Multilevel Modeling in Health ResearchApril 11, 2008

OutlineIntroductionResearch DesignModel BuildingSoftware ToolsExample with Florida infant health and Florida CHARTS

Multilevel ModelingThe multilevel model is also known as a mixed and random-effects model, variance component model and hierarchical model.Multilevel modeling tries to avoid two problems confronted in data analysis:Atomistic fallacy: individual level analysis misses the context in which behavior occursEcological fallacy: aggregate results might not apply to individual behavior

Multilevel ModelingSingle-level AnalysisRandom Intercepts

Multilevel ModelingMLM helps resolve the tension between the atomistic and ecological fallacy.

Multilevel ModelingTwo level models: individuals and communities, the key feature of multilevel models is that they specify the potentially different intercepts and slopes for each community as coming from a distribution at a high level. The alpha and beta parameter in the above equations are fixed, while the variances and covariance of the error term are random.

Multilevel ModelingThe most important point in favor of multilevel models is that they are more realistic and faithful to the nature of the social world with its many layers and complex structure. Previously, researchers have been on the horns of a dilemma. They have had to work at either the level of the aggregate or the individual. Choosing to work at the aggregate level lays one open to the charge of the ecological fallacy and aggregation bias, while choosing to work at the individual level risks being found guilty of the atomistic fallacy. The latter approach misses the context in which individual behavior occurs, while the former fails to recognize that it is individuals who act, not aggregates (Jones 1995, 255).

Multilevel ModelingTechnical advantages of multilevel modeling:

1. Fix for autocorrelation: single level models are misspecified, this causes incorrect standard errors, confidence limits and tests, and incorrect estimates of precision2. Higher-level variables are included: both macro and micro-level analysis is considered 3. Precision-weighted estimation is used: multilevel modes are precision weighted so as to reflect the number of observations on which they are based (Jones 1993).

Multilevel ModelingCritiques of this method are that it requires a discrete set of spatial units and assumes a discontinuous spatial process. Large samples are needed to examine within group and between group variation 30/30 rule

Software ToolsSASSTATARMLwiN

ExampleMy case: I am interested in individual determinants of low birth weight infants, but I understand that place is interesting and has a role in health, and that place characteristics can help substitute for the lack of information about individuals.Apply the Gllamm model in STATAPlot results, residualsPlot results on mapDiscuss results and way forward for research

Using Florida Birth Records to Study Infant Health

Odds Ratios for Key Paths from Three Generation Biosocial Model (singletons). Mother (G2) LBWMother (G2) LTHSMother (G2) UNMARInfant (G3) LBWTotal (N=55,430)aGrandmother (G1) Unmarried1.446**2.593**2.178**1.041Mother (G2) Low Birth Weight1.080*0.9721.781**Mother (G2) Low Education4.567**1.260**Mother (G2) Unmarried1.336**

White (N=34,267)Grandmother (G1) Unmarried1.467**3.423**2.358**1.061Mother (G2) Low Birth Weight1.176**0.9931.939**Mother (G2) Low Education4.726**1.496**Mother (G2) Unmarried1.336**

Black (N=20,808)Grandmother (G1) Unmarried1.435**1.981**2.005**1.042Mother (G2) Low Birth Weight1.0280.9541.688**Mother (G2) Low Education3.996**1.110*Mother (G2) Unmarried1.212**

* p

Births of Residents in Two Generation Dataset

. gllamm birth_weight mother_education, i(county)

Iteration 0: log likelihood = -508012.85 Iteration 1: log likelihood = -507870.83 Iteration 2: log likelihood = -507863.57 (not concave)Iteration 3: log likelihood = -507863.42 Iteration 4: log likelihood = -507862.58 Iteration 5: log likelihood = -507862.51 Iteration 6: log likelihood = -507862.51 number of level 1 units = 64813number of level 2 units = 67 Condition Number = 2403.9866 gllamm model log likelihood = -507862.51 ------------------------------------------------------------------------------ birth_w | Coef. Std. Err. z P>|z| [95% Conf. Interval]-------------+---------------------------------------------------------------- mothered | 45.22001 1.577136 28.67 0.000 42.12888 48.31114 _cons | 3064.606 6.542607 468.41 0.000 3051.782 3077.429------------------------------------------------------------------------------ Variance at level 1------------------------------------------------------------------------------

374160.99 (2079.2281) Variances and covariances of random effects------------------------------------------------------------------------------

