Example L8 Bivariate binary (survival) response model

This example is 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 It involves modelling a job vacancy duration until either it is successfully filled or withdrawn from the market.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.

There In example L7 we treated 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. The combined dataset, has 780,864 observations, each of the 12,840 vacancies being represented twice, with each sequence of vacancy responses ending in a 1 at the point where the vacancy is filled for a 'filled' risk, the 'lapsed' risk is right censored at this point and vice versa for a 'lapsed' risk.

The data set vac4-filled-lapsed.dat is the stacked versions of the two data sets from Example L7.

Sabre commands

out filled-lapsed.log

trace filled-lapsed.trace

data ij r 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_math &

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 r1 r2 &

r1d_1 r1d_2 r1d_3 r1d_4 r1d_5 r1d_6 r1d_7 r1d_8 r1d_9 r1d_10 r1d_11 &

r1d_12 r1d_13 r1d_14 r1d_15 r1d_16 r1d_17 r1d_18 r1d_19 r1d_20 r1d_21 &

r1d_22 r1d_23 r1d_24 r1d_25 r1d_26 r1noemps2 r1noemps3 r1noemps4 &

r1sic0 r1sic1 r1sic2 r1sic3 r1sic4 r1sic5 r1sic7 r1sic8 r1sic9 &

r1centre r1provider r1lnwd1_n r1dn r1lnwdn r1n1_d r1nonman r1skilled &

r1maths r1eng_math r1science r1othersub r1olderapp r1written r1lnu18 &

r1lnvj r1lnpopden r1lnrelstaff r1year2 r1year3 r1year4 r1year5 &

r1year6 r1year7 r1year8 r1month1 r1month2 r1month3 r1month4 r1month5 &

r1month6 r1month7 r1month8 r1month9 r1month10 r1month11 r1month12 &

r2d_1 r2d_2 r2d_3 r2d_4 r2d_5 r2d_6 r2d_7 r2d_8 r2d_9 r2d_10 r2d_11 &

r2d_12 r2d_13 r2d_14 r2d_15 r2d_16 r2d_17 r2d_18 r2d_19 r2d_20 r2d_21 &

r2d_22 r2d_23 r2d_24 r2d_25 r2d_26 r2noemps2 r2noemps3 r2noemps4 &

r2sic0 r2sic1 r2sic2 r2sic3 r2sic4 r2sic5 r2sic7 r2sic8 r2sic9 &

r2centre r2provider r2lnwd1_n r2dn r2lnwdn r2n1_d r2nonman r2skilled &

r2maths r2eng_math r2science r2othersub r2olderapp r2written r2lnu18 &

r2lnvj r2lnpopden r2lnrelstaff r2year2 r2year3 r2year4 r2year5 &

r2year6 r2year7 r2year8 r2month1 r2month2 r2month3 r2month4 r2month5 &

r2month6 r2month7 r2month8 r2month9 r2month10 r2month11 r2month12

case vacnum

model b

yvar y

rvar r

fit r1d_1 r1d_2 r1d_3 r1d_4 r1d_5 r1d_6 r1d_7 r1d_8 r1d_9 r1d_10 r1d_11 &

r1d_12 r1d_13 r1d_14 r1d_15 r1d_16 r1d_17 r1d_18 r1d_19 r1d_20 r1d_21 &

r1d_22 r1d_23 r1d_24 r1d_25 r1d_26 r1noemps2 r1noemps3 r1noemps4 &

r1sic0 r1sic1 r1sic2 r1sic3 r1sic4 r1sic5 r1sic7 r1sic8 r1sic9 &

r1centre r1provider r1lnwd1_n r1dn r1lnwdn r1n1_d r1nonman r1skilled &

r1maths r1eng_math r1science r1othersub r1olderapp r1written r1lnu18 &

r1lnvj r1lnpopden r1lnrelstaff r1year2 r1year3 r1year4 r1year5 r1year6 &

r1year7 r1year8 r1month1 r1month2 r1month3 r1month4 r1month6 r1month7 &

r1month8 r1month9 r1month10 r1month11 r1month12 &

r2d_1 r2d_2 r2d_3 r2d_4 r2d_5 r2d_6 r2d_7 r2d_8 r2d_9 r2d_10 r2d_11 &

r2d_12 r2d_13 r2d_14 r2d_15 r2d_16 r2d_17 r2d_18 r2d_19 r2d_20 r2d_21 &

r2d_22 r2d_23 r2d_24 r2d_25 r2d_26 r2noemps2 r2noemps3 r2noemps4 &

r2sic0 r2sic1 r2sic2 r2sic3 r2sic4 r2sic5 r2sic7 r2sic8 r2sic9 &

r2centre r2provider r2lnwd1_n r2dn r2lnwdn r2n1_d r2nonman r2skilled &

r2maths r2eng_math r2science r2othersub r2olderapp r2written r2lnu18 &

r2lnvj r2lnpopden r2lnrelstaff r2year2 r2year3 r2year4 r2year5 r2year6 &

r2year7 r2year8 r2month1 r2month2 r2month3 r2month4 r2month6 r2month7 &

