Primary source: Hom, P. W., & Griffeth, R. W. (1995). Employee turnover. Cincinnati, OH: Southwestern College Publishing.

Survival Analysis and the Proportional Hazards Model for Predicting Employee Turnover

Tom Briggstbriggs@gmu.edu

November 2014

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AUDIENCE SURVEY

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“Our new Constitution is now established, and has an appearance that promises permanency; but in this world nothing can be said to be certain, except death and taxes.”

--Benjamin Franklin (1789)

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“In this world nothing can be said to be certain, except death, taxes, and employee turnover.”

--George Mason Student (2014)

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ROAD MAP

BACKGROUNDWHY

Survival Analysis

Survival AnalysisRESULTS

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BACKGROUND

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FIRST PIONEERS

Singer,  J.  D.,  &  Wille/,  J.  B.  (1991).  Modeling  the  days  of  our  lives:  using  survival    analysis  when  designing  and  analyzing  longitudinal  studies  of  duraCon    and  the  Cming  of  events.  Psychological  Bulle/n,  110(2),  268.  

Morita,  J.  G.,  Lee,  T.  W.,  &  Mowday,  R.  T.  (1989).  Introducing  survival  analysis  to    organizaConal  researchers:  A  selected  applicaCon  to  turnover  research.    Journal  of  Applied  Psychology,  74(2),  280–292.    

Peters,  L.  H.,  &  Sheridan,  J.  E.  (1988).  Turnover  research  methodology:  A  criCque    of  tradiConal  designs  and  a  suggested  survival  model  alternaCve.    Research  in  personnel  and  human  resources  management,  6,  231-­‐262.  

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WHO IS THIS MAN?

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SIR DAVID COX

#9 on the George Mason Department of Statistics list of “Great Statisticians” – just below Tukey and William Sealy Gosset.

Known for the Cox proportional hazards model, an application of survival analysis.

And yes…he rocks this look pretty much all the time.

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BY ANY OTHER NAME•  Survival  analysis  StaCsCcs  

•  Reliability  theory  •  Reliability  analysis  Engineering  

•  DuraCon  analysis  •  DuraCon  modeling  Economics  

•  Event  history  analysis  Sociology  

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WHY SURVIVAL ANALYSIS

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WHAT SIZE IS THE HERD?

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WHAT SIZE IS THE HERD?

A. 39 SHEEP

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WHAT SIZE IS THE HERD?

B. 40 SHEEP

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WHAT SIZE IS THE HERD?

C. DON’T KNOW

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WHAT SIZE IS THE HERD?

B. 40 SHEEP

A. 39 SHEEP

C. DON’T KNOW

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WHAT SIZE IS THE HERD?

C. DON’T KNOW - CORRECT!

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VOCABULARY: CENSORING

CENSORING is a missing data problem common to survival analysis (and cross-sectional studies…)

In the herd example, our cross-sectional “view” was censored in two respects: what came before and what is yet to come!

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HOM & GRIFFETH ON WHY •  Cross-sectional study start and end dates

are usually arbitrary•  Short measurement periods weaken

correlations – fewer employees leave – smaller numbers of “quitters” shrink turnover variance

•  Cross-sectional approach distorts results by arbitrarily dictating which participant is a stayer and which is a leaver

•  Cross-sectional approach neglects tenure – 10 days or 10 years treated the same

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NOT WHETHER, BUT WHEN

Death, taxes, and employee turnover:

All employees will ultimately turn over, so the question is not whether, but when?

And a related question: what effects do potential predictor variables have on turnover probability?

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VISUAL: CENSORING

Right-censoring most common in turnover research; an employee could quit the day after the study ends!

leZ  

stayed  

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SURVIVAL ANALYSIS RESULTS

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SURVIVAL ANALYSIS RESULTS•  Generates conditional probabilities – the

“hazard rate” – that employees will quit during a given time interval.

•  Generates graphs of the survival function –

the cumulative probability of staying.

•  Allows for subgroup comparison based on predictor variables.

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SURVIVAL RATES

0.80

0.85

0.90

0.95

1.00

1.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Cum

ulat

ive

Surv

ival

Rat

e

Tenure (in months)

Survival Rates for New Staff Accountants

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SURVIVAL PREDICTORS

0.80

0.85

0.90

0.95

1.00

1.05

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

Cum

ulat

ive

Surv

ival

Rat

e

Tenure (in months)

Survival Rates for New Staff Accountants as Functions of RJPs and Job Tenure

Traditional Job Preview Realistic Job Preview

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PROPORTIONAL HAZARD•  Profile comparisons “ill-suited for estimating

the temporal effects of continuous predictors and of several predictors simultaneously.”

•  Uses regression-like models – the dependent

variable is the (log of) entire hazard function

•  Assumes a predictor shifts hazard profile up (RJP = 0) or down (RJP = 1) depending on predictor scores and that each subject’s hazard function is some constant multiple of the baseline hazard function

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PROPORTIONAL HAZARD BENEFITS

•  Can examine multiple predictors (continuous or categorical) and estimate unique contribution of each while statistically controlling other predictors

•  Estimated βs interpreted as regression

weights, or transformed into probability metrics by antilogging

•  RJP example: RJP subjects have 0.61 times the risk of quitting than control subjects (or hazard decreased by 39 percent)

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HAZARDS OF PROPORTIONAL HAZARD

•  Assumes different predictors all have same log-hazard shape – Singer and Willett (1991) found many examples of violations

•  Assumes different predictors are constant

over time (parallel hazard profiles)

Investigators should test assumptions of shape and parallelism (see Singer and Willett, 1991)

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CONCLUSIONSurvival analysis and the proportional hazard model can offer a compelling alternative to cross-sectional methodology for investigating dynamic relations between turnover and antecedents.

Contact:

Tom Briggstbriggs@gmu.eduTwitter @twbriggs