Fixed and Random Effects Shown

Chart2

03257.333181.083250.73362.673262.343270.893357.363261.423263.723264.473248.823298.953264.733336.383211.723274.93282.63181.282987.813276.453307.243232.013332.343230.043280.413332.983212.863314.433266.723444.533253.393244.843360.883229.273255.63262.393268.123235.973504.263188.613265.673260.13225.663298.393274.063240.773335.33256.043217.733265.233293.363259.023252.013262.033307.493305.663282.763256.993258.233224.313316.893223.863191.93271.193249.263342.873295.04

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43162.253333.163214.423544.033358.822982.253369.083453.023465.963569.313500.463300.672973.693402.943362.283179.023109.123278.282992.573037.013420.643337.733223.023231.643417.453475.743459.73344.713170.883411.853338.393078.763315.643147.433323.83265.953066.643360.373407.93108.013362.353426.943350.343488.073424.73460.973293.93156.323317.613163.233596.443352.543541.493263.033510.933319.463416.283359.513294.153104.913584.093239.743372.33367.073331.783402.753285.36

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Mother's Education (ranked - elementary school to professional degree)

Infant's Birth Weight (grams)

Predicted Slopes and Intercepts for Florida Counties

co_Slopes

MOTHER7SLOPES_MEAINTERCPT_M0.001.002.003.004.005.006.007.00LBWALACHUABAKERBAYBRADFORDBREVARDBROWARDCALHOUNCHARLOTTECITRUSCLAYCOLLIERCOLUMBIADADEDESOTODIXIEDUVALESCAMBIAFLAGLERFRANKLINGADSDENGILCHRISTGLADESGULFHAMILTONHARDEEHENDRYHERNANDOHIGHLANDSHILLSBOROUGHHOLMESINDIAN RIVERJACKSONJEFFERSONLAFAYETTELAKELEELEONLEVYLIBERTYMADISONMANATEEMARIONMARTINMONROENASSAUOKALOOSAOKEECHOBEEORANGEOSCEOLAPALM BEACHPASCOPINELLASPOLKPUTNAMSAINT JOHNSSAINT LUCIESANTA ROSASARASOTASEMINOLESUMTERSUWANNEETAYLORUNIONVOLUSIAWAKULLAWALTONWASHINGTON

