1. ASSESS, York 2013 Using SPSS to estimate demographic rates by ethnic group Paul Norman Centre for Spatial Analysis & Policy School of Geography University of Leeds ESRC Research Awards RES-189-25-0162 & RES-165-25-0032 What happens when international migrants settle? Ethnic group population trends and projections for UK local areas

2. Context Population projections Why by ethnic group How operationalised Estimating fertility rates by ethnic group Data sources Estimation steps Logistic regression (SPSS) Constraints & scaling (Excel) Nonlinear regression (SPSS) Estimating migration and mortality rates

3. Population projections? Census 2001Census 2011 Now ‘Latest available data’ PastFuture Estimates Forecasts Projections Based on available evidence of population counts or indicators of change Some predictions are made about what may happen to demographic trends

4. Population projections? Age-sex structure & demographic rates leads to different age-sex structure a.) TFR = 1.69 b.) TFR = 1.44 a.) 9,788 babies = 5,013 boys & 4,774 girls b.) 7,927 babies = 4,060 boys & 3,867 girls 2001 Population … & age-sex specific mortality & migration rates Age-Specific Fertility Rates …

5. Population projections by ethnic group: Why? Applied reasons Age-sex counts by ethnic group needed … for equal opportunities, education support, denominators e.g. health Output quality reasons If sub-groups ‘behave’ differently, the quality of the whole will be improved Fertility, Mortality, Migration ethnic group differences? Cultural choices, lifestyle, aspiration, socioeconomic position, etc

6. Population projections by ethnic group Specification: Time-frame: annually 2001-2051 Geography: Local authorities in England plus countries of Wales, Scotland, Northern Ireland Ethnic groups: 16 groups re 2001 Census Inputs: Age-sex populations for 2001 Demographic rates for 2001 & future ‘assumptions’ Fertility Mortality Subnational & International Migration All by 16 ethnic groups

7. Estimating fertility rates by ethnic group Data on fertility by ethnic group not directly collected Vital Statistics ASFRs for all women, LA LFS Sample ASFRs by ethnic group, national Populations Ethnic group, LA Estimate ASFRs by ethnic group 1. Labour Force Survey (5YA) ASFRs by ethnic group, national Microdata: estimate probability of child by ethnic group Logistic regression (SPSS) 2. Constrain / scale to VS (5YA) Adjust probabilities to sum to births to all women by Local Authority (Excel) 3. Estimate single year of age rates from the 5 year information Nonlinear regression (SPSS)

8. 1. Evidence of age-specific fertility by ethnic group Labour Force Survey Collected annually 1980s to date Respondent by age, sex, ethnic group Presence of dependent child (0-4) Derive time-trends in fertility Pros? All of the above Cons? Some of the above

9. 1. Labour Force Survey Data view 2001 sub-sample Syntax: Filter for year & subgroup Logistic regression

10. 1. Labour Force Survey Logistic regression outputs

11. 2. Constrain / scale to VS Estimating fertility rates: national

12. 2. Local variation in ethnic fertility Scale local ASFR(aw) by National ASFR (e) Scale ASFR(e) by local TFR (e) Calculate births by ethnic groups Fit births to VS For each LA … Recalculate ASFRs Iterate to fit Bradford

13. 3. Estimating single year of age information Projection model Time-frame: annually 2001-2051 Needs single year of age information Disaggregate 5 year ASFRs to be SYA By 16 ethnic groups by 350+ LAs Nonlinear model Use nonlinear regression in SPSS Predict rates by SYA based on 5YA information

14. 3. Nonlinear regression (NLR) NLR Not easy to get into doing Not covered in ‘how to’ textbooks Published papers define curves using algebra Scary definitions Difficult to work out how to implement What’s the point of NLR? Think of it as estimation (prediction) … … not explanation (prediction) as in OLS, etc.

