Sample enumeration: Forecasting from statistical models Dr Vernon Gayle and Dr Paul Lambert (Stirling University) Tuesday 29th April 2008.

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Sample enumeration: Forecasting from statistical models Dr Vernon Gayle and Dr Paul Lambert (Stirling University) Tuesday 29th April 2008

Communicating Results (to non-technically informed audiences) Davies (1992) Sample Enumeration Payne (1998) Labour Party campaign data Gayle et al. (2002) War against the uninformed use of odds (e.g. on breakfast t.v.)

Sample Enumeration Methods In a nutshell… “What if” – what if the gender effect was removed 1. Fit a model (e.g. logit) 2. Focus on a comparison (e.g. boys and girls) 3. Use the fitted model to estimate a fitted value for each individual in the comparison group 4. Sum these fitted values and construct a sample enumerated % for the group

Naïve Odds Naïvely presenting odds ratios is widespread (e.g. Connolly 2006) In this model naïvely (after controlling for other factors) Girls have an odds of 1.0 Boys have an odds of.58 We should avoid this where possible!

Logit Model Example from YCS 11 (these pupils took GCSE in 2001) y=1 5+ GCSE passes (A* - C) X vars gender; family social class (NS-SEC); ethnicity; housing tenure; parental education; parental employment; school type; family type

Naïve Odds Example from YCS 11 (these pupils took GCSE in 2001) In this model naïvely (after controlling for other factors) Girls have an odds of 1.0 Boys have an odds of.66 We should avoid this where possible!

Sample Enumeration Results Percentage with 5+ GCSE (A*-C) All52% Girls58% Boys47% (Sample enumeration est. boys)(50%) Observed difference11% Difference due ‘directly’ to gender3% Difference due to other things8%

Pseudo Confidence Interval Sample Enumeration Male Effect Upper Bound50.32% Estimate49.81% Lower Bound49.30% Bootstrapping to construct a pseudo confidence interval (1000 Replications)

Reference A technical explanation of the issue is given in Davies, R.B. (1992) ‘Sample Enumeration Methods for Model Interpretation’ in P.G.M. van der Heijden, W. Jansen, B. Francis and G.U.H. Seeber (eds) Statistical Modelling, Elsevier.