r2month8 r2month9 r2month10 r2month11 r2month12

dis m

dis e

stop

Sabre log file

<S> trace filled-lapsed.trace

<S> data ij r 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_math &

<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 r1 r2 &

<S>      r1d_1 r1d_2 r1d_3 r1d_4 r1d_5 r1d_6 r1d_7 r1d_8 r1d_9 r1d_10 r1d_11 &

<S>      r1d_12 r1d_13 r1d_14 r1d_15 r1d_16 r1d_17 r1d_18 r1d_19 r1d_20 r1d_21 &

<S>      r1d_22 r1d_23 r1d_24 r1d_25 r1d_26 r1noemps2 r1noemps3 r1noemps4 &

<S>      r1sic0 r1sic1 r1sic2 r1sic3 r1sic4 r1sic5 r1sic7 r1sic8 r1sic9 &

<S>      r1centre r1provider r1lnwd1_n r1dn r1lnwdn r1n1_d r1nonman r1skilled &

<S>      r1maths r1eng_math r1science r1othersub r1olderapp r1written r1lnu18 &

<S>      r1lnvj r1lnpopden r1lnrelstaff r1year2 r1year3 r1year4 r1year5 &

<S>      r1year6 r1year7 r1year8 r1month1 r1month2 r1month3 r1month4 r1month5 &

<S>      r1month6 r1month7 r1month8 r1month9 r1month10 r1month11 r1month12 &

<S>      r2d_1 r2d_2 r2d_3 r2d_4 r2d_5 r2d_6 r2d_7 r2d_8 r2d_9 r2d_10 r2d_11 &

<S>      r2d_12 r2d_13 r2d_14 r2d_15 r2d_16 r2d_17 r2d_18 r2d_19 r2d_20 r2d_21 &

<S>      r2d_22 r2d_23 r2d_24 r2d_25 r2d_26 r2noemps2 r2noemps3 r2noemps4 &

<S>      r2sic0 r2sic1 r2sic2 r2sic3 r2sic4 r2sic5 r2sic7 r2sic8 r2sic9 &

<S>      r2centre r2provider r2lnwd1_n r2dn r2lnwdn r2n1_d r2nonman r2skilled &

<S>      r2maths r2eng_math r2science r2othersub r2olderapp r2written r2lnu18 &

<S>      r2lnvj r2lnpopden r2lnrelstaff r2year2 r2year3 r2year4 r2year5 &

<S>      r2year6 r2year7 r2year8 r2month1 r2month2 r2month3 r2month4 r2month5 &

<S>      r2month6 r2month7 r2month8 r2month9 r2month10 r2month11 r2month12

780864 observations in dataset

<S> case vacnum

<S> model b

<S> yvar y

<S> rvar r

<S> fit r1d_1 r1d_2 r1d_3 r1d_4 r1d_5 r1d_6 r1d_7 r1d_8 r1d_9 r1d_10 r1d_11 &

<S>     r1d_12 r1d_13 r1d_14 r1d_15 r1d_16 r1d_17 r1d_18 r1d_19 r1d_20 r1d_21 &

<S>     r1d_22 r1d_23 r1d_24 r1d_25 r1d_26 r1noemps2 r1noemps3 r1noemps4 &

<S>     r1sic0 r1sic1 r1sic2 r1sic3 r1sic4 r1sic5 r1sic7 r1sic8 r1sic9 &

<S>     r1centre r1provider r1lnwd1_n r1dn r1lnwdn r1n1_d r1nonman r1skilled &

<S>     r1maths r1eng_math r1science r1othersub r1olderapp r1written r1lnu18 &

<S>     r1lnvj r1lnpopden r1lnrelstaff r1year2 r1year3 r1year4 r1year5 r1year6 &

<S>     r1year7 r1year8 r1month1 r1month2 r1month3 r1month4 r1month6 r1month7 &

<S>     r1month8 r1month9 r1month10 r1month11 r1month12 &

<S>     r2d_1 r2d_2 r2d_3 r2d_4 r2d_5 r2d_6 r2d_7 r2d_8 r2d_9 r2d_10 r2d_11 &

<S>     r2d_12 r2d_13 r2d_14 r2d_15 r2d_16 r2d_17 r2d_18 r2d_19 r2d_20 r2d_21 &

<S>     r2d_22 r2d_23 r2d_24 r2d_25 r2d_26 r2noemps2 r2noemps3 r2noemps4 &

<S>     r2sic0 r2sic1 r2sic2 r2sic3 r2sic4 r2sic5 r2sic7 r2sic8 r2sic9 &

<S>     r2centre r2provider r2lnwd1_n r2dn r2lnwdn r2n1_d r2nonman r2skilled &

<S>     r2maths r2eng_math r2science r2othersub r2olderapp r2written r2lnu18 &

<S>     r2lnvj r2lnpopden r2lnrelstaff r2year2 r2year3 r2year4 r2year5 r2year6 &

<S>     r2year7 r2year8 r2month1 r2month2 r2month3 r2month4 r2month6 r2month7 &

<S>     r2month8 r2month9 r2month10 r2month11 r2month12

Initial Homogeneous Fit:

Iteration       Log. lik.       Difference

__________________________________________

1          -773913.39

2          -166449.82       0.6075E+06

3          -87154.822       0.7929E+05

4          -67064.257       0.2009E+05

5          -62859.783        4204.

