SPER LatentGrowthCurve 2016-06-17b · OHSU-PSU School of Public Health 1 ... Freely es@mate slope...
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6/17/16 1 Latent growth curve analysis in perinatal and pediatric epidemiology SPER Advanced Methods Workshop Miami, FL June 20, 2016 Janne Boone-Heinonen, PhD, MPH Sheila Markwardt, MPH Oregon Health & Science University OHSU-PSU School of Public Health 1 Objec@ves ParJcipants will be able to: • Describe the strengths and general approach of latent growth curve analysis in exisJng research • Evaluate whether latent growth curve analysis is appropriate for their research • Apply basic latent growth analysis in Mplus (example: infant growth) 2 Growth Curves Predictors (e.g., SES) Outcomes (e.g., diabetes) Generalized EsJmaJng EquaJons (average trajectories) Intercepts Slope 2 Mixed effects models (individual trajectories) Latent growth curves (individual trajectories) Slope 1 3 Structural Equa@on Modeling (SEM) T1 T2 T3 i s Exposure 1 X1 X2 X3 C Latent class analysis Factor analysis T4 Latent growth curve Path analysis Exposure 2 Outcome Maternal pre- pregnancy BMI GestaJonal Weight Gain Infant growth CogniJve development Observed variable Latent variable 4
Transcript of SPER LatentGrowthCurve 2016-06-17b · OHSU-PSU School of Public Health 1 ... Freely es@mate slope...
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Latentgrowthcurveanalysisinperinatalandpediatricepidemiology
SPERAdvancedMethodsWorkshopMiami,FLJune20,2016JanneBoone-Heinonen,PhD,MPHSheilaMarkwardt,MPHOregonHealth&ScienceUniversityOHSU-PSUSchoolofPublicHealth
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Objec@ves
ParJcipantswillbeableto:• Describethestrengthsandgeneralapproachoflatentgrowth
curveanalysisinexisJngresearch• Evaluatewhetherlatentgrowthcurveanalysisisappropriate
fortheirresearch• ApplybasiclatentgrowthanalysisinMplus(example:infant
growth)
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GrowthCurves
Predictors(e.g.,SES)
Outcomes(e.g.,diabetes)
GeneralizedEsJmaJngEquaJons(averagetrajectories)
Intercep
ts Slope
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Mixedeffectsmodels(individualtrajectories)
Latentgrowthcurves(individualtrajectories)
Slope1
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StructuralEqua@onModeling(SEM)
T1 T2 T3
i s
Exposure1
X1 X2 X3
C
LatentclassanalysisFactoranalysis
T4
Latentgrowthcurve
Pathanalysis
Exposure2
Outcome
Maternalpre-pregnancyBMI
GestaJonalWeightGain
Infantgrowth
CogniJvedevelopment
Observedvariable
Latentvariable4
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LatentGrowthCurves
Weight1 Weight2 Weight3
I S
Weight4
11 1
1 01 2
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RI RS
I,InterceptS,SlopeRI,RS,InterceptandSloperesidualse1-e4,errorterms
e1 e2 e3 e4
Intercep
ts
Slope1
Slope2
Missingvaluesallowed!
