Temporal GIS and Statistical Modelling of

Personal LifelinesMarius Thériault, Christophe Claramunt, Anne-Marie Séguin and Paul Villeneuve

July 2002

Spatial Data Handling

Ottawa

Funded by the Canadian SSHRC, the Canadian NSERC, the Quebec Province’s FCAR and GEOIDE’s project SOC#8

Introduction

Urban modelling must consider decision-making behaviour of urban actors using disaggregate data Activity location, home choice, commuting and travel decision Household and professional profiles of persons

Probabilistic discrete-choice theory is becoming the central tenet of urban modelling research Implemented using logistic and Cox regression techniques Aimed at modelling individual’s and household’s behaviour

Needing dynamic spatial tools for analysing complex urban systems where Uncertainties exist in the system (aggregation is not straightforward) Decision rules for individuals and households can be intricate System processes are path and location dependent

- future system state depends partly on past and current states (thus needing event history analysis)

Purpose and Objectives

Purpose Detect the unintentional consequences, at the macro scale

(E.g. urban spread), of intentional actions and strategies occurring at the micro-scale (statistical aggregation)

Objective : develop a logical database model to handle personal biographies and to restructure individual lifelines data in a format suitable for statistical analysis

Needing to build a new spatio-temporal dataset (flat file) for any question at hand (data restructuring for statistical analysis)

GIS needed to study influence of neighbourhood on individual decisions and to summarise their combined effect on the evolution of the overall urban system

Why Studying Individual Biographies? Focus of this work

Household, residential and professional history of citizens

Life course of most individuals Is built around three interlocking series of events:

- a household history; an occupational career; a residential trajectory During the last decades, these trajectories generated patterns of

events of increasing complexity:- more divorces- extension of contractual short-term employment- increasing geographical mobility, etc.

Within cities, these individual trajectories intersect and combine, yielding demographic and residential patterns –driving city evolution and transportation demand

Understanding processes by which personal biographies aggregate and evolve cannot be derived from censuses They give only the barest spatio-temporal snapshot reports on

complex situations and they do not relate facts

Example of an Individual’s Biography

Leaving Parent's HomeTime Line

Census 1 Census 2

RESIDENTIALTRAJECTORY

CAREERTRAJECTORY

CONSULTANT

UNEMPLOYED

STUDENT

CONSULTANT

PROFESSIONAL

TECHNICIAN

UNEMPLOYED

Survey date

A B C D E F G H I J K L

Temporal intersection ofepisodes along a trajectory

A 1 aCONSULTANT MOTHER Episodes

Lifeline

HOUSEHOLD TRAJECTORY

FamilySPOUSE

SON MOTHERUNCLE TOM

SPOUSE

IN COUPLESINGLE

MARRIEDDIVORCEDSINGLE

Maritalstatus

ROOM-MATE

ROOM-MATE

Otherspersons

2 14 16 22

1 4 6

3 7 9 10 12 17 21 23 24

1 2 3 4 5 6 7

Occupation

CHALET

Secondaryhouse

TOWN HOUSE

Mainhome

ROOM STUDIO FLATROOM

APARTMENTSTUDIO FLAT APARTMENT

3 5 8 11 13 15 18 19 20 25

a b c d e f g h i j k

buy

birt

h

mar

iage

sepa

ratio

n

divo

rce

arriv

al

depa

rtur

e

arriv

al

sell

depa

rtur

e

rent

sell

leav

e

buy

leav

e

rent

leav

e

rent

leav

e

arriv

al arriv

al

depa

rtur

e

arriv

al

buy

rent

leav

e

rent

Event1

Location

TECHNICIAN

Changes in Personal Life

An individual’s history is altered When an event occurs modifying at least one important aspect of his

personal status (marital, family, job, home, education, income, etc.) Such an event may alter simultaneously status on more than one

trajectory - or have effect on several individuals in the family Some events (E.g. new born baby) can be anticipated and may

potentially lead to prior adjustment (actions linked to expectation) Effects can also be delayed (after the enabling event occurs)

Life trajectories show interlocked evolution Behaviour based on personal values, beliefs and strategy They associate episodes (time periods with stable attributes) which

intersect to depict global life status of the person Hypothesis: their ordering builds logical sequences (evolution

patterns) related to life cycles (E.g. young couples, retired persons, etc.)