15. 3. Nonlinear regression (NLR) Generic terms Smoothing Graduation Curve fitting / estimation Terms in widespread use Loose definitions Different techniques Ragged data Grouped data

16. 3. Nonlinear regression (NLR): How? Exploratory Scatterplot gives idea of shape of curve in data Pick function likely to be appropriate (h * exp( – (x – p)**2 / r)) Where: x = the increments (e.g. age) h = height of the curve p = position on the x axis r = rate of ascent & descent exp = exponential function (h * exp( – rd * (x – p) – exp( – ra * (x – p)))) Where: ra = rate of ascent rd = rate of descent

17. 3. Nonlinear regression (NLR): How? (h * exp(r * x)) (h * exp( – r * x)) a / (1 + exp(b + c * x)) a * exp(– exp(b – c * x))

18. 3. Disaggregating grouped data using NLR a. Take grouped data & / 5 (or similar)

19. 3. Disaggregating grouped data using NLR b.) Having eye-balled the type of curve c.) Pick appropriate function d.) Make intelligent guess on starting parameters Not always clear what to use! NLR routine estimates parameters during the modelling

20. 3. Disaggregating grouped data using NLR e.) Write (edit) SPSS syntax (dialogue box iffy) MODEL PROGRAM h=50 p=25 r=0.5. COMPUTE curve1_pr = (h*exp(-(unit-p)**2/r)). NLR curve1 /PRED curve1_pr /SAVE PRED /CRITERIA ITER 1000. VARIABLE LABELS curve1_pr 'Predicted Data'. *. *Estimated curve. TSPLOT VARIABLES= curve1 curve1_pr /ID= unit /NOLOG. f.) Run the syntax

21. 3. Disaggregating grouped data using NLR g.) Look at SPSS Output & Data Editor

22. 3. Disaggregating grouped data using NLR h.) Assessing model fit (& comparing models) Statistical measures: R 2 & others Interpretive: Parameters might mean something Practical: Use the outputs (apply rates to population) Visual: How pretty are the smooth curves?!

23. Modelling demographic rates Fertility curves: MODEL PROGRAM a=1 b=4 c=28. COMPUTE White_Pr = (a*b/c)*(c/age)**(3/2)*exp(-b*b*(c/age+age/c-2)). NLR wht /PRED White_Pr /SAVE PRED /CRITERIA ITER 10000. VARIABLE LABELS White_Pr 'White Pred_Val Hadwiger'.

24. Modelling demographic rates Mortality curves: MODEL PROGRAM A=1 B=1 C=1 D=1 E=10 F=20 G=1 H=1 K=2. COMPUTE dth_pr = A**(age+B)**C + D*exp(-E*(ln(age)-ln(F))**2) + G*H**age / 1+K*G*H**age. NLR pr_death /PRED dth_pr /SAVE PRED /CRITERIA ITER 1000. VARIABLE LABELS dth_pr 'Predicted Data'.

25. Modelling demographic rates Migration curves: * 4 component (with elderly & retirement) with constant. *. MODEL PROGRAM h1=1 r1=0.1 h2=1 ra1=0.1 rd1=0.1 p1=25 h3=1 ra2=0.1 rd2=0.1 p2=55 h4=1 r2=0.1. COMPUTE c1_in4pr = (h1*exp(-r1*age)) + (h2*exp(-rd1*(age-p1)-exp(-ra1*(age-p1)))) + (h3*exp(-rd2*(age-p2)-exp(- ra2*(age-p2)))) + (h4*exp(r2*age)) + 0.005. NLR c1_in /PRED c1_in4pr /SAVE PRED /CRITERIA ITER 1000.

