Model,specifications,

To!test!whether!there!is!significant!variation!in!the!outcome!variables!at!the!area!level,!the! relationship!between!exposure!and!outcome!variables!was!examined!mainly!using!random! intercept! models.! Random! intercept! models! were! chosen! because! the! strength! of! the! association! between! individual! characteristics! and! outcomes! was! not! expected! to! vary! between! areas.! However,! it! was! also! tested! whether! associations! with! neighbourhood! characteristics!were!dependent!on!childNand!familyNlevel!factors,!using!random!coefficients! models!as!described!in!section!5.2.8.!!!

Analyses! were! run! with! neighbourhoods! defined! at! the! LSOA! level.! TwoNlevel! random! intercept! models! were! run! in! Stata! version! 12.1! using! the! NxtmixedN! command! for! continuous! and! the! NxtmelogitN! command! for! binary! outcomes.! CrossNclassified! models! were! estimated! in! MLwiN! version! 2.26! (Rasbash! et! al.,! 2009),! via! the! userNwritten! command! NrunmlwinN! which! enables! running! MLwiN! from! within! Stata! (Leckie! and! Charlton,!2011).!

Models! were! first! run! as! empty! models! without! any! explanatory! variables,! to! obtain! estimates! of! the! overall! betweenNneighbourhood! and! betweenNschool! variance.! Models! then!sequentially!adjusted!for!child!and!family!characteristics,!neighbourhood!and!school! characteristics,! and! potentially! mediating! factors.! Individual! level! control! variables! were! selected!a!priori,!informed!by!the!review!of!the!literature.!For!each!model,!the!betweenN group!variance,!withinNgroup!variance,!percentage!of!the!total!variance!explained!at!each! level!and!the!VPC!are!reported.!In!multilevel!modelling,!the!variances!that!are!estimated! are!always!the!variances!that!are!unexplained!by!the!model.! The!specific!modelling!strategies!and!variables!included!in!the!analyses!are!presented!for! each!research!aim!at!the!beginning!of!the!relevant!results!chapter.!

Issues'of'weighting'in'multilevel'models'

The! use! of! complex! survey! weights! is! not! supported! by! the! NxtmixedN! and! NrunmlwinN commands! for! estimating! multilevel! models.! To! get! around! this! problem,! advice! was! followed! to! include! the! MCS! design! strata! into! the! models! as! explanatory! variables!

(Professor! R.! Wiggins,! personal! communication,! 22nd_{! August! 2012).! This! approach! to! the!}

multilevel!analysis!of!MCS!data!has!also!been!taken!elsewhere!(Flouri!et!al.,!2009).!Because!

the!MCS!design!strata!already!contain!information!on!area!deprivation1_{,!their!coefficients!}

are!shown!for!all!analyses.!!

However,! as! stated! above,! all! descriptive! analyses! used! the! Stata! survey! command! and! MCS!survey!weights.!

5.2.8 CrossJlevel,interactions,and,complex,variation,

It! is! possible! that! the! relationship! between! a! neighbourhoodNlevel! characteristic! and! the! outcome!varies!by!some!individualNlevel!characteristic,!for!example!the!gender!of!the!child.! This!can!be!tested!by!including!a!crossNlevel!interaction!term!in!the!fixed!part!of!the!model.! In!addition,!the!variance!components!can!be!estimated!for!each!category!of!the!individualN level! variable! separately.! For! example,! including! a! random! coefficient! for! child! gender! allows! to! estimate! the! betweenNneighbourhood! variance! for! boys! and! girls! separately.! If! the! betweenNneighbourhood! variability! in! the! outcome! differs! by! gender,! this! would! indicate! that! neighbourhood! factors! affect! one! gender! more! than! the! other.! It! is! also! possible!that!the!levelNone!variance!(the!withinNneighbourhood!variance)!depends!on!some! explanatory!variable.!For!example,!there!might!also!be!more!variation!in!the!outcome!at! the!individual!level!for!one!gender!compared!to!the!other.!This!is!known!as!complex!levelN1! variation! or! heteroskedasticity! (unequal! variance)! of! levelN1! residuals.! Differences! in! the! betweenNneighbourhood!variability!can!be!called!complex!levelN2!variation!(Steele,!2008).! In!chapters!seven!and!eight,!crossNlevel!interactions!and!complex!variation!were!tested!for! child!gender!and!family!relative!poverty!status,!to!examine!whether!neighbourhood!factors! affected!children!differently!depending!on!their!gender!or!whether!they!were!poor!or!not! poor.!This!was!however!done!only!on!twoNlevel!models!using!Stata’s!NxtmixedN!command,!

as!the!inclusion!of!additional!random!effects!in!the!crossNclassified!models!resulted!in!too! much!model!complexity!and!led!to!problems!with!convergence.!

