School Work

Mixed Models

Description
Statistics in Psychology
Categories
Published
of 4
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Related Documents
Share
Transcript
  Week12: Linear Mixed Models ã Standard linear models (ANOVA, regression etc.) only look at fixed effects ã LMM consider subect!s ecific effects by modeling t#em as a random effect. ã LMM are flexible in t#at t#ey account for grou ings of data and subect s ecific effects ã $sed to analyse different ty es of data (longitudinal, re eated measures, multile%el or #ierarc#ical data, clustered data, block designs) ã &lustered data' obser%ations made on subects it#in same grou ã ixed effects' restricted factor le%els of study, co%ariates (e.g. gender, drug treatment   le%els a, b, c) ã *andom effects' randomly selected from o ulation of all ossible factor le%els (rats from + different litters   is t#ere a correlation from multi le obser%ations of a grou ) o Sam le of teet# in atients mout# Tutorial Slide Examples (below) ã ixed effects' diet, cou on ty es ã *andom effects' adults, s#o ing locationLecture e.g. uestion -. ã ixed effect' dosage, counseling, gender (e%en t#oug# it/s a co%ariate) ã *andom effect' atient (multi le obser%ations from one artici ants, see if e can generalise it to all atients) ã 0y e 111 ixed effects s#os same sig as 2stimates of fixed effects box ã 1f modeled as fixed effect' treats one as baseline (3)   #o %ariables are labeled ã 4arameter effects   #o to rite model ã &o%ariance arameters' is t#ere a significant effect of atient (random) MIXED MODELS TUTORIAL SOLUTIONS (81!Ne Dr#$%s e&&e' on lo erin$ )lood *ress#re +#esion 2 *andom effect' country (can e generalise t#ese effects to ot#er countriesixed effect' treatment (drug, lacebo), sex5e endent %ariable' blood ressure c#ange5on/t include random effect in redicted model (i! T,e -odel is 6 ik  7 8 9 :    9 ; x ik  9 d k  9 e ik 6 ik  7 <4c#ange of i t#   erson (i 7 , =, > n k ) assigned  t#  treatment ( 7 , =) from k t#  country (k 7 , =, >, ?), #ere n k  is t#e total number of obser%ations from t#e k t#  country =@--33B3.doc4age  of @  8 7 interce t :    7 t#e effect of t#e  t#  treatment, modelled as a 1C25 effect; 7 slo e t#at describes t#e linear trend beteen t#e res onse (<4c#ange) and sexx ik  7  if i t#   erson assigned  t#  treatment from k t#  country is female, 3 ot#erised k  7 t#e effect of t#e k t#  country, modelled as a *AN5OM effectd k  D N(3, E d= ) and e ik  D N(3,E e= )   Obser%ations of normality and #omogeneity of %ariance (ii! o#.# &ro- S*SS In&or-aion /rieria a B?.@=@B.@=@B.F3+=.33++3.33+!= *estricted LogLikeli#ood AkaikeGs 1nformation&riterion (A1&)Hur%ic# and 0saiGs&riterion (A1&&)<oIdoganGs &riterion(&A1&)Sc#arIGs <ayesian&riterion (<1&)0#e information criteria are dis layed insmaller!is!better forms.5e endent Variable' <4c#ange.a. 0ixed E&&e's Significant effects on %ariable (b c#ange)5escri ti%e statistics if you ant to look at direction of effects (use to rite out results)   ill tell you mean b c#ange (female' =+, male' B@ com arison)Jreater effect for drug treatment t#an lacebo T.e III Tess o& 0ixed E&&e's a B.3@=.