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What is… Quantitative Longitudinal Analysis? Paul Lambert and Vernon Gayle University of Stirling Prepared for: National Centre for Research Methods, Research Methods Festival, St Catherine’s College, Oxford, 2 July 2008. www.longitudinal.stir.ac.uk.

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www longitudinal stir ac uk
What is… Quantitative Longitudinal Analysis? Paul Lambert and Vernon GayleUniversity of StirlingPrepared for: National Centre for Research Methods, Research Methods Festival, St Catherine’s College, Oxford, 2 July 2008


July 2008: LDA

so what is quantitative longitudinal analysis
So what is quantitative longitudinal analysis?

You already know..

  • Working with (survey) datasets with longitudinal information (data about time) and the specialist techniques of statistical analysis that are appropriate

You maybe don’t realise..

  • Complex data and data management components
  • Groups of techniques and data types
  • Reasons why longitudinal analysis is advocated

July 2008: LDA

quantitative longitudinal research in the social sciences
Quantitative longitudinal research in the social sciences
  • Survey resources
  • Longitudinal
    • Data concerned with more than one time point
      • [e.g. Taris 2000; Blossfeld and Rohwer 2002]
    • Repeated measures over time
      • [e.g. Menard 2002; Martin et al 2006]

Data analysis is used to give a parsimonious summary of patterns of relations between variables in the survey dataset

July 2008: LDA

motivations for qnla
Motivations for QnLA
  • Focus on change / stability
  • Focus on the life course
      • Distinguish age, period and cohort effects
      • Career trajectories / life course sequences
  • Focus on time / durations
      • Substantive role of durations (e.g. Unemployment)
  • Getting the ‘full picture’
      • Causality and residual heterogeneity
      • Examining multivariate relationships
      • Representative conclusions

[e.g. Abbott 2006; Mayer 2005; Menard 2002; Baltagi 2001; Rose 2000; Dale and Davies 1994; Hannan and Tuma 1979; Moser 1958]

July 2008: LDA

some comments on quantitative longitudinal analysis
Some comments on quantitative longitudinal analysis
  • Working with secondary surveys
    • Expense of long-term data collection
    • Complex data files, need good habits

in data management (using syntax)

    • In practical terms – lots of gruelling

computer programming

  • Resources for supporting researchers

Easy access to data, e.g.

    • http://www.data-archive.ac.uk/
    • http://www.esds.ac.uk/longitudinal/

Training in relevant analytical methods and data management, e.g.

    • http://www.longitudinal.stir.ac.uk/
  • Distinctive research traditions and research centres..

July 2008: LDA

research traditions methodology
Research traditions (methodology)
  • Statistical methods for quantitative longitudinal data
      • [esp. Dale & Davies 1994]
  • Research on data quality
    • Variable constructions in longitudinal research
      • www.longitudinal.stir.ac.uk/variables/
      • Harmonisation, standardisation, comparability
    • Missing data and attrition

July 2008: LDA

research traditions applications
Research traditions (applications)
  • ‘geographers study space and economists study time’ [adage quoted in Fotheringham et al. 2000:245]
    • Vast economics literature using techniques for temporal analysis
    • Other social science disciplines are mostly catching up
    • ..we’ll come back to geography later
  • Data expansions c1990 -> new substantive applications areas
    • For example:
    • [Platt 2005] - ethnic minorities’ social mobility 1971-2001
    • [Pahl & Pevalin 2005] – Friendship patterns over time
    • [Verbakel & de Graaf 2008] – spouses effect on careers 1941-2003
    • Here, one critical challenge is getting used to talking about time in a more disciplined way: e.g. traditional sociological characterisations of ‘the past’ and ‘social change’ may not be empirically satisfactory

July 2008: LDA

some detail five traditions in quantitative longitudinal analysis cf www longitudinal stir ac uk
Some detail: Five traditions in Quantitative Longitudinal Analysis cf. www.longitudinal.stir.ac.uk

July 2008: LDA

repeated cross sections
Repeated cross sections
  • Easy to communicate & appealing: how things have changed between certain time points
  • Partially distinguishes age / period / cohort
  • Easier to analyse – less data management


    • Don’t get other QnLR attractions (nature of changers; residual heterogeneity; causality; durations)
    • Hidden complications: are sampling methods, variable operationalisations really comparable?
      • cf. http://www.longitudinal.stir.ac.uk/variables/ => measures are more often robust than not...

