Flora Macleod and Paul Lambe
School of Education and Lifelong Learning
St Luke’s Campus
Heavitree Road
University of Exeter
Exeter
f.j.macleod@exeter.ac.uk
p.j.lambe@exeter.ac.uk
Time invariant and time varying influences on the
likelihood of participation in post compulsory formal
learning opportunities
A paper presented as part of the symposium ‘Dimensions of Diversity in
University Learning’ at the Society for Research into Higher Education’s
Annual Conference 12-14 December, 2006, Brighton, UK: Beyond
Boundaries New Horizons for Research into Higher Education
This working paper was produced as part of the Learning Lives Project. Copyright lies with the authors. If you
cite or quote, please be sensitive to the fact that this is work in progress. The Learning Lives: Learning, Identity
and Agency project (see learninglives.org) is a collaboration between the Universities of Exeter, Brighton, Leeds
and Stirling and is funded by the Economic and Social Research Council as part of their Teaching and Learning
Research Programme (TLRP) see www.tlrp.org
Time invariant and time varying influences on the
likelihood of participation in post compulsory
formal learning opportunities
Flora Macleod and Paul Lambe, University of Exeter
Abstract
Policy makers place emphasis on enabling more people to take up post
compulsory education and training opportunities. However, there is little
longitudinal evidence on who actually participates over time. This paper takes a
life course perspective and uses event history frameworks to explore the power of
time invariant and time varying predictors of whether and when a sample of 1997
initial phase leavers in England (n=463) return to adult learning for the first time.
Our data source, the British Household Panel Survey (BHPS), allowed us to track
these leavers over a six-year period (1997-2003). We found that the occurrence
and timing of the first adult education episode was influenced by the time invariant
individual characteristics of gender, qualifications, occupational status, household
per capita income and household tenure upon leaving initial full time education
and the time varying role transitions into marriage/cohabitation, unemployment
and parenthood. The paper concludes by outlining how next phase of analysis is
exploring the power of these early influences and the timing of role transitions for
an individual’s learning trajectory.
Key words: time-invariant predictors, time-varying predictors, event history
analysis, panel data, gender differences, early adulthood, income status
Introduction
Returning to adult education or training is an event that will eventually occur for
more than two thirds of us in the UK. The reasons why most of us return are
various and have, from an adult education policy perspective at least, changed
over time. Traditionally adult educationalists, notably Friere (1970), emphasised
grander outcomes for adult education such as improving the lot of mankind
through growth, development, empowerment and emancipation than the more
mundane instrumental individual outcomes more prominent in current policy
documents. These include getting a better job or being able to do our current job
better.
Education is no longer seen by policymakers as a phase completed in the early
stages of life. Increasingly in the developed world participation in post initial
education is seen by those in power not just as an option but a duty for which
individuals must take responsibility as their employability and financial security
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depend on the continual acquisition of new skills and knowledge in relation to the
world of work (e.g. OECD, 2003). This shift has been recognised by economists
who, in the past, were more interested in studying the economic rates of return
from qualifications obtained in initial education (e.g. Bundell, et al 1999) are now
beginning to study the economic benefits of education undertaken by adults (e.g.
Jenkins, 2006). So it seems that, on the one hand, policy makers are pushing for
continual skill (re) formation as a necessary response to a rapidly changing society
and an ever-expanding skill need within the labour market and, on the other, there
is a growing body of evidence that appears to suggest that participation in adult
education leads to improved employment prospects and well being.
Yet, in spite of all the attention being given to post compulsory education and
training by politicians, economists and educationalists, the area remains undertheorized and under-explored using reliable longitudinal quantitative data. To the
best of our knowledge there has been no systematic analysis on when the initial
transition into adult education takes place, for how many and for whom the
transition never takes place at all and identification of the factors that constrain or
release an individual to make the transition. This area of investigation is important
not least because standard explanations tend to be that determinants of
participation in adult education predate the first adult education episode (Gorard
and Rees, 2002). That is, the factors that determine whether an individual
participates early in adult education opportunities also determine their participation
(or non-participation) patterns later in the life course. This paper is an attempt to fill
this gap by focusing on a cohort of young people in England and following them
through for a six year period.