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LatentGrowthCurvesflexibilityandopJons
1. Non-lineargrowth2. Covariates3. Subgroupdifferences4. ScalingofJme
T1 T2 T3
i s
T4
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1.Non-lineargrowth(a,b)
T1 T2 T3
i s
T4
(a)Higherorderslopes
(b)Piecewise
q
T1 T2 T3
i s1
T4 T5 T6
s2
1 1 11
11 1 11
1
10
23 0
1 49
01 22
02
001 2
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1stlinearpiece
2ndlinearpiece 7
1.Non-lineargrowth(c,d)
(d)Structuredlatentcurves
(c)Freelyes@mateslopefactorloadings
T1 T2 T3
i s
T4
1 1 11
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λ1λ2
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e.g.,exponenJal,Gompertz
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2.Covariates
T1 T2 T3
i s
T4
ParentaleducaJon
ParJcipanteducaJon
Race/ethnicity
Timevaryingcovariates
Timeconstantcovariates
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3.Subgroupdifferences
T1 T2 T3
i s
T4
X1 X2
Race/ethnicity
Covariate/interac@on Mul@plegroups
Sex
Race/eth*sex
T1 T2 T3
i s
T4
X1 X2
Race/ethnicity
T1 T2 T3
i s
T4
X1 X2
Race/ethnicity
BoysGirls
Test:interacJonterm
Test:overallmodelfitinmodelsthat(a)constrainparameter(s)tobeequalinboysandgirlsand(b)parameter(s)todifferinboysingirls
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4.Individuallyvarying@mepoints
Exam1 Exam2 Exam3 Exam4 Exam5 Exam6
Age(target) Birth 3mo 6mo 9mo 12mo 18mo
Age(actual) Birth 2-4mo 5-7mo 8-10mo 11-13mo 14-19mo
Exam1 Exam2 Exam3 Exam4 Exam5 Exam6
Child1 Birth 2.9mo 6.2mo 9.8mo 12.2mo 19.7mo
Child2 Birth 1.2mo 1.8mo 4.4mo 9.7mo 12.1mo
Scenario1
Scenario2
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Othertopics
T1 T2 T3
i s
T4
G(a)Growthmixturemodeling
(b)Binary,ordinaldependentvariables
X1a X1b X1c
C1
X2a X2b X2c
C2
X3a X3b X3c
C3
ic sc
Cogni9vedevelopmentfactors
(c)Latentgrowthcurveoflatentvariables
T1 T2 T3
i s
T4
(d)Parallelprocessmodel
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PRACTICALAPPLICATIONOFLATENTGROWTHCURVES
PartII
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SEMsohware
• Mplus• AMOS• LISREL• Stata• R
1.Datamanagement(Stata,SAS)
3.SEMprogram(Mplus)
2.Export/Import
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Dataprocessing1.Datamanagement
(Stata,SAS)
3.SEMprogram(Mplus)
2.Export/Import Stata:stata2mplusfuncJonSAS:hip://www.ats.ucla.edu/stat/mplus/faq/sas2mplus.htm
• Limittokeyvariables• 0/1codingforbinaryvariables• Create“dummy”variables• Createhigherorderterms(otherthanJme)• CreateinteracJonterms• 8-charactervariablenames• “Wide”datastructure• (Missingvaluecode)
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2b.ImporttoMplusStata:stata2mpluscreatesthisMpluscode
SAS:analystcreatesanalogouscode
Title: Stata2Mplus conversion for X:\SPH\Shared\Obesity\Infants.dta List of variables converted shown below
… Data: File is X:\SPH\Shared\Obesity\Infants.dat; Variable: Names are id wt0-wt6 a0-a6; Missing are all (-9999); Analysis: Type = basic ;
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3.Mplusanalysis
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Example:Infantgrowth
LiveBirth
2years
KaiserPermanenteNWRegion(KPNW)ElectronicMedicalRecordDataMATMORB(CDC-Funded,KPNW-basedstudy)
Kaiser-basedcollaboratorsStephenP.Fortmann,MDKimberlyVesco,MD
• Dependentvariable:weight(kg),2weeksto24months– Inthisexample,selectedmeasurewithinageintervals,closesttothefollowingJmepoints:birth,3months,6months,9months,12months,18months,24months
• LatentGrowthCurveanalysis(MPlus7.4)
N=21,899livebirthsin2000-2007
