Session 4: Methods of Analysis

• Different levels of analysis require different methods of analysis.
• Simple cross-sectional (one wave) analysis is straightforward but does not benefit from the longitudinal nature of the data.
• Analysis of consecutive pairs of waves is straightforward. For instance,
  • cross-tabulate state at $t_i$ and $t_{i+1}$ for categorical variables (loglinear models of transitions)
  • logistic regression on yes-no change of state (can be extended to duration modelling, i.e., ``event history analysis'')
  • linear regression models of the form
    $y_t = \alpha + \beta \mathbf{x}_{t-1} + \gamma y_{t-1} + \epsilon$    and
    $y_t - y_{t-1} = \alpha + \beta \mathbf{x}_{t-1} + \epsilon$
• More sophisticated models (fixed-effects, random-effects):
  
  $$y_{it} = \alpha + \beta \mathbf{x}_{it} + \nu_i + \epsilon_{it}$$
  
  

• The overall error is partitioned into an individual-specific component $\nu_i$ which is time invariant, and $\epsilon_{it}$, which varies from period to period.
• Depending on the partitioning we get, inter alia, fixed effects and random effects models.
• These are conveniently fitted in Stata: will discuss further in Week 2 (see xt set of commands).
• Conceptually related to these models are multi-level models which also take account of grouping of observations (individuals within households, or wave-observations within individuals).
• What they have in common is allowing separate random error processes at observation (i.e., $it$) level and group ($i$) level.

• These models are repeated-measurement in their orientation: longitudinality enters as repeated (and perhaps ordered) observations.
• A major alternative perspective is to model durations (hazard rate models, event history models)
• Exploratory methods such as sequence analysis are also useful.

• All methods have shortcomings: time is hard to deal with
• Methods which relate $t$ to $t-1$ (even pooling $n-1$ such transitions for $n$ waves) focus only on annual transition patterns
• Most hazard modelling approaches focus only on single spells (even when all spells are pooled)
• Holistic methods such as sequence analysis give a better general descriptive overview, but have no analytical power