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