The purpose of the paper is to answer two questions: (1) how long does it take
leavers from initial full time education to return to adult education? (2) Can we
predict the likelihood of an early return from a selection of time invariant and time
varying predictors? We consider both time variant and time varying predictors
important as decisions to participate (or not to participate) must be seen alongside
the complexities of the social context in which individuals find themselves at a
given point and place as well as their personal and social background
characteristics. By including time-varying predictors we can study how social role
changes over time shape the likelihood of an early return to adult education.
Theoretical framework
Time invariant predictors are relatively straightforward to identify as they describe
those stable characteristics of an individual like their gender or some other static
status such as qualifications at a given point which remain immutable over time.
The ones we use here are gender and various background characteristics such as
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qualifications at the point of leaving and occupational status, household per capita
income and household tenure during the first year from leaving.
Time varying predictors are more complex as they are those values that may differ
over time and are frequently subject to natural change such as moving from school
to work. To help us identify these we take a life course perspective. Specifically we
draw on Elder’s (1985) conceptualization of the life course as a series of
interlocking trajectories of social roles over time. Movement through a social
institution normally involves taking on an institutionally defined role such as being
a student, an employee, a husband or wife, a mother or father with each role
configuration giving an indication of the extent to which a particular individual is
embedded in a given social institution over time. Trajectories are seen as
longitudinal involvement in or connection to social institutions such as work,
marriage and parenthood. Entry into (and exit from) these often ordered and age
structured social institutions is normally characterized by an event such as getting
married, getting divorced. The specific event that moves an individual into or out of
a life course institutional context is referred to as a transition. Transitions indicate
when a particular trajectory of a given social role begins, ends, and lasts.
Trajectories and transitions are thus useful conceptual tools when it comes to
identifying the value of a time-varying predictor at a given point as the life course
unfolds. The ones we are interested in here are movement from paid employment
to labour market inactivity, entry into marriage or cohabitation and procreation. Our
intention here is to study how experiencing these role transitions impacts upon
decisions to participate or not in adult education.
Methodology and methods
Data and sample
Our source of data is the British Household Panel Survey (BHPS) waves 8 to 13
(1997-2003). The BHPS uses a representative sample (5000+) of UK household
resulting in 10,000+ individual interviews. Our sample was made up of all BHPS
respondents living in England who had left initial full time education at some point
between wave 7 (1997) and wave 8 (1998). 463 individuals aged between 16 and
23 (at wave 8) in England who at the BHPS 1998 interview (wave 8) were
recorded as not being in full time education but who were recorded as being in full
time education at the 1997 (wave 7) BHPS interview were identified as eligible to
enter our sample. Because the BHPS interview takes place between September
and November each year, these 463 individuals can be said to have left initial full
time education at some point between September/November 1997 and
September/November 1998.
Event history analysis
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How long it takes a leaver to become a returner might seem a straightforward
enough question. Yet it is a question that is fraught with methodological difficulty.
Event occurrence represents an individual’s transitions from one “state” to another.
In this paper state one is represented as “being a non-returner” and state two is
represented as “being a returner”. The methodology does not permit definition
overlap. So, in order to track the occurrence of an event and its timing, the state of
being a non-returner and being a returner must be mutually exclusive such that
each member of our sample can only occupy one of the two states at a given point
in time. As our interest here is in whether a target event occurs at all during the
period for which data are available and, if it does, when it occurs during that
period, we must have a clear definition of our target event that will allow us to
make a clear distinction between each state. This condition must be met so that
we can pinpoint the timing of the transition if or when it occurs.
Our target event
The point of transition of central interest is moving from being a leaver to “being a
returner”. As pinpointing this transition is primarily a measurement issue precision
and clarity is essential. To achieve this we had to settled for a definition of ‘being
a returner’ that would unambiguously indicate what constituted one state and what
constituted another. We operationalised our target event as “return to adult
learning for the first time” by using one BHPS item requiring a “yes” or “no”
response which was asked at all waves since 1998. That question was:
(Apart from the full-time education you have already told me about)
Have you taken part in any other training schemes or courses at all
since September 1st [the previous year] or completed a course of
training which led to a qualification? Please include part-time college
or university courses, evening classes, training provided by an
employer either on or off the job, government training schemes,
Open University courses, correspondence courses and work
experience schemes. (interviewees were instructed not to include
leisure courses)
In settling for this definition we fully acknowledge its limitations in that it represents
only a very particular subset of all lifelong learning. However, we judged that this
question represented a meaningful basis for our analysis because it tapped into a
wide range of adult learning provision leading potentially to the full range of
qualifications available to adults studying in England from the lowest to the
highest.