6          -62295.359        564.4

7          -62263.928        31.43

8          -62263.603       0.3248

9          -62263.603       0.1654E-03

10          -62263.603       0.2059E-08

Iteration       Log. lik.         Step      End-points     Orthogonality

length    0          1      criterion

________________________________________________________________________

1          -62881.121        1.0000    fixed  fixed       8.7557

2          -62877.876        0.1250    fixed  fixed       39.757

3          -62267.853        1.0000    fixed  fixed       5.9047

4          -62260.130        1.0000    fixed  fixed       10.118

5          -62224.536        0.5000    fixed  fixed       4.0438

6          -62205.210        0.2500    fixed  fixed       22.213

7          -62156.699        1.0000    fixed  fixed       6.4209

8          -62152.815        1.0000    fixed  fixed       2.2264

9          -62152.549        1.0000    fixed  fixed       1.9658

10          -62152.542        1.0000    fixed  fixed       1.4662

11          -62152.542        1.0000    fixed  fixed

<S> dis m

X-vars            Y-var             Case-var

________________________________________________

r1d_1             y                 vacnum

r1d_2

r1d_3

r1d_4

r1d_5

r1d_6

r1d_7

r1d_8

r1d_9

r1d_10

r1d_11

r1d_12

r1d_13

r1d_14

r1d_15

r1d_16

r1d_17

r1d_18

r1d_19

r1d_20

r1d_21

r1d_22

r1d_23

r1d_24

r1d_25

r1d_26

r1noemps2

r1noemps3

r1noemps4

r1sic0

r1sic1

r1sic2

r1sic3

r1sic4

r1sic5

r1sic7

r1sic8

r1sic9

r1centre

r1provider

r1lnwd1_n

r1dn

r1lnwdn

r1n1_d

r1nonman

r1skilled

r1inhouse

r1dayrel

r1appren

r1english

r1maths

r1eng_math

r1science

r1othersub

r1olderapp

r1written

r1lnu18

r1lnvj

r1lnpopden

r1lnrelstaff

r1year2

r1year3

r1year4

r1year5

r1year6

r1year7

r1year8

r1month1

r1month2

r1month3

r1month4

r1month6

r1month7

r1month8

r1month9

r1month10

r1month11

r1month12

r2d_1

r2d_2

r2d_3

r2d_4

r2d_5

r2d_6

r2d_7

r2d_8

r2d_9

r2d_10

r2d_11

r2d_12

r2d_13

r2d_14

r2d_15

r2d_16

r2d_17

r2d_18

r2d_19

r2d_20

r2d_21

r2d_22

r2d_23

r2d_24

r2d_25

r2d_26

r2noemps2

r2noemps3

r2noemps4

r2sic0

r2sic1

r2sic2

r2sic3

r2sic4

r2sic5

r2sic7

r2sic8

r2sic9

r2centre

r2provider

r2lnwd1_n

r2dn

r2lnwdn

r2n1_d

r2nonman

r2skilled

r2inhouse

r2dayrel

r2appren

r2english

r2maths

r2eng_math

r2science

r2othersub

r2olderapp

r2written

r2lnu18

r2lnvj

r2lnpopden

r2lnrelstaff

r2year2

r2year3

r2year4

r2year5

r2year6

r2year7

r2year8

r2month1

r2month2

r2month3

r2month4

r2month6

r2month7

r2month8

r2month9

r2month10

r2month11

r2month12

Correlated bivariate model

Standard complementary log-log/complementary log-log

Gaussian random effects

Number of observations             =  780864

Number of cases                    =   12840

X-var df           =   162

Scale df           =     3

Log likelihood =     -62152.542     on  780699 residual degrees of freedom

<S> dis e

Parameter              Estimate         Std. Err.