Studying these patterns is more relevant to urban studies than knowing the exact timing of events for each individual

Using Retrospective Surveys Retrospective surveys

Provide detailed information about changes occurring during the life of the respondents

However, this spatio-temporal data must be properly structured and carefully analysed to reveal spatio-temporal structures and patterns

Advantages Phenomena are measured for individuals (micro-level) The follow-up cover long periods of time (E.g. since birth,

marriage or departure from the parent’s home) Information can be structured using lifelines and personal

trajectories

Specific issues Data reliability and questionnaire structure - respondents have to

remember places and events that were happening many years earlier However, sequence of events are more reliable than dates Spatial and temporal data may be fuzzy Need appropriate data modelling to handle historical sequences and

to allow comprehensive time-based statistical analysis

The 1996 Retrospective Survey for Quebec City In Quebec City, a retrospective survey collecting, in one interview,

information about all changes occurred over a long period of time, since the departure of the parental home

A spatially stratified sample of two cohorts of professional workers Sample of 418 respondents stratified by municipality, gender and age

cohort (36-40 and 46-50). Interviews realized at the respondent’s home, mean duration 1.5 hour Three trajectories:

Residential trajectory : every home occupied (three months or more) since the departure of parent’s home, with their location (civic address) and other characteristics (tenure, price, choice criteria, reasons to leave, etc.)

Household trajectory : each change in the composition of the respondent’s household (arrival or departure of a spouse, birth, death, arrival of a child from an other household, relatives, roommates, cotenants, etc.)

Professional trajectory : each change in employer, each work place, with their characteristics (including secondary jobs, education and unemployment episodes)

Collecting dates of every change (starting- and ending-time of each episode)

Spatio-Temporal Modelling of Biographies Relate to the integration of time in GIS

Triad framework proposed by Peuquet (space - time - theme) Integrate the notion of event-process and jointly-related entities

described in Claramunt et al.

Main task Design a relational database schema of individual’s trajectories

and providing query mechanisms needed to restructure spatio-temporal data in a format suitable for statistical analysis (using GIS and DBMS)

Main characteristics Entity-based implementation within RDBMS and GIS to describe

individuals, events, processes, households, jobs, diploma, etc. Building multi-dimensional sequences of events combining lifelines

and trajectories Providing flat files needed for statistical analysis of ad hoc queries

Modelling Life Trajectories

Specific conceptual modelling issue How can we express the temporal structure of biography as an

ordered sequence of intertwined statuses and events, using database modelling concepts, while retaining its behavioural meaning?

Personal biographies Are a complex mix of real world phenomena (E.g. persons,

dwellings, etc.) generating abstract temporal features (E.g. episodes, events)

Episodes are ordered along lifelines to form sequences of independent or joint evolution (linked trajectories or related individuals)

Trajectories hold sets of relationships Aggregation (household made of persons), combination (mix of jobs

held simultaneously), or collaboration (renting or buying a dwelling is using another type of entity and starts a new residential episode)

Database Modelling of Trajectories

Modelling concepts Trajectories are combining events and episodes describing a

multi-dimensional aspect of personal life

Each trajectory (E.g. household) groups a set of related lifelines (E.g. marital status, family composition)

Each lifeline describes a specific dimension of a trajectory, ordering episodes (periods of time) during which a given status was stable (E.g. single or married).

When an event occurs, there is some change in status, leading to a new episode (E.g. birth of a child in an household changes its composition)

Events and episodes form sequences ordered along lifelines (directional from past to future)

Quebec City - Trajectories and Lifelines Our survey questionnaire leads us to define nine lifelines related to the

three trajectories The first lifeline is used to depict the Respondent life (from birth up

to the interview) Residential trajectory

Is simple; it’s a formed by one lifeline – Home tenure episodes and home related events (rent, buy, sell, etc.)