5.2.9 Testing,mediation,

A!mediator!variable!is!commonly!defined!as!a!variable!that!accounts!at!least!partly!for!the! relationship!between!an!exposure!and!an!outcome!variable!in!the!form!of!a!causal!chain! (Baron!and!Kenny,!1986).!Baron!and!Kenny!(1986)!proposed!the!following!three!conditions:! 1. Changes! in! the! exposure! variable! are! significantly! associated! with! changes! in! the!

mediator!variable!(path!a!in!Figure!5N4).!

2. Changes! in! the! mediator! variable! are! significantly! associated! with! changes! in! the! outcome!variable!(path!b).!

3. When! path! a! and! path! b! are! controlled,! a! previously! significant! association! between! exposure!and!outcome!(path!c)!is!no!longer!statistically!significant!or!greatly!reduced.!!

!

Figure,5J4,,,Mediation,(adapted,from,Baron,and,Kenny,,1986),

More!recently,!this!approach!has!been!criticised!especially!when!applied!to!observational! data.!It!has!been!argued!that!formal!testing!of!mediation!is!anything!but!trivial,!especially! when! it! comes! to! making! causal! inferences! which! is! only! possible! with! data! from! experimental!research!(Green,!Ha!and!Bullock,!2010).!!

Here,! the! investigation! was! restricted! to! testing! whether! the! results! of! the! multilevel! regression! analyses! were! compatible! with! the! hypothesised! indirect! pathways,! without! inferring! causality.! In! the! multilevel! context,! if! maternal! psychological! distress! and/or! parenting! practices! were! indeed! on! the! pathway! between! neighbourhood! characteristics! and!child!outcomes,!adding!these!measures!to!the!fully!adjusted!models!should!result!in!at! least!one!of!the!following:!! Exposure) Mediator) Outcome) a) c) b)

a) A"marked"reduction"in"the"fixed"effects"for"the"neighbourhood"characteristics"that" are" included" in" the" model," which" should" have" been" previously" statistically" significant"(consistent"with"mediation),""

b) A"reduction"in"the"unexplained"neighbourhood"level"variance."This"should"happen"if" maternal" levels" of" distress" are" associated" with" unknown" neighbourhood" factors" that"are"not"included"in"the"model."

5.2.10 Considerations0regarding0multilevel0models0with0sparse0data0

It"is"common"for"the"multilevel"structure"of"large"surveys"that"there"are"large"numbers"of" groups"(e.g."neighbourhoods"or"schools),"while"the"average"number"of"observations"within" these"groups"is"small."This"is"true"also"for"the"MCS,"especially"at"the"later"sweeps"due"to" families"moving."For"example,"the"sweep"four"crossFsectional"analysis"sample"that"was"used" in" chapter" seven" to" examine" neighbourhood" effects" on" children’s" socioFemotional" outcomes" (N=" 9,840)" included" 4,374" neighbourhoods" and" 3,882" schools." The" average" number"of"observations"per"neighbourhood"was"2.2,"and"61%"of"them"were"“singletons”," i.e." contained" only" one" observation" (the" average" number" of" observations" per" school" was" 2.5," with" 57%" singletons)." Generally," sparseness" is" not" much" of" a" problem" for" the" fixed" effects"estimates,"but"can"lead"to"biased"estimates"of"the"random"effects"if"there"are"not" enough"groups."The"literature"on"multilevel"models"with"sparse"data"agrees"that"it"is"the" number"of"groups"that"matters"most"for"the"estimation"of"betweenFgroup"variance,"with" the"number"of"observations"per"group"becoming"less"important"the"larger"the"number"of" groups"at"the"higher"level"(Maas"and"Hox,"2005;"Gelmann"and"Hill,"2007;"Bell,"Ferron"and" Kromrey," 2008;" Clarke," 2008)." This" is" because" small" groups" are" given" less" weight" in" the" estimation"of"group"level"residuals"due"to"shrinkage."Clarke"(2008)"showed"that"unbiased" estimates" of" fixed" effects" can" be" obtained" with" multilevel" models" even" with" extremely" sparse" data" (group" size" <2)," and" that" random" effects" can" also" be" reliably" modelled" with" sparse" data" when" there" is" a" large" number" of" groups," which" is" here" the" case." Bell" et" al." (2008)"demonstrated"in"a"simulation"study"that"a"percentage"of"singletons"of"up"to"70%"did" not"lead"to"biased"estimates"as"long"as"the"number"of"groups"was"large"(>500)."Therefore," the"sparseness"of"the"data"was"not"a"concern.""

Chapter'6!!

Results'–!Maternal(psychological+

In document Neighbourhoods and children’s social and cognitive development – pathways of effects (Page 117-121)