modelling time of unemployment via cox proportional model
DESCRIPTION
MODELLING TIME OF UNEMPLOYMENT VIA COX PROPORTIONAL MODEL. Jan Popelka Department of Statistics and Probability University of Economics , Prague. Previous model. LABOR OFFICE IN PRIBRAM Subjects registered in January 2002 Follow-up period: from January 2002 to June 2003 (18 months) - PowerPoint PPT PresentationTRANSCRIPT
MODELLING TIME MODELLING TIME OF OF
UNEMPLOYMENT UNEMPLOYMENT VIA COX VIA COX
PROPORTIONAL PROPORTIONAL MODELMODEL
Jan Popelka Jan Popelka Department of Statistics and Department of Statistics and
Probability University of EconomicsProbability University of Economics,, PraguePrague
Applied Statistics 2005
Previous Previous modelmodel
LABOR OFFICE IN PRIBRAMLABOR OFFICE IN PRIBRAM►Subjects registered in January 2002Subjects registered in January 2002►Follow-up period: Follow-up period:
from January 2002 to June 2003 from January 2002 to June 2003 (18 (18 months)months)
►597 unemployed597 unemployed(175 right censored)(175 right censored)
FACTORSFACTORS►age, sex, educationage, sex, education
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Previous Previous modelmodel
►AGE and AGE^2 variables (continuous)AGE and AGE^2 variables (continuous)
DISPUTABLEDISPUTABLE CONCLUSIONS: CONCLUSIONS:►No relationship between sex and the No relationship between sex and the
probability of exiting to a job probability of exiting to a job ►No difference between subjects with No difference between subjects with
tertiary and basic educationtertiary and basic education
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NewNew model model
LABOR OFFICE IN PRIBRAMLABOR OFFICE IN PRIBRAM►Subjects registered in Subjects registered in 20022002►Follow-up period: Follow-up period:
January 2002 – July 2004 (30 months)January 2002 – July 2004 (30 months)►4275 unemployed4275 unemployed
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New modelNew model
FACTORSFACTORS►AgeAge►SexSex►EducationEducation►Season of registration by Season of registration by LLabor officeabor office►Place of livingPlace of living►State of healthState of health►Martial statusMartial status
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New model - New model - FFactorsactors
AGEAGE►MMinimum 15 inimum 15
yearsyears►MMaximum 61 aximum 61
yearsyears►MMean 33 yearsean 33 years►MMedian 30 yearsedian 30 years
SEXSEX►Females 51% Females 51% (52%)(52%)
►MMales 49% ales 49% (48%)(48%)
PLACE OF LIVINGPLACE OF LIVING►TTowns 58%owns 58%►Villages 42%Villages 42%
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New model - New model - FFactorsactors
EDUCATIONEDUCATION►Basic 16% Basic 16% (18%)(18%)
►Secondary without GCE 48% Secondary without GCE 48% (50%)(50%)
►Secondary with GCE 32% Secondary with GCE 32% (29%)(29%)
►Tertiary 4% Tertiary 4% (3%)(3%) (180 subjects)(180 subjects)
Applied Statistics 2005
New model - New model - FFactorsactors
SEASON OF REGISTRATIONSEASON OF REGISTRATION► Spring 20%Spring 20%► Summer 28%Summer 28%► Autumn 35%Autumn 35%►Winter 17%Winter 17%
MARTIAL STATUSMARTIAL STATUS► SSingle, divorced or widowedingle, divorced or widowed 56% 56% ►Married or common-law marriage 44% Married or common-law marriage 44%
STATE OF HEALTHSTATE OF HEALTH► Perfect 89%Perfect 89%►Disabled 4%Disabled 4%► Full or partial disability Full or partial disability
pension 7%pension 7%
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Arguments for survival Arguments for survival analysisanalysis
► 1309 observations is right censored - no exit to 1309 observations is right censored - no exit to job or lost to follow upjob or lost to follow up
►Duration of unemployment is positively skewedDuration of unemployment is positively skewed
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0-100 101-200 201-300 301-400 401-500 501-600 601-700 701-800 801-900
Time of unemployment (days)
Fre
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Cox proportional modelCox proportional model
►Distribution of duration of Distribution of duration of unemployment and error components unemployment and error components is not knownis not known
►Cox proportional hazard modelCox proportional hazard modelT
0( , , ) ( ) exp( )h t h tx β x β
T
1 0 1 0( , , ) exp[( ) ]t x x x x β
►Estimated hazard ratios are easy to explainEstimated hazard ratios are easy to explain
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Comparison of alternative Comparison of alternative modelsmodels
Model Variable AGE No. of variables AIC
1 AGE, AGE^2Continuous age model
13 44890,9 44916,9
2 AGEMInterval classified age model
19 44873,02 44911,02
Compared models G Df p-value
2 vs 1 17,88 6 0,007
ˆ2 log L
Likelihood ratio test
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Cox proportional model Cox proportional model estimation estimation
Variable Parameter estimation
Hazard ratio
Variable Parameter estimation
Hazard ratio
AGE (21-25) 0.32874*** 1.389 EDU2 0.61716*** 1.854
AGE (26-30) 0.15007** 1.162 EDU3 0.65555*** 1.926
AGE (31-35) 0.27294*** 1.314 EDU4 0.71576*** 2.046
AGE (36-40) 0.24667*** 1.280 SPRING -0.11240** 0.894
AGE (41-45) 0.12471 1.133 SUMMER -0.09577* 0.909
AGE (46-50) 0.08754 1.091 AUTUMN -0.12567** 0.882
AGE (51-55) -0.33129*** 0.718 FAMILY 0.00774 1.008
AGE (56 >) -1.16671*** 0.311 HEALTH2 -0.67898*** 0.507
MALE 0.20277*** 1.225 HEALTH3 -1.03489*** 0.355
TOWN -0.08930** 0.915
(* P<0.1, ** P<0.05, *** P<0.01)
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Age 21 - 25
Age 31 - 35
Age 51 - 55
Baseline survivalfunction (age 15 - 20)
Survival function estimationSurvival function estimation
Interval classified age model. Estimated survival function for female, basic education, registered in winter, perfect health condition, village, single. Distinction by age.
Continuous age model.Female, basic education, registered in winter, perfect health condition, village, single. Distinction by age.
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Age 21
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Age 54
Baseline survivalfunction (age 0)
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Survival function estimationSurvival function estimation
Interval classified age model. Female, 33 years old, registered in winter, perfect health condition, village, single. Distinction by
level of education.
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Basic education
Secondary educationwithout GCE
Secondary education withGCE
Tertiary education
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Survival function estimationSurvival function estimation
Interval classified age model. Male, 33 years old, secondary education with GCE, registered in winter, village, single.
Distinction by state of health.
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Perfect
Disabled
Full or partial disability pension
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Next researchNext research
►Orientation on the Czech Republic as a Orientation on the Czech Republic as a complexcomplex
► Influence of regional diversification Influence of regional diversification should be examined should be examined
► Influence of other factorsInfluence of other factors►Relationship between the length of Relationship between the length of
unemployment and the age of subjectsunemployment and the age of subjects