ALACHUA-23.773257.333257.333233.563209.793186.023162.253138.483114.713090.94ELEM13233.56

BAKER38.023181.083181.083219.103257.123295.143333.163371.183409.203447.22SOMEHS23209.79

BAY-9.073250.703250.703241.633232.563223.493214.423205.353196.283187.21HS33186.02

BRADFORD45.343362.673362.673408.013453.353498.693544.033589.373634.713680.05SOMECOL43162.25

BREVARD24.123262.343262.343286.463310.583334.703358.823382.943407.063431.18COLL53138.48

BROWARD-72.163270.893270.893198.733126.573054.412982.252910.092837.932765.77MS63114.71

CALHOUN2.933357.363357.363360.293363.223366.153369.083372.013374.943377.87PROF73090.94

CHARLOTTE47.903261.423261.423309.323357.223405.123453.023500.923548.823596.72

CITRUS50.563263.723263.723314.283364.843415.403465.963516.523567.083617.64

CLAY76.213264.473264.473340.683416.893493.103569.313645.523721.733797.94

COLLIER62.913248.823248.823311.733374.643437.553500.463563.373626.283689.19

COLUMBIA0.433298.953298.953299.383299.813300.243300.673301.103301.533301.96

DADE-72.763264.733264.733191.973119.213046.452973.692900.932828.172755.41

DESOTO16.643336.383336.383353.023369.663386.303402.943419.583436.223452.86

DIXIE37.643211.723211.723249.363287.003324.643362.283399.923437.563475.20

DUVAL-23.973274.903274.903250.933226.963202.993179.023155.053131.083107.11

ESCAMBIA-43.373282.603282.603239.233195.863152.493109.123065.753022.382979.01

FLAGLER24.253181.283181.283205.533229.783254.033278.283302.533326.783351.03

FRANKLIN1.192987.812987.812989.002990.192991.382992.572993.762994.952996.14

GADSDEN-59.863276.453276.453216.593156.733096.873037.012977.152917.292857.43

GILCHRIST28.353307.243307.243335.593363.943392.293420.643448.993477.343505.69

GLADES26.433232.013232.013258.443284.873311.303337.733364.163390.593417.02

GULF-27.333332.343332.343305.013277.683250.353223.023195.693168.363141.03

HAMILTON0.403230.043230.043230.443230.843231.243231.643232.043232.443232.84

HARDEE34.263280.413280.413314.673348.933383.193417.453451.713485.973520.23

HENDRY35.693332.983332.983368.673404.363440.053475.743511.433547.123582.81

HERNANDO61.713212.863212.863274.573336.283397.993459.703521.413583.123644.83

HIGHLANDS7.573314.433314.433322.003329.573337.143344.713352.283359.853367.42

HILLSBOROUGH-23.963266.723266.723242.763218.803194.843170.883146.923122.963099.00

HOLMES-8.173444.533444.533436.363428.193420.023411.853403.683395.513387.34

INDIAN RIVER21.253253.393253.393274.643295.893317.143338.393359.643380.893402.14

JACKSON-41.523244.843244.843203.323161.803120.283078.763037.242995.722954.20

JEFFERSON-11.313360.883360.883349.573338.263326.953315.643304.333293.023281.71

LAFAYETTE-20.463229.273229.273208.813188.353167.893147.433126.973106.513086.05

LAKE17.053255.603255.603272.653289.703306.753323.803340.853357.903374.95

LEE0.893262.393262.393263.283264.173265.063265.953266.843267.733268.62

LEON-50.373268.123268.123217.753167.383117.013066.643016.272965.902915.53

LEVY31.103235.973235.973267.073298.173329.273360.373391.473422.573453.67

LIBERTY-24.093504.263504.263480.173456.083431.993407.903383.813359.723335.63

MADISON-20.153188.613188.613168.463148.313128.163108.013087.863067.713047.56

MANATEE24.173265.673265.673289.843314.013338.183362.353386.523410.693434.86

MARION41.713260.103260.103301.813343.523385.233426.943468.653510.363552.07

MARTIN31.173225.663225.663256.833288.003319.173350.343381.513412.683443.85

MONROE47.423298.393298.393345.813393.233440.653488.073535.493582.913630.33

NASSAU37.663274.063274.063311.723349.383387.043424.703462.363500.023537.68

OKALOOSA55.053240.773240.773295.823350.873405.923460.973516.023571.073626.12

OKEECHOBEE-10.353335.303335.303324.953314.603304.253293.903283.553273.203262.85

ORANGE-24.933256.043256.043231.113206.183181.253156.323131.393106.463081.53

OSCEOLA24.973217.733217.733242.703267.673292.643317.613342.583367.553392.52

PALM BEACH-25.503265.233265.233239.733214.233188.733163.233137.733112.233086.73

PASCO75.773293.363293.363369.133444.903520.673596.443672.213747.983823.75

PINELLAS23.383259.023259.023282.403305.783329.163352.543375.923399.303422.68

POLK72.373252.013252.013324.383396.753469.123541.493613.863686.233758.60

PUTNAM0.253262.033262.033262.283262.533262.783263.033263.283263.533263.78

SAINT JOHNS50.863307.493307.493358.353409.213460.073510.933561.793612.653663.51

SAINT LUCIE3.453305.663305.663309.113312.563316.013319.463322.913326.363329.81

SANTA ROSA33.383282.763282.763316.143349.523382.903416.283449.663483.043516.42

SARASOTA25.633256.993256.993282.623308.253333.883359.513385.143410.773436.40

SEMINOLE8.983258.233258.233267.213276.193285.173294.153303.133312.113321.09

SUMTER-29.853224.313224.313194.463164.613134.763104.913075.063045.213015.36

SUWANNEE66.803316.893316.893383.693450.493517.293584.093650.893717.693784.49

TAYLOR3.973223.863223.863227.833231.803235.773239.743243.713247.683251.65

UNION45.103191.903191.903237.003282.103327.203372.303417.403462.503507.60

VOLUSIA23.973271.193271.193295.163319.133343.103367.073391.043415.013438.98

WAKULLA20.633249.263249.263269.893290.523311.153331.783352.413373.043393.67

WALTON14.973342.873342.873357.843372.813387.783402.753417.723432.693447.66

WASHINGTON-2.423295.043295.043292.623290.203287.783285.363282.943280.523278.10

co_Slopes

Mother's Education (ranked - elementary school to professional degree)

Infant's Birth Weight (grams)

Predicted Slopes and Intercepts for Florida Counties

Other Variables of Interest that are Contextual

Other Variables of Interest that are Contextual

Correlation between Slope for Mothers Education on LBW and County-Level Variables

Conclusions and DiscussionMultilevel modeling offers a way to address structural constrains, neighborhood context, social networks and individual behavioral factors simultaneous.Multilevel modeling embodies a family of statistical approaches, some of which are linear and some of which are non-linear.What are the ways that you see multilevel modeling potentially fitting into your analyses?

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