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Mplus:basicsyntax Title: Linear LGM; DATA: File is X:\SPH\Shared\Obesity\Infants.dat; VARIABLE: Names are id wt0-wt6 a0-a6;
Usevariables are wt0-wt6;
Missing are all (-9999); ANALYSIS: …
Any(preferablyinformaJve)Jtle
FilelocaJon
ALLvariablesindataset
Variablesinthecurrentanalysis
Missingdatacodeassignedinexportstep
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Latentgrowthcurve:linear[input]
Title: Linear LGM; DATA: File is X:\SPH\Shared\Obesity\Infants.dat; VARIABLE: Names are id wt0-wt6 a0-a6; Usevariables are wt0-wt6; Missing are all (-9999); MODEL: i l | wt0@0 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]; OUTPUT: TECH1;
User-specifiednames:i=interceptterml=linearslopeterm
WeightvariablesatJme0…6
Slopefactorloadings(months/10)
Note:FIML(formissingdata)isthedefault
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Latentgrowthcurve:linear[output(1)]
THE MODEL ESTIMATION TERMINATED NORMALLY MODEL FIT INFORMATION Loglikelihood H0 Value -174480.963 H1 Value -108311.313 Information Criteria Akaike (AIC) 348985.927 Bayesian (BIC) 349081.857 Sample-Size Adjusted BIC 349043.721 (n* = (n + 2) / 24) Chi-Square Test of Model Fit Value 132339.300 Degrees of Freedom 23 P-Value 0.0000 …
Usefulforcomparingmodels(BICdiff>10)
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Latentgrowthcurve:linear[output(2)]
… RMSEA (Root Mean Square Error Of Approximation) Estimate 0.513 90 Percent C.I. 0.510 0.515 Probability RMSEA <= .05 0.000 CFI/TLI CFI 0.000 TLI -0.247 Chi-Square Test of Model Fit for the Baseline Model Value 96903.981 Degrees of Freedom 21 P-Value 0.0000 SRMR (Standardized Root Mean Square Residual
Value 1.208
<=0.05isgood
>0.95Isgood
<=0.05isgood
Usuallysig
Thismodelhasterriblefit 22
Latentgrowthcurve:linear[output(2)]
MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value I | WT0 1.000 0.000 999.000 999.000 WT1 1.000 0.000 999.000 999.000 WT2 1.000 0.000 999.000 999.000 WT3 1.000 0.000 999.000 999.000 WT4 1.000 0.000 999.000 999.000 WT5 1.000 0.000 999.000 999.000 WT6 1.000 0.000 999.000 999.000 L | WT0 0.000 0.000 999.000 999.000 WT1 0.300 0.000 999.000 999.000 WT2 0.600 0.000 999.000 999.000 WT3 0.900 0.000 999.000 999.000 WT4 1.200 0.000 999.000 999.000 WT5 1.800 0.000 999.000 999.000 WT6 2.400 0.000 999.000 999.000
Fixedat1
Fixedpathloadingsfor
eachJmepoint
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Latentgrowthcurve:linear[output(2)]
MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value L WITH I 0.139 0.004 33.084 0.000 Means I 3.847 0.009 411.701 0.000 L 4.097 0.009 456.723 0.000 Intercepts WT0 0.000 0.000 999.000 999.000 WT1 0.000 0.000 999.000 999.000 WT2 0.000 0.000 999.000 999.000 WT3 0.000 0.000 999.000 999.000 WT4 0.000 0.000 999.000 999.000 WT5 0.000 0.000 999.000 999.000 WT6 0.000 0.000 999.000 999.000
Covariancebetweeninterceptandslope
Meaninterceptandslope
Errors
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Latentgrowthcurve:linear[output(3)]
Two-Tailed Estimate S.E. Est./S.E. P-Value Variances I 0.067 0.004 16.916 0.000 L 0.440 0.010 46.095 0.000 Residual Variances WT0 0.380 0.009 40.987 0.000 WT1 0.903 0.012 78.024 0.000 WT2 2.467 0.034 73.090 0.000 WT3 2.153 0.031 69.375 0.000 WT4 1.466 0.022 66.852 0.000 WT5 0.031 0.015 2.021 0.043 WT6 2.097 0.038 54.466 0.000
Varianceofindividualinterceptsandslopesaroundtheaverageintercept/slope
ErrorsateachJmepoint(observedvaluevs.individualpredictedvalue)
Intercep
ts
Slope1
Slope2
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Lineargrowth?!