26. Nonlinear regression Approach described above appropriate … Disaggregate grouped information Smoothing ragged data … as an estimate & to understand data better Bronchiolitis epidemic: Onset, peak & decay Symmetrical cf asymmetrical? OriginalPredicted

27. Nonlinear regression Can I use other software than SPSS? Yes: Stata, R, Minitab Can I do this using different techniques? Yes: functions in linear regression Quadratic, Cubic, Quartic Relational models Kernel density, splines

28. Population projections by ethnic group Estimating demographic rates by ethnic group Fertility using logistic regression, constraints & scaling & nonlinear regression Resources Material in this presentation drawn from: Norman P, Marshall A, Thompson C, Williamson L & Rees P. (2012) Estimating detailed distributions from grouped sociodemographic data: ‘get me started in’ curve fitting using nonlinear regression. Journal of Population Research 29(2): 173-198 DOI: 10.1007/s12546-012-9082-9 Norman P, Rees P & Wohland P (2013) The use of a new indirect method to estimate ethnic-group fertility rates for subnational projections for England. Population Studies: A Journal of Demography DOI: 10.1080/00324728.2013.810300 SPSS files to try nonlinear regression Curve-examples-Table1.sav Curve-fitting-Table1.sps

29. Projections by ethnic group, 2001-2051 Project outputs http://ethpop.org/ Selected publications Demographic components Boden P & Rees P (2010) International migration: the estimation of immigration to local areas in England using administrative sources, Journal of the Royal Statistical Society, Series A (Statistics in Society) Norman P, Gregory I, Dorling D & Baker A (2008) Geographical trends in infant mortality: England and Wales, 1970–2006. Health Statistics Quarterly 40: 18-29 Norman P, Rees P & Wohland P (2013) The use of a new indirect method to estimate ethnic-group fertility rates for subnational projections for England. Population Studies: A Journal of Demography DOI: 10.1080/00324728.2013.810300 Norman P, Rees P, Wohland P & Boden P (2010) Ethnic group populations: the components for projection, demographic rates and trends. Chapter 14 in Stillwell, J. and van Ham, M. (eds.) Ethnicity and Integration. Series: Understanding Population Trends and Processes. Springer: Dordrecht: 289-315 Rees P, Wohland P & Norman P (2009) The estimation of mortality for ethnic groups at local scale within the United Kingdom. Social Science & Medicine 69: 1592–1607 Stillwell J, Hussain S & Norman P (2008) The internal migration propensities and net migration patterns of ethnic groups in Britain. Migration Letters 5(2): 135-150 Tromans N, Natamba E, Jefferies J & Norman P (2008) Have national trends in fertility between 1986 and 2006 occurred evenly across England and Wales? Population Trends 133: 7-19 Wohland P & Rees P (2009) Life Expectancy Variation across England’s Local Areas by Ethnic Group in 2001, Journal of Maps, v2010, 354-359. 10.4113/jom.2010.1110

30. Projections by ethnic group, 2001-2051 Project outputs http://ethpop.org/ Selected publications Methods Marshall A, Norman P & Plewis I (2013) Developing a relational model of disability. European Journal Population (accepted) Norman P, Marshall A, Thompson C, Williamson L & Rees P. (2011) Estimating detailed distributions from grouped sociodemographic data: ‘get me started in’ curve fitting using nonlinear regression. Journal of Population Research 29(2): 173-198 DOI: 10.1007/s12546-012-9082-9 Williamson L & Norman P (2011) Developing strategies for deriving small population fertility rates. Journal of Population Research 28(2): 149-183, doi:10.1007/s12546-011-9059-0 Wohland P, Rees P, Norman P, Boden P & Jasinska M (2010) Ethnic Population Projections for the UK and Local Areas, 2001-2051. Working Paper 10/02, School of Geography, University of Leeds, Leeds Projections Rees P, Wohland P & Norman P (2012) The demographic drivers of future ethnic group populations for UK local areas 2001-2051. Geographical Journal Rees P, Wohland P, Norman P & Boden P (2011) A local analysis of ethnic group population trends and projections for the UK. Journal of Population Research 28(2): 129-148 doi: 10.1007/s12546-011-9047-4 Rees P, Wohland P, Norman P & Boden P (2012) Ethnic population projections for the UK, 2001-2051. Journal of Population Research 29: 45-89 DOI 10.1007/s12546-011-9076-z