Household trajectory Is more complex; it relates 3 types of lifelines – Marital status

(including identification of successive spouses, union, separation) – Children (ordering events and episodes related to children : birth, adoption, departure after a divorce) – Household lifeline makes the synthesis of any family change

Professional trajectory Is complex; it relates 4 types of lifelines – Educational (including

degrees), Occupational (mix of independent or simultaneous jobs) and Work place histories – They combine to form the Professional lifeline

Spatio-temporal Database Modelling

Episode

PK EpisodeId

FK3,I3 SpatialIdFK1,I1 LifeLineIdFK2,I2 RespondId

EpisodeSequences

PK EpChainId

FK1,I1 EpBeforeIdFK2,I2 EpAfterId

is before

is after

ActingIndividuals

PK ActingId

FK2,I2 PersonIdFK1,I1 EpisodeId

involves

Individual

PK PersonId is

Respondent

PK,FK1,I1 RespondId

is

belongs to

LifeLines

PK LifeLineIdbelongs to

Trajectories

PK TrajectId

LifeDimension

PK LifeDimId

FK1,I1 LifeLineIdFK2,I2 TrajectId

has

has

Spatial

PK SpatialIdhas

MAPINFO_MAPCATALOG

U1 TABLENAME

Episodesand events

Link to GISspatialware

Orderedtime

Links topersons

Ontology oftrajectoriesand lifelines

Lifeline

Episode

is before > < is after

Eve

nt

Eve

nt

Episode Episode

The core of the spatio-temporal model is formed by an EPISODE table combining events and episodes ordered by the EpisodeSequences table.

The ontology of lifelines and trajectories is stored directly in the database, and each event and episode is typified

Episodes are related to the respondent, but also to any other acting individual in the household (E.g. linking the respondent to his/her spouse)

Every episode and event is related to space through the SPATIAL table providing locations managed by Spatialware functionalities (E.g. ODBC link with Access)

Modelling of Residential Trajectory

The Residential trajectory is made of only one lifeline describing the attributes and occupation modes of successive homes inhabited by the respondent during his/her adult life

Each home is located in space using street addresses and location is managed, for each episode, by the SPATIAL table

Integrity constrains are enforced

GIS operations are realized within MapInfo using ODBC technology with Spatialware features generating points in Map Views

Episode

PK EpisodeId

FK3,FK4 RespondIdFK2 SpatialIdFK1 LifeLineId

Home

PK,FK1,I1 HomeId

FK2 PersonId

is

Respondent

PK,FK1 RespondId

belongs to

inhabited by

EventsRent, Buy, Inhabit

EpisodesTenant, Owner, Cotenant or roomate

Residentialepisodes

Spatial

PK SpatialId

has

The Home lifeline handle home tenure related events (Rent, Buy, Inhabit) and episodes (Tenant, Owner, Cotenant, etc.)

Modelling of Household Trajectory

Respondent

PK,FK1,I1 RespondId

Household

PK,FK1 HoushldId

FK3 RespondIdFK2 SpouseIdFK4 Child1Id

Episode

PK EpisodeId

FK3,I3 SpatialIdFK1,I1 LifeLineIdFK2,I2 RespondId

belongs to

Child

PK,FK1,I1 ChildId

FK2,I2 PersonId

has

Marital

PK,FK1,I1 MaritalId

FK2 RespondIdFK3 PersonIdFK4 SpouseId

has

Spouse

PK,FK1,I1 SpouseId

FK2,I2 PersonIdFK3 RespondId

has

Individual

PK PersonId

is

is

is

is

has

has

has

has

Householdepisodes

Householdcomposition

EventsMarital : Alone, Union, Separation

Children: Birth, Arrival, Departure, Adoption

EpisodesMarital : Single, Couple, Separated

Children: At home, Departed from homeHousehold: Composition episode

has

hashas

Modelling of Professional Trajectory

EventsEducational : Begin education, College

Degree, Bachelor Degree, Master Degree,PhD Degree, PDF completed, End educationOccupational : Begin a new job,End a job,Become unemployed, End unemploymentWork place : Change to a new work place