• (very)poormodelfit
• Large,varyingerrorsoverJme
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Latentgrowthcurve:cubic[input]
Title: Cubic LGM Binned; DATA: File is X:\SPH\Shared\Obesity\Infants.dat; VARIABLE: Names are id wt0 wt1 wt2 wt3 wt4 wt5 wt6 ; USEVAR = wt0-wt6; Missing are all (-9999); MODEL: i l q c |
wt0@0 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected];
User-specifiednames:i=interceptterml=linearslopetermq=quadra@cslopetermc=cubicslopeterm 27
T1 T2 T3
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q
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23 0
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c0
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Cubicgrowth?
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Beiermodelfit;furtherimproveswithsubgroups,covariatesRMSEA=0.157|CLI=0.917|TLI=0.883|SRMR0.061
BIC(linear)=349081|BIC(cubic)=224917
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Latentgrowthcurve:predictor(s)[input]
Title: Cube LGM, race as covariate; DATA: File is X:\SPH\Shared\Obesity\Infants.dat; VARIABLE: Names are id wt0-wt6 race1 race2 race3; Usevariables are wt0-wt6 race1 race2 race3; Missing are all (-9999) ; MODEL: i l q c |
wt0@0 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]; i on race1 race2 race3; l on race1 race2 race3; q on race1 race2 race3; c on race1 race2 race3;
Regresseachgrowthtermonraceindicatorvariables
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Race/ethnicity
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Title: Cube LGM, BMI as outcome; DATA: File is X:\SPH\Shared\Obesity\Infants_BMI.dat; VARIABLE: Names are id wt0-wt6 bmi; Usevariables are wt0-wt6 bmi; Missing are all (-9999) ; MODEL: i l q c |
wt0@0 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]; bmi on i; bmi on l; bmi on q; bmi on c;
Latentgrowthcurve:outcomes[input]
BMIatage5
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Title: Cube LGM, by gender; DATA: File is X:\SPH\Shared\Obesity\Infants_Gender.dat; VARIABLE: Names are id wt0-wt6 bmi; Usevariables are wt0-wt6 gender; Missing are all (-9999) ; GROUPING = gender(0=Male 1=Female); MODEL: i l q c |
wt0@0 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected];
Latentgrowthcurve:subgroupdifferences[input]
Test:overallmodelfitinmodelsthat(a)constrainparameter(s)tobeequalinboysandgirlsand(b)parameter(s)todifferinboysingirls
Title: Cube LGM, by gender w/ equal parameters; DATA: File is X:\SPH\Shared\Obesity\Infants_Gender.dat; VARIABLE: … GROUPING = gender(0=Male 1=Female); MODEL: i l q c |
wt0@0 [email protected] [email protected] [email protected] [email protected] [email protected] [email protected]; Model: [i] (1); [l] (2); [q] (3); [c] (4); Model Female: [i] (1); [l] (2); [q] (3); [c] (4);
Intercept&slopesvarybygender:BIC237906Intercept&slopesequal:BIC239834
Constraints:Maleintercepts=FemaleinterceptMalelinearslope=FemalelinearslopeMalequadraJcslope=FemalequadraJcslopeMalecubicslope=Femalecubicslope
Latentgrowthcurve:subgroupdifferences[input]
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Issuesandchallenges
• Conceptualchallenges– Flexibilityàmoredecisions,reliesonstrongtheoreJcalframework
• OperaJonalchallenges:– Specializedsohwarerequired(ohenMplus)– Mpluslearningcurve– DifficulJesinmodelconvergence
• SpecifystarJngvalues• IncreasenumberofiteraJons• Fixingvariances,means,covariances
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Ques@ons?
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JanneBoone-Heinonen,PhD,[email protected],[email protected]