-B.333F=.3@3?.F3.33=FB.F.B-.3Source1nterce t0reatmentsexNumerator df 5enominator dfSig.5e endent Variable' <4c#ange.a. =@--33B3.doc4age = of @  Esi-aes o& 0ixed E&&e's  !=3.3-@+B.F3-3+==.@3!+.@-.333!=F.FB-B?!=.@3+3??!3.FB.@@3F??F=.3@3!B.+.33=!F.+3-=B?!B.?=+33B3 a 3.....!-.-+@=?3B.@B+F@FB.F!=.+F.3!+.BF3@!=.3F@F4arameter 1nterce tK0reatment75K0reatment74sex2stimateStd. 2rrordftSig.Loer <ound$ er <ound?+ &onfidence 1nter%al0#is arameter is set to Iero because it is redundant.a. 5e endent Variable' <4c#ange.b. 0reat one %ariable as baseline and look at ot#er %ariable/s effect (one is 3, and t#e ot#er is t#edifference) /o3arian'e *ara-eers 0elling you #et#er or not t#ere is a significant relations#i beteen eac# country and b scores (no t#ere is no c#ange beteen eac# country and blood ressure scores   non significant)   Esi-aes o& /o3arian'e *ara-eers a +=.F+?=+.?-=-??.=@@.333@=.@?+.F@+B+.=FF+3B=.B-FF?.3-F.=FF+.-3F===B.+-3-B4arameter *esidualVariance1nterce t Ksubect7 &ountry2stimateStd. 2rrorald Sig.Loer <ound$ er <ound?+ &onfidence 1nter%al   5e endent Variable' <4c#ange.a. (iii! S#--ar .ara$ra., ã 0#e treatment co%ariate is significant it# !%alue 7 3.33=. On a%erage, t#e drug treatment reduced <4c#ange by 3.F units, all ot#er t#ings ePual. ã 0#e sex co%ariate is significant it# !%alue 7 3.3. On a%erage, females #ad a reduction of -.-+@ units com ared to males, all ot#er t#ings ePual. ã 0#e random interce t term, #ic# measures t#e %ariation in t#e <4c#ange beteen countries, #as a !%alue 7 3.=FF, #ic# is not significant. (i3! 0#e a%erage <4c#ange for a erson taking t#e lacebo (i.e. no drug treatment) is a reduction of =3.3-@+, all ot#er t#ings ePual (!=3.3-@)6 7 !=3.3-@ 9 3 6 7 !=3.3-@0#e a%erage <4c#ange for a male taking t#e drug treatment is a reduction B3.-3 units(!=3.3-@+ Q 3.F 7 !B3.-3), all ot#er t#ings ePual6 7 !=3.3-@ !3.FF (! -.-+@ x 3)6 7 ! B3.-3 =@--33B3.doc4age B of @  0#e a%erage <4c#ange for a female taking t#e drug treatment is a reduction B?. units(!=3.3-@+ Q 3.F Q -.-+@B 7 !B?.++@), all ot#er t#ings ePual (3!  0#e correlation beteen t#e <4c#ange %alues from t#e k t#  country is&orr(6 km ,6 kn ) 7 E d=  R (E d=  9 E e= )   7 B+.=F- R (B+.=F- 9 +=.F+?=) 7 3.3=F 0#e <4c#ange %alues from atients in t#e k t#  country #a%e a 3er lo 'orrelaion 4eo le from t#e same country are no more similar t#an eo le from different countries. ã &an generalise result o%er different countries (3i!  0#e re%ious model, it# sex co%ariate, #ad A1& 7 @B.@= and t#e current model, it#out sex co%ariate, #as A1& 7 +@.+. *etain t#e sex term in t#e model as t#at model #as a loer A1& %alue. (#ig#er t#e number t#e oorer t#e fit, so retain sex in model) In&or-a(ion /ri(eria a +3.+33+@.+33+@.+-=.-F+3.-F+!= *estricted LogLikeli#ood AkaikeGs 1nformation&riterion (A1&)Hur%ic# and 0saiGs&riterion (A1&&)<oIdoganGs &riterion(&A1&)Sc#arIGs <ayesian&riterion (<1&)0#e information criteria are dis layed insmaller!is!better forms.5e endent Variable' <4c#ange.a. T1.e III Tes(s o& 0ixed E&&e'(s a  A.-3+ @.3- .333 F=.A+@ ?.?@ .33=Source1nterce t0reatmentNumerator df 5enominator df ) Sig.5e endent Variable' <4c#ange.a. =@--33B3.doc4age @ of @
Search
Tags
Related Search
We Need Your Support
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks