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Mathematical Approaches to Analysing Area-Level Effects on Health

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Neighbourhood Structure and Health Promotion

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Abstract

This chapter discusses how and why multilevel modelling is a flexible and powerful tool for analysing data with a hierarchical structure. Such data are often found in social science and public health research (e.g. when analysing pupils who are nested in classes or schools, patients in clinics or hospitals).

The aim of multilevel modelling is to integrate the regression equation at a lower level of data grouping (usually individuals) with that at higher levels (such as classes, schools, neighbourhoods) into one regression equation and to incorporate covariates at appropriate levels. By using multilevel models, it is possible to adjust for similarity of the lower level units belonging to the same group of a higher level and to make overall inferences about relationships between lower level as well as higher level characteristics and the outcome of interest.

Using example data sets, we explain step by step how to conduct linear or logistic multilevel modelling. Additionally, we provide syntax commands for several software packages and demonstrate how to interpret the results of multilevel analyses.

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Notes

  1. 1.

    Note that every regression line is defined by only two points.

  2. 2.

    Note: for the random effects in STATA and R, the standard deviation is given, while in SAS and SPSS, the variance (the square of the standard deviation) is given in the output.

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Author information

Authors and Affiliations

  1. Department for Biostatistics and Clinical Epidemiology, Charité-University Medicine, Charitéplatz 1, 10117, Berlin, Germany

    Ulrike Grittner

  2. Center for Alcohol and Drug Research, School of Business and Social Science, Aarhus University, Artillerivej 90, 2300, Copenhagen S, Denmark

    Kim Bloomfield

Authors
  1. Ulrike Grittner
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  2. Kim Bloomfield
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Corresponding author

Correspondence to Ulrike Grittner .

Editor information

Editors and Affiliations

  1. , Unit for Health Promotion Research, University of Southern Denmark, Niels Bohrs Vej 9-10, Esbjerg, 6700, Denmark

    Christiane Stock

  2. , MRC Social & Public Health Sciences Unit, University of Glasgow, Lilybank Gardens 4, Glasgow, G12 8RZ, United Kingdom

    Anne Ellaway

Appendix

Appendix

Syntax commands for the examples in STATA, R and SPSS. In R, we used the following libraries: nlme (Pinheiro et al. 2011), MASS (Venables and Ripley 2002) and lme4 (Bates et al. 2011).

Multilevel Linear Regression: The Intercept-Only Model

In STATA:

xtmixed perform || school:, var

In R:

library (nlme)

L1 <- lme (fixed=perform~1, random= ~1 | school, data=walk)

summary (L1)

In SPSS:

MIXED perform

/PRINT = SOLUTION TESTCOV

/FIXED = INTERCEPT

/RANDOM = INTERCEPT | SUBJECT (school) .

Multilevel Linear Regression: Random Intercept Model with One Individual-Level Covariate

In STATA:

xtmixed perform activ|| school:, var

In R:

library (nlme)

L2 <- lme (fixed=perform ~ 1+activ , random = ~1 | school, data=walk)summary (L2)

In SPSS:

MIXED perform WITH activ

/PRINT = SOLUTION TESTCOV

/FIXED = INTERCEPT activ

/RANDOM = INTERCEPT | SUBJECT (school).

Multilevel Linear Regression: Random Intercept and Slope Model with One Individual-Level Covariate

In STATA:

xtmixed perform activ|| school: activ, var

In R:

library (nlme)

L3 <- lme (fixed=perform ~ 1+active, random=~activ|school, data=walk)

Summary (L3)

In SPSS:

MIXED perform WITH activ

/PRINT = SOLUTION TESTCOV

/FIXED = INTERCEPT activ

/RANDOM = INTERCEPT activ| SUBJECT (school).

Multilevel Logistic Model for Binary Outcome: Intercept-Only Model

In STATA:

xtset school

xtlogit walkschool

In R:

library (MASS)

library (lme4)

L4<-glmer (walkschool~1+(1|school),family=binomial, data=walk)

summary (L5)

In SPSS:

GENLINMIXED

/DATA_STRUCTURE SUBJECTS=school

/FIELDS TARGET=walkschool

/TARGET_OPTIONS DISTRIBUTION=BINOMIAL LINK=LOGIT

/FIXED USE_INTERCEPT=TRUE

/random use_intercept=true subjects=school.

Multilevel Logistic Model for Binary Outcome: Random Intercept Model with Individual-Level and School District-Level Covariates and Cross-Level Interaction

In STATA:

xtlogit walkschool perform less_farm perform_less_farm, or

In R:

library (MASS)

library (lme4)

L5<-glmer (walkschool~1+perform+less_farm+perform_less_farm+ (1|school),family=binomial, data=walk)

summary (L5)

In SPSS:

GENLINMIXED

/DATA_STRUCTURE SUBJECTS=school

/FIELDS TARGET=walkschool

/TARGET_OPTIONS reference=0 DISTRIBUTION=BINOMIAL LINK=LOGIT

/FIXED effects= perform less_farm perform_less_farm USE_INTERCEPT=TRUE

/random use_intercept=true subjects=school COVARIANCE_TYPE =UNSTRUCTURED.

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Grittner, U., Bloomfield, K. (2013). Mathematical Approaches to Analysing Area-Level Effects on Health. In: Stock, C., Ellaway, A. (eds) Neighbourhood Structure and Health Promotion. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-6672-7_10

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  • DOI: https://doi.org/10.1007/978-1-4614-6672-7_10

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  • Print ISBN: 978-1-4614-6671-0

  • Online ISBN: 978-1-4614-6672-7

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