01

written               -0.64987          0.77768E-01

lnu18                 -0.58011E-01      0.42425E-01

lnvj                  -0.15297          0.32358E-01

lnpopden               0.29189          0.37510E-01

lnrelstaff            -0.89345E-01      0.61954E-01

year2                  0.13240          0.14710

year3                  0.13616          0.14716

year4                 -0.17674E-01      0.15284

year5                  0.95654E-01      0.16840

year6                  0.14673          0.17017

year7                 -0.13054E-01      0.16805

year8                  0.62634          0.19125

month1                 0.16514          0.10961

month2                -0.69156E-01      0.10606

month3                -0.12619          0.10201

month4                 0.38386E-01      0.10008

month6                 0.22889          0.99563E-01

month7                 0.27570          0.10760

month8                 0.17218          0.10254

month9                 0.40648          0.10018

month10                0.33295          0.10397

month11                0.17680          0.11188

month12               -0.19514          0.14418

scale                   1.4426          0.13612

<S> stop