Measuring the passage of time
All members of our sample were asked the above question in1998, 1999, 2000,
2001, 2002 and 2003. Our interest was purely in identifying the first time they
5
answered “yes”, or more precisely, the first BHPS wave at which they answered
“yes”. For example at wave 8 (1998), our sample of leavers who had left school at
some point between this wave and the previous one were asked “……..Have you
taken part in any other training schemes or courses at all since September 1st
1997 …….” Thus they were being asked to reflect back on the year in which they
had left initial full time education and say whether they had had any spells of adult
learning formally organised on a part-time basis since they had left. Those who
answer “yes” leave our sample at this point because they have experienced our
target event and are thus no longer eligible to experience it for the first time again.
Those who remain have their wave 9 (1999) responses examined. If they answer
“yes” at wave 9 they leave, if “no” they remain in the sample and so on until we
reach a wave where they answer “yes”. If they had not answered “yes” by the
2003 BHPS interview they were ‘right-censored’ meaning they left at the end of the
period for which information is available having yet to experience the target event.
The metric for recording the passage of time is BHPS waves, that is, one yearly
discrete time intervals from September 1, 1997 or the point thereafter when they
left initial full time education prior to the 1998 interview. This is because the
“beginning of time” in this paper is the point at which sample members became
eligible to experience the target event. According to how we defined our target
event, it could not happen until after completion of full time initial education. There
is thus no ‘left-censoring’ meaning everyone is in state one at the “beginning of
time” because each individual in the sample is a non-returner until they become a
returner.
As we do not know precisely when between wave 7 (1997) and wave 8 (1998)
respondents actually left full time initial education, this means that during year 1
(1st Sept 1997 – 1998 BHPS interview date) members of our sample could have
had a longer or shorter period of eligibility to experience the event. For example,
someone who left initial full time education on 1st October 1997 would have been
eligible to experience the event from that date to the 1998 interview date, whilst
someone who left initial full time education on 31st July 1998 would only have been
eligible from that date to the 1998 interview date – the latter period being a
substantially shorter period than the former and both being less than one full year.
Also for this initial discrete time period the data do not allow us to differentiate
between participation pre and post leaving, should the former have occurred.
Models and statistical methods
As the possibility of each sample member experiencing the target event, is in
discrete 12 month intervals or periods of time (BHPS waves), a discrete event
6
history model is appropriate for our analysis. The application of regular statistical
tools such as means and standard deviations is, however, inappropriate. This is
because there are individuals for whom information on the occurrence and timing
of the event is not available and excluding these cases would produce misleading
results. To get round the problem of right censored cases (i.e. cases who leave at
the end of the observation period without having experienced the event) three new
statistical ways of summarising data are introduced: the hazard function, the
survival function and the median lifetime (Singer and Willett, 2003). The
terminology surrounding time duration methodology, such as survival and hazard
functions, has mainly come from its two main areas of application, medicine and
economics, where the first event is called the original event and the second is
typically referred to as death or failure. Medical researchers are interested in how
long patients survive after treatment.
The main tool for describing event occurrence is the ‘life table’ which provides
three key statistics: the median lifetime, the hazard function and the survival
function. The median lifetime identifies the point in time at which half the sample
members are estimated to have experienced the target event. The hazard function
assesses the risk of the target event occurring among those eligible to experience
it within each discrete time period. The survivor function assesses the probability
that a given individual will survive from one discrete period to the next without
having experienced the event.
Findings
For our methodology tabular and graphic displays are powerful ways of identifying
and summarising trends over time.
