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
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?
Past
Now
‘Latest
available
data’
Based on available
evidence of population
counts or indicators of
change
Forecasts
Projections
Estimates
Census 2001
Future
Census 2011
Some predictions are
made about what may
happen to
demographic trends
Population projections?
• Age-sex structure & demographic rates leads to
different age-sex structure
2001 Population
Age-Specific Fertility Rates …
140
a.) TFR = 1.69
120
100
b.) TFR = 1.44
80
60
40
20
0
<20
20-24
25-29
30-34
35-39
40+
a.) 9,788 babies = 5,013 boys & 4,774 girls
b.) 7,927 babies = 4,060 boys & 3,867 girls
… & age-sex specific mortality & migration 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
improved
Fertility, 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
1. Labour Force Survey (5YA)
• ASFRs by ethnic group, national
• Microdata: estimate probability
of child by ethnic group
• Logistic regression (SPSS)
Estimate
ASFRs by
ethnic group
2. Constrain / scale to VS (5YA)
• Adjust probabilities to sum to
births to all women by Local
Authority (Excel)
Populations
• Ethnic group, LA
LFS Sample
• ASFRs by
ethnic group,
national
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
160
140
120
ASFR, 2001
100
80
60
40
20
0
<20
20-24
25-29
30-34
35-39
40+
White
Black-Caribbean
Black-African
Indian
Pakistani
Bangladeshi
Chinese
Other
2. Local variation in ethnic fertility
For each LA …
Scale local ASFR(aw)
by National ASFR (e)
Scale ASFR(e) by
local TFR (e)
Calculate births by
ethnic groups
Fit births to VS
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)
Ragged data
Grouped data
Generic terms
• Smoothing
• Graduation
• Curve fitting / estimation
Terms in widespread use
• Loose definitions
• Different techniques
3. Nonlinear regression (NLR): How?
Exploratory
• Scatterplot gives idea of shape of curve in data
• Pick function likely to be appropriate

  x  p 2  


f ( x)  h  e


r



(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
f ( x)  h  e rd  x  p   e ra  x  p 
(h * exp( – rd * (x – p) – exp( – ra * (x – p))))
Where:
ra = rate of ascent
rd = rate of descent
3. Nonlinear regression (NLR): How?
f ( x)  h  er  x
f ( x)  h  e r  x
(h * exp(r * x))
(h * exp( – r * x))
f ( x)  a /1  eb  c  x
a / (1 + exp(b + c * x))
f ( x)  a  e eb  c  x
a * exp(– exp(b – c * x))
3. Disaggregating grouped data using NLR
a. Take grouped data & / 5 (or similar)
Group
0-4
Original
50
5-9
100
10-14
150
15-19
200
etc
etc
Units
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
etc
Initial
10
10
10
10
10
20
20
20
20
20
30
30
30
30
30
40
40
40
40
40
etc
3. Disaggregating grouped data using NLR
b.) Having eye-balled the type of curve
c.) Pick appropriate function

  x  p 2  

f ( x)   h  e


r



d.) Make intelligent guess on starting parameters
• Not always clear what to use!
• NLR routine estimates parameters during the modelling
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:
ab  c 
f ( x) 
 
c  x
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' .
3
2

c x

exp  b 2    2 
x c


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
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
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
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