assess, york 2013 using spss to estimate demographic rates by ethnic group paul norman centre for...
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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