___________________________________________________

r1d_1                  -6.7637          0.58888

r1d_2                  -7.2994          0.57362

r1d_3                  -7.9930          0.56982

r1d_4                  -7.9439          0.56658

r1d_5                  -7.8290          0.56330

r1d_6                  -7.7369          0.56020

r1d_7                  -7.3836          0.55591

r1d_8                  -7.1142          0.55172

r1d_9                  -7.3963          0.54976

r1d_10                 -7.6487          0.54916

r1d_11                 -7.4781          0.54680

r1d_12                 -7.4545          0.54527

r1d_13                 -7.4292          0.54385

r1d_14                 -7.2799          0.54180

r1d_15                 -7.3133          0.53224

r1d_16                 -7.3070          0.52650

r1d_17                 -7.4120          0.52357

r1d_18                 -7.4938          0.52229

r1d_19                 -7.6696          0.52279

r1d_20                 -7.7535          0.52365

r1d_21                 -7.8621          0.51814

r1d_22                 -7.8888          0.52045

r1d_23                 -7.9840          0.52738

r1d_24                 -8.1745          0.54416

r1d_25                 -8.0956          0.55860

r1d_26                 -7.6916          0.54054

r1noemps2              0.79477E-01      0.45072E-01

r1noemps3              0.17392          0.55371E-01

r1noemps4              0.21485          0.65447E-01

r1sic0                -0.35744          0.15904

r1sic1                -0.25553          0.33466

r1sic2                 0.12720          0.15363

r1sic3                 0.11532          0.59317E-01

r1sic4                -0.37538E-01      0.52267E-01

r1sic5                 0.18272          0.74081E-01

r1sic7                 0.14278          0.14061

r1sic8                 0.16433          0.67586E-01

r1sic9                 0.75468E-02      0.61090E-01

r1centre               0.29138          0.41270E-01

r1provider            -0.15402          0.39218E-01

r1lnwd1_n              0.45629E-01      0.78722E-01

r1dn                  -0.30016          0.10640

r1lnwdn                0.53196E-01      0.26347

r1n1_d                 0.52250E-01      0.49868E-01

r1nonman              -0.41597          0.65422E-01

r1skilled              0.15128          0.63418E-01

r1inhouse              0.13007E-01      0.74146E-01

r1dayrel              -0.34554          0.64042E-01

r1appren              -0.48624          0.85036E-01

r1english              0.12400E-02      0.85215E-01

r1maths                0.23858          0.11707

r1eng_math             0.11912E-02      0.11650

r1science             -0.19923E-01      0.88902E-01

r1othersub             0.44213E-01      0.11368

r1olderapp            -0.38523          0.51331E-01

r1written              -1.1252          0.80457E-01

r1lnu18                0.30512          0.35605E-01

r1lnvj                 0.52067E-01      0.25638E-01

r1lnpopden             0.74936E-02      0.27130E-01

r1lnrelstaff          -0.19543          0.47579E-01

r1year2                0.13676E-01      0.10601

r1year3               -0.80618E-02      0.10668

r1year4                0.10349          0.11049

r1year5                0.25427          0.12441

r1year6                0.39614          0.12711

r1year7                0.68346          0.12750

r1year8                0.57439          0.14644

r1month1               0.40156          0.85587E-01

r1month2              -0.17290E-01      0.83759E-01

r1month3              -0.62767E-01      0.79473E-01

r1month4              -0.49664E-01      0.78483E-01

r1month6               0.42664          0.79304E-01

r1month7               0.38964          0.86931E-01

r1month8               0.32778          0.81221E-01

r1month9               0.27303          0.79514E-01

r1month10              0.46707          0.84715E-01

r1month11              0.38740          0.90840E-01

r1month12              0.26158          0.10776

