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Thinking About Longitudinal Data

• (or Cross-sectional v Longitudinal Analysis)

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A glib claim that longitudinal data analysis is
important because it permits insights into the
processes of change is inadequate and certainly
fails to convince many social science researchers
who are concerned with substantive rather than
methodological challenges...
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What is required is an understanding on the
limitations of cross-sectional analysis.
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Cross-sectional V Longitudinal Data
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Four Main Issues

• Age and Cohort Effects
• Direction of Causality
• State Dependence
• Residual Heterogeneity

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Age And Cohort Effects
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Should I buy a new car?

• An example..

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Owners Experience Of Car Reliability Over The
Last Twelve Months - Specific Model
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What happens when these cars get older (ageing
effects)?
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Owners Experience Of Car Reliability Over The
Last Twelve Months - Specific Model
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The manufacture tells me that there is a cohort
effect The more recently made cars are now much
more reliable than the ones made five years
ago.Could this be true?
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Owners Experience Of Car Reliability Over The
Last Twelve Months - Specific Model
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• Cross-sectional data are completely
  uninformative as to whether age or cohort effects
  (or a combination of each) provide correct
  explanations. We would need longitudinal data to
  find out!

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Direction Of Causality
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There is unequivocal evidence from
cross-sectional data that, overall, the
unemployed have poorer health.
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This is consistent with botha) unemployment
causing ill health andb) ill health causing
unemployment
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Ill Health
?
Unemployment
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Ill Health
Unemployment
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If we had a cross-sectional survey that asked how
long people had been unemployed and also their
level of health, generally, we would find a
negative relationship.
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Negative Lower levels of health for people who
had been unemployed for longer.
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This is consistent with a) unemployment causing
ill health
Ill Health
Unemployment
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HOWEVER.
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If ill health causes unemploymentthen people
with comparatively modest levels of ill health
will tend to recover more quickly and return to
work.
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This is consistent with b) ill health causing
unemployment
Ill Health
Unemployment
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With the increasing duration of unemployment
those with less severe ill health will be
progressively under represented while those with
more severe ill health will be over represented.

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This is known as asample selection bias and
could therefore explain the cross-sectional
picture of declining ill health with duration of
unemployment.

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It is not possible to untangle this conundrum
with cross-sectional data.Longitudinal data are
required!
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State Dependence
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Past Behaviour
Current Behaviour
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Young People Aged 19
APRIL
MAY
Employed
Unemployed
Employed
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Residual Heterogeneity(Omitted Explanatory
Variables)
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• The advantage of longitudinal data over
  cross-sectional data is that it not only
  facilitates analysis between cases but also
  facilitates analysis within cases.

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A simplified view of a difficult concept!
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CROSS-SECTIONAL EXPLANATORY VARIABLES
OUTCOME
Person A
Person B
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My two hypothetical identical twin daughters
The Gayle sisters.
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CROSS-SECTIONAL EXPLANATORY VARIABLES
OUTCOME A
WENDY VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
BELOWNA VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
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This is often called between cases analysis.

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There is no way of accounting for omitted
explanatory variables in cross-sectional analysis.
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CROSS-SECTIONAL EXPLANATORY VARIABLES
OUTCOME A
WENDY VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
BELOWNA VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
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LONGITUDINAL EXPLANATORY VARIABLES
TIME POINT 1
TIME POINT 2
Person A
Person A
Person B
Person B
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This is often called within cases analysis.
There are techniques for accounting for omitted
explanatory variables if we have data at more
than one time point.
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TIME 2
OUTCOME A
WENDY VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
OUTCOME B
BELOWNA VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
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HOW GOOD HAVE THE EXPLANATORY VARIABLES BEEN AS
FAR AS HELPING US TO UNDERSTAND THE OUTCOME?
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TIME 2
WENDY VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
OUTCOME
Unexplained
BELOWNA VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
Unexplained
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RESIDUAL HETEROGENEITY
WENDY VARIABLE A1 VARIABLE B1 VARIABLE
C2 VARIABLE D2
Omitted Explanatory Variables
Unexplained
Unmeasured or Unmeasurable Variables
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• It is sometimes claimed that the main advantage
  of longitudinal data is that it facilitates
  improved control for the plethora of variables
  that are omitted from any analysis.

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• Because surveys fail to capture the detailed
  nature of social life there is, almost
  inevitably, considerable heterogeneity in
  response variables even amongst respondents that
  share the same characteristics across all of the
  explanatory variables.

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• The possibility of substantial variation between
  similar individuals due to unmeasured and
  possibly unmeasureable variables is known as
  residual heterogeneity.

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BEWARE

• We can begin to see why cross-sectional analysis
  might incorrectly estimate the effects of
  explanatory variables, and therefore result in
  misleading conclusions being drawn.

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• Cross-sectional V Longitudinal
• 0 4

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Four Main Issues

• Age and Cohort Effects
• Direction of Causality
• State Dependence
• Residual Heterogeneity

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THINKING ABOUT CHANGE

• COHORT A common group being studied.
• AGE Amount of time since cohort was
  constituted.
• PERIOD Moment of observation.

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THREE YOUTH COHORT STUDIES
AGE 16 17 18 19 20 21 (COHORT 1) AGE 16 17 18 19
(COHORT 2) AGE 16 17 (COHORT 3)
We can study the effects of age or ageing.
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THREE YOUTH COHORT STUDIES
AGE 16 17 18 19 20 21 (COHORT 1) AGE 16 17 18 1
9 (COHORT 2) AGE 16 17 (COHORT 3)
We can study the effects of cohort.
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THREE YOUTH COHORT STUDIES
AGE 16 17 18 19 20 21 (COHORT 1) AGE 16 17 18 1
9 (COHORT 2) AGE 16 17 (COHORT 3)
Period of high unemployment
Period of low unemployment
We can study the effects of period.
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Beware Age, Cohort and Period effects are often
very hard to untangle See the relevant
literature to become frightened and confused!
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Longitudinal data are not a panacea there are
problems