ASSESS, York 2013

Using SPSS to estimate demographic rates by ethnic group

Paul Norman

Centre for Spatial Analysis & PolicySchool of Geography

University of Leeds

ESRC Research Awards RES-189-25-0162 & RES-165-25-0032What happens when international migrants settle? Ethnic group population trends and

projections for UK local areas

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

Population projections?

Census 2001 Census 2011

Now‘Latest

available data’

Past Future

Estimates

ForecastsProjections

Based on available evidence of population counts or indicators of change

Some predictions are made about what may happen to demographic trends

Population projections?

• Age-sex structure & demographic rates leads to different age-sex structure

0

20

40

60

80

100

120

140

<20 20-24 25-29 30-34 35-39 40+

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 …

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

improvedFertility, Mortality, Migration ethnic group differences?

• Cultural choices, lifestyle, aspiration, socioeconomic position, etc

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

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)

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

1. Labour Force Survey

Data view• 2001 sub-sample

Syntax:• Filter for year & subgroup• Logistic regression

1. Labour Force Survey• Logistic regression outputs

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

0

20

40

60

80

100

120

140

160

<20 20-24 25-29 30-34 35-39 40+

AS

FR

, 20

01

White Black-Caribbean Black-African Indian

Pakistani Bangladeshi Chinese Other

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

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

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.

3. Nonlinear regression (NLR)

Generic terms• Smoothing• Graduation• Curve fitting / estimation

Terms in widespread use• Loose definitions• Different techniques

Ragged data

Grouped data

3. Nonlinear regression (NLR): How?

Exploratory• Scatterplot gives idea of shape of curve in data• Pick function likely to be appropriate

r

pxehxf

2

)( (h * exp( – (x – p)**2 / r))

Where:x = the increments (e.g. age)h = height of the curvep = position on the x axisr = rate of ascent & descentexp = exponential function

pxrepxrehxf ad )(

(h * exp( – rd * (x – p) – exp( – ra * (x – p))))

Where:ra = rate of ascentrd = rate of descent

3. Nonlinear regression (NLR): How?

xrehxf )(

xrehxf )(

xcbeaxf 1/)(

xcbeeaxf )(

(h * exp(r * x))

(h * exp( – r * x))

a / (1 + exp(b + c * x))

a * exp(– exp(b – c * x))

3. Disaggregating grouped data using NLR

a. Take grouped data & / 5 (or similar)Group Original Units Initial

0-4 50 0 10 1 10 2 10 3 10 4 10

5-9 100 5 20 6 20 7 20 8 20 9 20

10-14 150 10 30 11 30 12 30 13 30 14 30

15-19 200 15 40 16 40 17 40 18 40 19 40

etc etc etc etc

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

r

pxehxf

2

)(

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

3. Disaggregating grouped data using NLR

g.) Look at SPSS Output & Data Editor

3. Disaggregating grouped data using NLR

h.) Assessing model fit (& comparing models)• Statistical measures: R2 & others• Interpretive: Parameters might mean something• Practical: Use the outputs (apply rates to population)• Visual: How pretty are the smooth curves?!

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' .

2exp)( 2

23

c

x

x

cb

x

c

c

abxf

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' .

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 .

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?

Original Predicted

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

Population projections by ethnic group

Estimating demographic rates by ethnic group• Fertility using logistic regression, constraints & scaling &

nonlinear regression

ResourcesMaterial 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

Projections by ethnic group, 2001-2051Project outputs

http://ethpop.org/

Selected publications

Demographic componentsBoden 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: 18-29Norman 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: 10.1080/00324728.2013.810300Norman 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

Projections by ethnic group, 2001-2051Project outputs

http://ethpop.org/

Selected publications

MethodsMarshall 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

ProjectionsRees 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