r2d_1                  -6.4227          0.80378

r2d_2                  -5.6290          0.78749

r2d_3                  -5.8999          0.78162

r2d_4                  -5.7426          0.77666

r2d_5                  -5.5793          0.77233

r2d_6                  -5.5724          0.76967

r2d_7                  -4.9585          0.76399

r2d_8                  -4.6750          0.76000

r2d_9                  -4.7498          0.75791

r2d_10                 -5.0292          0.75793

r2d_11                 -4.8516          0.75607

r2d_12                 -4.9356          0.75592

r2d_13                 -4.9474          0.75558

r2d_14                 -4.6272          0.75319

r2d_15                 -4.3371          0.74497

r2d_16                 -4.0788          0.74291

r2d_17                 -3.7783          0.74316

r2d_18                 -3.5892          0.74472

r2d_19                 -3.4705          0.74731

r2d_20                 -3.3662          0.74998

r2d_21                 -3.0425          0.75337

r2d_22                 -2.7700          0.76572

r2d_23                 -2.1767          0.77867

r2d_24                 -1.9401          0.79534

r2d_25                 -1.9795          0.81378

r2d_26                 -1.1766          0.82235

r2noemps2             -0.16839          0.68105E-01

r2noemps3             -0.18015          0.80982E-01

r2noemps4             -0.13718          0.90746E-01

r2sic0                -0.65256E-01      0.22073

r2sic1                 -1.2528          0.45953

r2sic2                 0.84621E-01      0.21755

r2sic3                -0.13122          0.90673E-01

r2sic4                -0.13764          0.79006E-01

r2sic5                -0.50453E-01      0.11346

r2sic7                -0.56554          0.22883

r2sic8                -0.29270          0.10201

r2sic9                -0.15785          0.87552E-01

r2centre              -0.11659          0.59846E-01

r2provider            -0.90154E-01      0.56311E-01

r2lnwd1_n              0.25502          0.11171

r2dn                  -0.18168          0.15114

r2lnwdn                0.40614          0.35338

r2n1_d                -0.50501E-01      0.73196E-01

r2nonman               0.21099          0.89859E-01

r2skilled             -0.69966E-01      0.88567E-01

r2inhouse              0.16867E-02      0.10744

r2dayrel              -0.60187          0.94502E-01

r2appren              -0.39784          0.12129

r2english             -0.11847          0.12163

r2maths               -0.46673          0.17392

r2eng_math            -0.37967          0.17403

r2science             -0.31352          0.12903

r2othersub            -0.44853          0.16931

r2olderapp             0.12010          0.67000E-01

r2written             -0.63169          0.87265E-01

r2lnu18               -0.90519E-01      0.48933E-01

r2lnvj                -0.15638          0.35367E-01

r2lnpopden             0.31657          0.42983E-01

r2lnrelstaff          -0.79829E-01      0.69144E-01

r2year2                0.14261          0.16658

r2year3                0.14845          0.16637

r2year4               -0.35715E-01      0.17286

r2year5                0.68220E-01      0.18987

r2year6                0.10980          0.19212

r2year7               -0.10375          0.19305

r2year8                0.62759          0.21538

r2month1               0.14877          0.12335

r2month2              -0.77735E-01      0.11825

r2month3              -0.13451          0.11405

r2month4               0.51312E-01      0.11164

r2month6               0.20548          0.11145

r2month7               0.25406          0.12114

r2month8               0.14943          0.11506

r2month9               0.40019          0.11160

r2month10              0.31041          0.11641

r2month11              0.14824          0.12667

r2month12             -0.21959          0.16197

scale1                  1.0968          0.13089

scale2                  1.7344          0.46075E-01

corr                  -0.26896          0.23543E-01

<S> stop