EpisodesEducational : Attending College,

University, SchoolOccupational :Job episode,

Unemployment episodeWork place : Work place episode

Professional : Status episode

Episode

PK EpisodeId

FK3,FK4 RespondIdFK2 SpatialIdFK1 LifeLineId

Respondent

PK,FK1 RespondId

belongs to

Education

PK,FK1 EpisodeId

FK2 DiplomaId

Diploma

PK,FK1,I1 DiplomaId

FK2,I2 PersonId

is awarded

has

Occupation

PK,FK1 EpisodeId

Profession

PK,FK3,FK4 EpisodeIdPK,FK1 ProfessId

is

ends

has

is

has

is

has

has

has

Professionalstatus

Professionalepisodes

WorkPlace

PK,FK1 WPlaceId

is

Spatial

PK SpatialId

has

has

Querying Using Temporal Sequence Views These trajectories and

lifelines are related into a unified database structure describing their successive temporal, spatial and thematic attributes

The relational model allows for building relationships across lifelines, events and trajectories using state transition views similar to the example shown here

These integrated views are later used to ease formulation of spatio-temporal query building ad hoc event history datasets needed for statistical analysis

Episode_Transition

PersonId N-Decimal(10,0)Gender C-Fixed Length(1)BirthDate T-DateEpis1Id N-Decimal(10,0)Epis1Name C-Variable Length(40)Epis1LifeL C-Variable Length(40)Epis1Beg T-DateEpis1End T-DateEpis1Dur N-Decimal(10,0)Epis1Age N-Decimal(10,2)Epis1Spatial N-Decimal(10,0)Epis1Munic C-Variable Length(40)Epis1Neighb C-Variable Length(40)Epis1Long N-Floating PointEpis1Lat N-Floating PointEventId N-Decimal(10,0)EventName C-Variable Length(40)EventBeg T-DateEventEnd T-DateEventDur N-Decimal(10,0)EventAge N-Decimal(10,2)EventSpatial N-Decimal(10,0)EventMunic C-Variable Length(40)EventNeighb C-Variable Length(40)EventLong N-Floating PointEventLat N-Floating PointEpis2Id N-Decimal(10,0)Epis2Name C-Variable Length(40)Epis2LifeL C-Variable Length(40)Epis2Beg T-DateEpis2End T-DateEpis2Ended L-True or FalseEpis2Dur N-Decimal(10,0)Epis2Age N-Decimal(10,2)Epis2Spatial N-Decimal(10,0)Epis2Munic C-Variable Length(40)Epis2Neighb C-Variable Length(40)Epis2Long N-Floating PointEpis2Lat N-Floating Point

EpisEvent

Epis1Id N-Decimal(10,0)Epis1Name C-Variable Length(40)Epis1LifeL C-Variable Length(40)Epis1Beg T-DateEpis1End T-DateEpis1Ended L-True or FalseEpis1Spatial N-Decimal(10,0)Event2Id N-Decimal(10,0)Event2Name C-Variable Length(40)Event2Beg T-DateEvent2End T-DateEvent2Ended L-True or FalseEvent2Spatial N-Decimal(10,0)

EventEpis

PersonId N-Decimal(10,0)Gender C-Fixed Length(1)BirthDate T-DateEvent1Id N-Decimal(10,0)Event1Name C-Variable Length(40)Event1Beg T-DateEvent1End T-DateEvent1Ended L-True or FalseEvent1Spatial N-Decimal(10,0)Epis2Id N-Decimal(10,0)Epis2Name C-Variable Length(40)Epis2LifeL C-Variable Length(40)Epis2Beg T-DateEpis2End T-DateEpis2Ended L-True or FalseEpis2Spatial N-Decimal(10,0)