July 2008: LDA

example 1 1 uk census
Example 1.1: UK Census
  • Directly access aggregate statistics from census reports, books or web, e.g.:
  • Census v’s Surveys: larger scale surveys often have more data points and more reliable measures

July 2008: LDA

panel datasets
Panel Datasets

Information collected on the same cases at more than one point in time

  • ‘classic’ longitudinal design
  • incorporates ‘follow-up’, ‘repeated measures’, and ‘cohort’
  • Large and small scale panels are common

July 2008: LDA

panel data advantages
Panel data advantages
  • Study ‘changers’ – how many of them, what are they like, what caused change
  • Control for individuals’ unknown characteristics (‘residual heterogeneity’)
  • Develop a full and reliable life history
    • e.g. family formation, employment patterns

July 2008: LDA

challenges for panel data analysis
Challenges for Panel data analysis
  • Complex data analysis and data management
      • need for training & good habits (syntax programming)
  • Data issues
      • confidential data; time lag until most useful data
      • variable constructions and comparability
  • Unbalanced panels and attrition
    • Balanced data is still required for many analytical techniques
      • transition tables; dynamic effects; trajectory profiles
    • Unbalanced cases and attrition as missing data
      • Complete case analysis = ‘MCAR’
      • Ad hoc methods and imputatin
      • Missing data models, e.g. www.missingdata.org.uk

July 2008: LDA

analytical approaches
Analytical approaches

Panel data models:

Yit = ΒXit + … + Є

panel data model types
Panel data model types
  • Fixed and random effects
    • Ways of estimating panel regressions
  • Growth curves
    • Time effect in panel regression (cf. multilevel models)
  • Dynamic Lag-effects models
    • Theoretically appealing...

Analytically complex and often need advanced or specialist software

      • Econometrics literature
      • Stata / GLLAMM; R; S-PLUS; SABRE / GLIM; LIMDEP; MLwiN; MPLUS; …

July 2008: LDA

cohort datasets
Cohort Datasets

Information on a group of cases which share a common circumstance, collected repeatedly as they progress through a life course

  • Intuitive type of repeated contact data
    • e.g. ‘7-up’ series
  • Cohort comparisons
    • e.g. UK Birth cohort studies in 1946, 1958, 1970 and 2000

July 2008: LDA

cohort data and analysis in the social sciences
Cohort data and analysis in the social sciences
  • Many circumstances parallel other panel types:
      • Large scale studies ambitious & expensive
      • Small scale cohorts still quite common…
  • Attrition problems often more severe
  • Considerable study duration limits
  • Glenn (2005) argues that ‘cohort analysis’ should be specifically directed to understanding effects of ageing/progression over time
    • Other uses of cohort data are just = panel data
    • It remains hard - even with extensive cohort data - to authoritatively understand ageing effects (age = period – cohort)

July 2008: LDA

event history data analysis esp blossfeld et al 2007
Event history data analysis[esp. Blossfeld et al 2007]

Focus shifts to length of time in a ‘state’ -

analyses determinants of time in state

  • Alternative data sources:
    • Panel / cohort (more reliable)
    • Retrospective (cheaper, but recall errors)
  • Aka: ‘Survival data analysis’; ‘Failure time analysis’; ‘hazards’; ‘risks’; ..

July 2008: LDA

event histories differ
Event histories differ:
  • In form of dataset (cases are spells of time in a state)
    • Raises data management challenges
    • Comment: data analysis techniques are not well suited to complex variates; some argue than many Event History applications are artificially simplistic in their variables
  • In types of analytical method
    • Many techniques are new (and/or not well known), and specialist software may be needed
  • Time to labour market transitions
  • Time to recidivism
  • Time to end of cohabitation

July 2008: LDA

event history analysis software
Event history analysis software

SPSS – limited analysis options

Stata – wide range of pre-prepared methods

SAS – as Stata

S-Plus/R – vast capacity but non-introductory

GLIM / SABRE – some unique options

TDA – simple but powerful freeware

MLwiN; lEM; {others} – small packages targeted at specific analysis situations

July 2008: LDA

Sequences / Trajectories: characterise event history progression through states into clusters / sequences / frameworks
  • Growing recent social science interest

Optimal matching analysis / Correspondence analysis / log-linear models / Latent growth curves

  • Often analyse membership of cluster as an outcome

(Problem – neutrality of data, e.g., cluster 1= Men in full time employment)

July 2008: LDA

time series data
Time series data

Statistical summary of one particular concept, collected at repeated time points from one or more subjects


  • Unemployment rates by year in UK
  • University entrance rates by year by country


    • Panel = many variables few time points

= ‘cross-sectional time series’ to economists

    • Time series = few variables, many time points

July 2008: LDA

time series analysis
Time Series Analysis
  • Descriptive analyses
    • charts / text commentaries on values by time periods and different groups
    • Widely used (=Repeated X-Sectional analysis)

ii) Time Series statistical models

Advanced methods of modelling data are possible, require specialist stats functions