All 1997 Leavers
The answer to our first research question is presented in table 1 which shows that
the average time it took our cohort of 1997 leavers to become returners was just
under three years. Average in a time table represents the median time, that is the
time it took for 50% of the sample to experience the event. Table 1 also shows that
at the end of the six year period of observation more than a quarter of the sample
(27% n=124) had yet to return.
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Table 1: Life Table Showing the Proportion of 1997 Initial Phase Leavers
Returning to Learning between 1998 and 2003
Time
interval
1998
1999
2000
2001
2002
2003
Respondents
at risk of
event
463
306
221
184
160
142
↑RISK SET
Event = 0
Event =1
Proportion
Event =1
Proportion
Event = 0
306
221
184
160
142
124
157
85
37
24
18
18
0.3391
0.2777
0.1674
0.1304
0.1125
0.1268
↑HAZARD
FUNCTION
0.6609
0.4773
0.3974
0.3456
0.3067
0.2678
↑SURVIVOR
FUNCTION
This shows that the average time it took our cohort of leavers to become returners
was just under three years. Average here represents the median time, that is the
time it took for 50% of the sample to experience the event. Table 1 also shows that
just under a third of our sample (31%, n=142) had yet to return.
The hazard function for the whole sample is shown in figure 1a and the survivor
function in figure 1b. Figure 1a is diagrammatic representation of the percentage
of the sample at risk of event of returning happening within each time period
(BHPS wave). The slope of the graph’s line shows that the risk of becoming a
returner was at its highest in the time period immediately after leaving but by three
years after leaving (2000) if a leaver had not yet become a returner their chances
(risk) of returning was greatly reduced and reached in lowest point in 2002. In
figure 1b, which shows the survivor function’s trajectory over time with the median
lifetime plotted across the trajectory, shows the percentage within each time period
that ‘survived’ without experiencing the event of returning with 27% surviving
beyond the period of observation.
8
Figure 1a: Hazard Function:
Lifetime:
All 1997 Leavers (n=463)
Figure 1b: Survivor Function and Median
All Leavers (n=463)
0.35
Hazard Function Sample
0.30
0.25
0.20
0.15
0.10
1998
1999
2000
2001
2002
2003
Year
Gender
When controlled by gender, figures 2a and 2b, the shape of the hazard functions
for female and male leavers were different. Although the probability of participation
within the first year after leaving is almost equal for males and females, as the
divergence of the hazard plot lines in figure 2a show, the probability for females
returning diminishes and within two years of leaving full-time education the
estimated probability of females becoming returners is almost a half of that of
males (see also tables 2 and 3). The relative level of hazard differs significantly by
gender, with the hazard function consistently higher for males than for females
over five of the six years after leaving. This difference evidences that the
conditional probability of becoming a returner is greater for the males in our
sample than for the females, and that this differential persists over time. In Figure
2b the intersection of the median lifetime and the plot lines for males and females
indicates that by the end of the second year after leaving half of the males and half
of the females in the sample had returned, however thereafter the cumulative
9
probability of female returning is persistently lower than that of males. Gender is
thus an important predictor in the probability of returning to adult learning.
Figure 2a: Hazard Function Contrasted by Gender
Median Lifetime
(females = 223 females, males = 240)
Figure 2b: Survivor Function and
Contrasted by Gender,
(females= 223, males =240).