Event_Transition

PersonId N-Decimal(10,0)Gender C-Fixed Length(1)BirthDate T-DateEvent1Id N-Decimal(10,0)Event1Name C-Variable Length(40)Event1Beg T-DateEvent1End T-DateEvent1Dur N-Decimal(10,0)Event1Age N-Decimal(10,2)Event1Spatial N-Decimal(10,0)Event1Munic C-Variable Length(40)Event1Neighb C-Variable Length(40)Event1Long N-Floating PointEvent1Lat N-Floating PointEpisId N-Decimal(10,0)EpisName C-Variable Length(40)EpisLifeL C-Variable Length(40)EpisBeg T-DateEpisEnd T-DateEpisEnded L-True or FalseEpisDur N-Decimal(10,0)EpisAge N-Decimal(10,2)EpisSpatial N-Decimal(10,0)EpisMunic C-Variable Length(40)EpisNeighb C-Variable Length(40)EpisLong N-Floating PointEpisLat N-Floating PointEvent2Id N-Decimal(10,0)Event2Name C-Variable Length(40)Event2Beg T-DateEvent2End T-DateEvent2Dur N-Decimal(10,0)Event2Age N-Decimal(10,2)Event2Spatial N-Decimal(10,0)Event2Munic C-Variable Length(40)Event2Neighb C-Variable Length(40)Event2Long N-Floating PointEvent2Lat N-Floating Point

EpisodeOut

Episode Event

EpisodeIn

ActingIndividuals

Individual

Spatial

Episode – Event - Episode Event – Episode - Event

Linking to Event History Regression Analysis

Most of the phenomena discussed in this research may be thought as events These events and their possible relationships are recorded using RDBMS We want to submit to statistical analysis these data and expressions based

on them in order to build event history models Ordinary multiple regression is ill-suited to the analysis of biographies,

because of two peculiarities: censoring and time-varying explanatory variables

Censoring refers to the fact that the value of a variable may be unknown at the time of survey, generally because the event did not occur (E.g. duration of marriage for a person who never divorce)

Considering time varying explanatory factors To study the effect of the family composition on residential location choice,

one needs to consider time-varying information A bio-statistical method called event history regression analysis can handle

such a problem (it combines survival tables and logistic regression) Our approach enable data restructuring that fulfil requirements for this

kind of statistical analysis

Event History Analysis

Survival tables are using conditional probabilities to estimate the mean proportion of people experiencing some change in their life after a significant event occurs (E.g. proportion of tenants buying a home after the arrival of the second child), computing the time delay after a specified enabling event (E.g. time to divorce after marriage)

However, these probabilities are not exactly the same for everyone because specific conditions may influence propensity to change

Finding those specific factors that condition individual propensity to do something requires a combination of survival tables and logistic regression in order to estimate the marginal effect of other personal attributes on the probability that an event occurs

The purpose of Event History Analysis (also called Cox Regression) is to model specific variations of the probability of state transition through time for individuals considering independent (even time-varying) variables describing their personal situation on other lifelines (E.g. What is the marginal effect of a 6-month unemployment period occurred less than five years ago, on the propensity to buy a home after the second child is born? Is their a significant effect? Is this effect stable over time and space?)

Survival Function

Proportion de locataires résiduels

Temps écoulé depuis le départ du foyer parental (années)

403020100-10

Cu

m S

urv

iva

l

1.2

1.0

.8

.6

.4

.2

0.0

COHORTE

2.00

1.00

One Minus Survival Function

Proportion de propriétaires

Temps écoulé depuis le départ du foyer parental (années)

403020100-10

On

e M

inu

s C

um

Su

rviv

al

1.0

.8

.6

.4

.2

0.0

-.2

COHORTE

2.00

1.00

Cohorts:1: respondents in their thirties2: respondents in their forties

Proportions of Tenants and Home-Owners Related to Time Elapsed Since Departure From

Parent’s Home (survival rates)

Time elapsed since departure from parent’s home (years)

Time elapsed since departure from parent’s home (years)

Proportion of tenants

Proportion of home-owners

Cohort

Cohort

Survival Function

Proportion de locataires résiduels

Âge du répondant (années)

50403020100

Cu

m S

urv

iva

l

1.2

1.0

.8

.6

.4

.2

0.0

COHORTE

2.00

1.00

One Minus Survival Function

Proportion de propriétaires

Âge du répondant (années)

50403020100

On

e M

inu

s C

um

Su

rviv

al

1.0

.8

.6

.4

.2

0.0

COHORTE

2.00

1.00

Cohorts:1: respondents in their thirties2: respondents in their forties

Proportions of Tenants and Home-Owners Related to Respondent’s Age (survival rates)

Respondent’s Age (years)

Proportion of tenants

Proportion of home-owners

Cohort

Cohort

Respondent’s Age (years)

Spatio-temporal Analysis of Retrospective DataAn Example

Study individual behaviour of persons making home-location choices under various conditions linked to their own personal history, considering the three trajectories

The retrospective survey and its implementation within a temporal GIS providing event-ordering functionalities will further our understanding of their strategies for moving through the city considering their own history, the impact of growing family, of changes in work place, their educational status, income, home price, stability in employment, etc.

