1. Handling attrition and non- response in longitudinal data Harvey Goldstein University of Bristol

2. Whats the problem? Loss of individuals in a survey over time can lead to smaller numbers –By aged 42 ~70% of original NCDS cohort gave information Non – random loss can lead to biases –Especially important when loss is associated with the variable values that are not subsequently available

3. Fixing the losses Preventing loss is another topic. This is a look at how you might compensate for it. –A brief look at traditional weighting procedures –Use of multiple imputation (MI) – a simple introduction and its application to attrition –Combining MI with weighting

4. Traditional approach to handling attrition and missing data Sets of weights –Sample design and any initial non-response provide basic weights for wave 1 –For several waves we can define typical pathways and provide weights for each one. e.g. LSYPE may require 12 or more depending on selected components –For item non-response hot deck single imputation (weighted?) often used

5. Problems with weighting procedures Inefficient – can only use the data available for each combination of variables analysed Restrictive, since weights are only provided for chosen pathways Possibly inconsistent results through different weights for different analyses Not very transparent for use

6. Problems with hot deck imputation Not theoretically based Selection of matched cases may not always be possible – especially in multilevel data Single imputation does not allow easy computation of standard errors

8. Multiple imputation – very briefly Consider the model of interest (MOI), assuming normal x, y We turn this into a multivariate normal response model and obtain residual estimates (from an MCMC chain) where x, or y are missing. Use these to fill in and produce a complete data set. Do this (independently) n (e.g. = 20) times. Fit MOI to each data set and combine according to rules to get estimates and standard errors. Note that other methods (listwise deletion, mean imputation, hot deck etc.) are either inefficient or biased.

9. Attrition treated as missing data A missing record at a follow up gives an individual with many known and many missing values. Even where no data at all are collected directly, auxiliary data may be available (interviewer observations etc.) Together with item missingness we can use MI to fill in all the missing data.

10. Distributional issues Existing methods assume normality. We would like to handle multilevel data and mixtures of normal and discrete variables with missing data. ESRC REALCOM project developed MCMC algorithm and software for these cases REALCOM-IMPUTE links REALCOM with MLwiN and can handle level 2 and discrete variables. It works by transforming discrete variables to normality using a latent variable model so that all response variables have a joint multivariate normal distribution and then applies MI theory.

11. Putting weights into MI Consider a 2-level model: Write level 2 weights as Level 1 weights for j-th level 2 unit as Final level 1 weights These weights can be used for MOI and also for imputation. This involves an MCMC estimation using weighted likelihoods, where variances are inversely proportional to weights.

12. References Multilevel models with multivariate mixed response types (2009) Goldstein, H, Carpenter, J., Kenward, M., Levin, K. Statistical Modelling (to appear) - Gives methodological background Handling attrition and non-response in longitudinal data. Goldstein. H. International Journal of longitudinal and Life Course studies. April 2009,. http://www.journal.longviewuk.com/index.php/llcs - Discusses issues for longitudinal studies in detail http://www.journal.longviewuk.com/index.php/llcs Web site for software: http://www.cmm.bristol.ac.uk/research/Realcom