Table 2: The Probability of an Early Return to Adult Education among Female 1997
Initial Phase Leavers (n=223)
Time
interval
1998
1999
2000
2001
2002
2003
Respondents
at risk of
event
223
149
110
92
82
71
↑RISK SET
Event = 0
Event =1
Proportion
Event =1
Proportion
Event = 0
149
110
92
82
71
63
74
39
18
10
11
8
0.3318
0.1748
0.1636
0.1087
0.1341
0.1127
↑HAZARD
FUNCTION
0.6682
0.4933
0.4126
0.3677
0.3183
0.2825
↑SURVIVOR
FUNCTION
10
Table 3: The Probability of an Early Return to Adult Education among Male 1997
Initial
Phase Leavers (n=240)
Time
interval
1998
1999
2000
2001
2002
2003
Respondents
at risk of
event
240
157
111
92
78
71
↑RISK SET
Event = 0
Event =1
Proportion
Event =1
Proportion
Event = 0
157
111
92
78
71
61
83
46
19
14
7
10
0.3458
0.2930
0.1711
0.1522
0.0897
0.1408
↑HAZARD
FUNCTION
0.6654
0.4625
0.3833
0.325
0.2958
0.2542
↑SURVIVOR
FUNCTION
Our other explanatory variables
Above we have showcased our analytic approach using the gender variable but
space does not permit a similar tabular and graphic displays for our other
explanatory variables even although tables and graphs are the most powerful
ways of identifying and ummarising trends over time. So, in summary, further
analysis controlling by qualifications on leaving, employment status at wave 8
(1998), parent’s (i.e. main earner’s) occupation at age 14, household per capita
income at wave 8, household tenure at wave 8, urban/rural dwellers at wave 8,
those who experienced a role transition into marriage/cohabitation during of
observation contrasted by those who had not, those who experienced a role
transition into parenthood contrasted by those who had not, those who had
experienced a role transition from employment to unemployment contrasted by
those who had not, those who had moved and most were found to be important
predictors.
Informed by these analysis we were able to specify statistical models to test the
power of each of these predictors by quantifying their effects. We hypothesised
that leavers will have different hazard functions if they have different values on
observed predictors. As discrete time models use binary variables (1- event
occurrence, 0=event non-occurrence) logistical regression can be used to fit
models to the data. In this analysis the closer the logit coefficient, that is the odds
11
ratio of event occurrence, is to 1.0 the more likely it is that the event will happen
with equal parity in the two groups being compared e.g. males/females. For
example if an odds ratio is 1.0 then the odds are even for both groups. If the odds
ratio is greater than 1.0 then the event is more likely to happen and less likely if
the odds ratio is less than 0.1.
The findings of this analysis are summarized below:








The estimated odds of females returning to adult education in any one of
the six discrete timeframes were 84% of those for males.
The estimated odds of those who had left initial phase education with no or
low qualifications were 51% of those who left with qualifications.
The estimated odds of those whose status was recorded as unemployed in
1998 returning were 54% of those who were recorded as employed.
The estimated odds of those whose household per capita income was
recorded as ‘poor’ in 1998 returning were 74% of those recorded as ‘not
poor’.
The estimated odds of those whose household tenure in 1998 was
recorded as non-owner/occupier returning was 70% of those who were
recorded as owner/occupiers
The estimated odds of those who experience a role transition into
marriage/cohabitation during the period of observation returning was 66%
of those who did not experience this role transition
The estimated odds of those who experienced a role transition into
parenthood returning was 37% of those who did not experience this role
transition
The estimated odds of those who experienced a role transition from paid
employment to labour market inactivity returning were 50% of those who did
not experience this role transition.
Discussion
These findings support the view that decisions to participate (or not to participate)
in formal learning opportunities must be considered alongside the complexities of
the social context in which adults find themselves at a given time and place as well
as their personal and social background characteristics. They raise important
questions about the link between temporal patterning found in early adulthood and
subsequent life paths followed. Our analysis is ongoing and this paper represents
only a sample of our emerging findings. The next step in our analysis, which is
now well underway, is to explore the extent to which we can accurately predict an
individual’s education trajectory on the basis of characteristics largely known by
the time an individual leaves initial full time education and thus influence an early
return to education. If we find this to be the case it does not imply that human
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agency or life crises cannot impact on trajectories but rather that human agency
and experience occur within a framework of opportunities, influences and social
expectations that may or may not be determined independently. Indeed the next
step in our analysis will contribute to an understanding of human agency and its
interplay with society’s institutions in the shaping of lives over time.
Trajectories, that is long term patterns of stability and change often involving many
transitions, require a different methodology to event history frameworks. In order to
explore more fully the ways in which an individual’s adult education trajectory is
embedded in social relations more widely and over time we need to identify
patterns of typical trajectories that effectively encapsulate the complexity of
individual learning biographies. For this we will use latent class modeling
(Macmillan and Eliason, 2003) which allows us to effectively model the life course
as an institutional whole by conceptualizing it as probabilistically distributed paths
through age-graded role configurations.
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