The next slide shows a preliminary event-history model of the propensity of tenants to buy a house after the birth of their first child

It was realised with a very preliminary version of the spatio-temporal database, but can help understand the advantages of such an approach

Event History Analysis Results What are the factors influencing the decision of tenants to buy a

house (with some delay) after their first child is born? Is there significant differences among persons? Yes (Chi Square)

Are their behaviour stable over time? No (Significant variations of propensity over time)

What are the factors influencing the propensity of changing status from tenant to home-owner? 1- Stability in employment, 2- Decade during which the child was born (time varying behaviour), 3- Willingness to move towards remote locations (related to house prices)

EPIS2DUR : Duration of stay at destination home (Years)

0.137 0.019 50.65 1 0.000 1.147

DIST : Distance from child birthplace to new home location (Km)

0.007 0.002 12.545 1 0.000 1.007

PERIODB : Decade of birth of the first child 26.687 3 0.000

Period60 1960-69 -2.115 0.734 8.311 1 0.004 0.121Period70 1970-79 -1.574 0.485 10.53 1 0.001 0.207Period80 1980-89 -0.267 0.426 0.393 1 0.530 0.765

Reference Period90 1990-95 0 1

Chi Square = 61.314; df = 5; probability < 0.0001

df Sig.Odds

B SE Wald Be

Preliminary model of propensity of tenant for buying a home after the first child is born

units quantities coefficient effectDuration of residential episode in the new house(proxy for employment status and stability) years 5 0.137 1.983772

Distance between the place where the child was born and the new home locationkm 5 0.007 1.03562(proxy of willingness to move far away to enhance market opportunities)

Decade during with the child was born 1960-69 0 -2.115 1(retain only one choice) 1970-79 0 -1.574 1

1980-89 1 -0.267 0.7656731990-96 0 0 1

Time elapsed after the first child is born years 2 Odds ratio 1.573024Survival table cumulative proportion 30.0%

Marginal probability 61.1%Probability to buy a house 18.3%

Example of Application in Excel(Activate the Spreadsheet to set parameters)

Event History Statistical Model

Survival Functions of Tenants After the First Child is Born (Cumulative proportions)

00.10.20.30.40.5

0.60.70.80.9

1

0 5 10 15 20

Years after the birth of the first child

Cu

mu

lati

ve

pro

po

rtio

n

Tenant

Home owner

Event History Analysis ResultsPropensity of Tenants to Buy a Home Conditional to

Decade and Elapsed Time after Birth of the First Child

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Years after birth of first child

Prob

abili

ty o

f bei

ng h

ome

owne

r

1960-69

1970-79

1980-89

1990-95

Propensity of Tenants to Buy a Home Conditional to Employment Status and Elapsed Time after

Birth of the First Child

0

0.2

0.4

0.6

0.8

1

0 5 10 15 20

Years after birth of first child

Pro

babi

lity

of b

eing

ho

me

owne

r Unstable

Stable

Very stableRate of access to property

ownership significantly increases through time

- from the sixties to the eighties

Stability in employment increases propensity to buy a home

Discussion and Conclusion The proposed database modelling approach is classical

It uses entity-relationship principles, combined with geo-relational technology

With the exception of minor enhancements to existing methods, the purpose was not to contribute to the advance of STDB modelling

Contribution To the best of our knowledge, this type of application for the spatial

monitoring of changes in population behaviour is original Keeping track of dynamics within GIS database is a very important

requirement for urban and transportation planning Towards a generic spatio-temporal life trajectories ST schema

Multidisciplinary approach Combining TGIS and event history analysis provide methodology well

suited for behavioural modelling applications We are now developing application-independent dialogs for querying

this spatio-temporal structure and build projections yielding flat files needed for statistical analysis using SPSS, SAS or SPlus