      • Autoregressive functions: Yt = Yt-1 + Xt + e
    • Widely employed in business / economics, but limited use in other disciplines

July 2008: LDA


July 2008: LDA

summary quantitative longitudinal analysis
Summary: Quantitative Longitudinal Analysis

1)Pro’s and cons to QnL research::

  • Appealing analytical possibilities:e.g. analysis of change, controls for residual heterogeneity
  • Pragmatic constraints: data access, management, & analytical methods; practical applications often over-simplify topics
  • Uneven penetration of applications between research fields at present

July 2008: LDA

summary quantitative longitudinal analysis42
Summary: Quantitative Longitudinal Analysis

2)Undertaking QnL research:

  • Needs a bit of effort:learn software syntax, data management routines – workshops and training facilities available; exploit UK networks
  • Remain substantively driven: dangers of ’methodolatry’ (applications ‘forced’ into favourite complex techniques) and simplification (simpler techniques in the more popular & influential reports)
  • Learn by doing (..with Stata syntax examples..!)

July 2008: LDA

summary quantitative longitudinal analysis43
Summary: Quantitative Longitudinal Analysis

3)Some speculation on the future

  • Process of mainstreaming QLA into social science discourses (so we all need to know ‘what is’!!)
  • Complex multi-process models:new data & software for complex longitudinal statistical models
  • More new longitudinal data resources
    • More and more micro-data (e.g. UKHLS)
    • Data linking (e.g. administrative datasets)
    • Geographical data over time

July 2008: LDA

  • Abbott, A. 2006. 'Mobility: What? When? How?' in Morgan, S.L., Grusky, D.B. and Fields, G.S. (eds.) Mobility and Inequality. Stanford: Stanford University Press.
  • Baltagi, B.H. 2001. Econometric Analysis of Panel Data. New York: Wiley.
  • Blossfeld, H.P. and Rohwer, G. 2002. Techniques of Event History Modelling: New Approaches to Causal Analysis, 2nd Edition. Mawah, NJ: Lawrence Erlbaum Associates.
  • Blossfeld, H. P., Grolsch, K., & Rohwer, G. (2007). Event History Analysis with Stata. New York: Lawrence Erlbaum
  • Davies, R.B. 1994. 'From Cross-Sectional to Longitudinal Analysis' in Dale, A. and Davies, R.B. (eds.) Analysing Social and Political Change : A casebook of methods. London: Sage.
  • Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2000). Quantitative Geography: Perspectives on Spatial Data Analysis. London: Sage.
  • Glenn, N. D. (2005). Cohort Analysis, 2nd Edition. London: Sage.
  • Hannan, M. T., & Tuma, N. B. (1979). Methods for Temporal Analysis. Annual Review of Sociology, 5, 303-328.
  • Lambert, P.S., Prandy, K. and Bottero, W. 2007. 'By Slow Degrees: Two Centuries of Social Reproduction and Mobility in Britain'. Sociological Research Online 12.
  • Martin, J., Bynner, J., Kalton, G., Boyle, P., Goldstein, H., Gayle, V., Parsons, S. and Piesse, A. 2006. Strategic Review of Panel and Cohort Studies. London: Longview, and www.longviewuk.com/
  • Mayer, K.U. 2005. 'Life courses and life chances in a comparative perspective' in Svallfors, S. (ed.) Analyzing Inequality: Life Chances and Social Mobility in Comparative Perspective. Stanford: Stanford University Press.
  • Menard, S. 2002. Longitudinal Research, 2nd Edition. London: Sage, Number 76 in Quantitative Applications in the Social Sciences Series.
  • Moser, C. A. (1958). Survey Methods in Social Investigation. London: Heinemann.
  • Pahl, R., & Pevalin, D. (2005). Between family and friends: a longitudinal study of friendship choice. British Journal of Sociology, 56(3), 433-450.
  • Platt, L. (2005). Migration and Social Mobility: The Life Chances of Britain's Minority Ethnic Communities. Bristol: The Policy Press.
  • Rose, D. 2000. 'Researching Social and Economic Change: The Uses of Household Panel Studies'. London: Routledge.
  • Taris, T.W. 2000. A Primer in Longitudinal Data Analysis. London: Sage.
  • Verbakel, E., & de Graaf, P. M. (2008). Resources of the Partner: Support or Restriction in the Occupational Career Developments in the Netherlands Between 1940 and 2003. European Sociological Review, 24(1), 81-95.