# Individual level synthetic regression models Session 4.

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Individual level synthetic regression models Session 4

Aims of practical 1.Fit a logistic regression model to predict the probability of a person having a mobility disability (age, age squared and age cubed, sex, LLTI and LLTI*age 2.Calculate the model probabilities of having a mobility disability at each single year of age for males and females and for those with and without an LLTI. 3.Generate district estimates of the population with a mobility disability by multiplying the model probabilities by the appropriate population counts (Census)

Let: =probability of mobility disability for individual i x i =the age of individual i j=0 (no LLTI) or 1 (has an LLTI) z ij =1 if j=1 (individual i has an LLTI) and 0 otherwise parameters represent the influence of age on log odds of having a disability Β gives the effect of having an LLTI and δ represents How this effect changes with age

We can use the parameter estimates from the logistic regression model to calculate model probabilities of having a mobility disability Note there is a probability (or rate) for each age (x) and LLTI group (j)

Number of people with a mobility disability at age x and district r Population count at age x, district r and LLTI group j (census) Model probability of mobility disability at age x and LLTI group j (Estimated using HSE data) J=0 no LLTI, j=1 has an LLTI

Synthetic regression assumptions and model limitations The model assumes that the explanatory variables in the HSE and the census are measured identically. The model requires population counts of crosstabulations of all explanatory variables. Have to drop lots of missing values of LLTI (in 2000 proxy interviews didnt include this question).

Comparison of Census and HSE LLTI schedules Lower rates of LLTI in the Census compared to Lower rates of LLTI in the census compared to the HSE at the younger ages

Stata commands xi: logit mobility i.llti*age agesq agecub if sex==1 [pweight=weight] predict MO_RT_M if sex==1 Start of with the HSE microdata (HSE data.dta)

Stata commands Repeat the model and generate predicted values for females Drop duplicate records in terms of the variables age, sex and LLTI Duplicates drop age sex llti, force This leaves us with a predicted probability of mobility disability for each single year of age, sex and LLTI status

Model rates of mobility disability

Stata commands FileDetails Practical 3 – task 1.dtaModel probabilities (age, sex and LLTI status) – file created during task 1 of practical 3 Pop data – practical 3.dta Population counts (age, sex and LLTI status) for each of the 6 casestudy districts Now merge two files using sex, age and LLTI status as the merge variable

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