Nested Logit - Box

1 Nested LogitBrad Jones11 Department of Political ScienceUniversity of California, DavisApril 30, 2008 JonesPOL 213: Research MethodsJonesPOL 213: Research MethodsNested LogitIInteresting model that does not have IIA candidate model for structured choice example:IJpolitical parties a votericould choose : Green, Workers, Social Dem., Moderate, CR, ExtremeRightIModels?IConditional Logit or MNL?IIIA property could be an 213: Research MethodsNested LogitIIIA says that the disturbances are independent are assumed to remain the same if some alternative : one left party is a close substitute (possibly) split their vote across two leftist parties,elimination of one from the choice set does not imply they willrandomly distribute over remaining is, they most likely will gravitate to the remaining so, odds ratios will change because of 213: Research MethodsNested LogitIUnder NL (or MNNL), the idea is to group comparablealternatives and then structure choice setting as a tree.

2 IVoteridecides to vote leftist, centrist, or this the top level this choice is made, the voter must decide whichoutcome to choose:ILeft: Green, Workers; Center: SD, Moderate; Right: CR,Extreme RightIBasic result from conditional probability: Prij= Prj|i PriIJoutcomes ( parties) 213: Research MethodsNested LogitIConditional probability says the probability of the bottomlevel choice is equal to the conditional probability of selectingjgiven branchitimes the probability that two levels of probability because two levels of the conditional probability statement, Prj| we specify a utility model:Uij= xij+ wiIAs in the CL presentation, thexijare covariates that canchange over the choices (bottom level) and thewiarecovariates that are attributes of the choice sets (top level).

3 JonesPOL 213: Research MethodsNested LogitIThe conditional probabilities can only be a function of thexij:Prj|i=exp( xij) exp( wi)exp( wi) Nik=1exp( xik)=exp( xij) Nik=1exp( xik)IThe top level probability is defined by first identifying whatis sometimes called an inclusive value parameter:Ii= log(Ni k=1exp( xik))IThe probability of branchiis thenPri=exp( wi+ iIi) Cm=1exp( wi+ mIm)JonesPOL 213: Research MethodsNested LogitIThe inclusive value parameter, , is the weight accordedeach of the CL (or MNL), we assume this weight is fixed at is done via full information maximum likelihood:logL=N ilog[Prj|i Pri].IModel has many requires a lot of work to job to show you how.

4 IStatais actually quite good w/this 213: Research MethodsNested Logit : IllustrationII m going to continue with theStatadata set provided bytheir used it with conditional s consider the data 213: Research Methods. list family_id restaurant chosen kids rating distance cost income in 1/21+----------------------------------- ---------------------------------------- ------+| family~d restaurant chosen kids rating distance cost income ||-------------------------------------- ---------------------------------------- ---|1. | 1 Freebirds 1 1 0 39 |2. | 1 MamasPizza 0 1 1 39 |3.

5 | 1 CafeEccell 0 1 2 39 |4. | 1 LosNortenos 0 1 3 39 |5. | 1 WingsNmore 0 1 2 39 ||-------------------------------------- ---------------------------------------- ---|6. | 1 Christophers 0 1 4 39 |7. | 1 MadCows 0 1 5 39 |8. | 2 Freebirds 0 3 0 58 |9. | 2 MamasPizza 0 3 1 58 |10. | 2 CafeEccell 0 3 2 58 ||-------------------------------------- ---------------------------------------- ---|11.

6 | 2 LosNortenos 1 3 3 58 |12. | 2 WingsNmore 0 3 2 58 |13. | 2 Christophers 0 3 4 58 |14. | 2 MadCows 0 3 5 58 |15. | 3 Freebirds 1 3 0 30 ||-------------------------------------- ---------------------------------------- ---|16. | 3 MamasPizza 0 3 1 30 |17. | 3 CafeEccell 0 3 2 30 |18. | 3 LosNortenos 0 3 3 30 |19.

7 | 3 WingsNmore 0 3 2 30 |20. | 3 Christophers 0 3 4 30 ||-------------------------------------- ---------------------------------------- ---|21. | 3 MadCows 0 3 5 30 |+-------------------------------------- ---------------------------------------- ---+JonesPOL 213: Research Methods. nlogitgen type=restaurant(fast: Freebirds | MamasPizza,family: CafeEccell | LosNortenos | WingsNmore, fancy: Christophers | MadCows)This returns:new variable type is generated with 3 groupslabel list lb_typelb_type:1 fast2 family3 fancy.

8 Nlogittree restaurant type <-GIVES US THE TREE is the branch; restaurants are the "twigs."tree structure specified for the Nested Logit modeltop --> bottomtype restaurant--------------------------fast FreebirdsMamasPizzafamily CafeEccellLosNorte~sWingsNmorefancy Christop~sMadCowsJonesPOL 213: Research Methods\newpage. nlogit chosen (restaurant= cost rating distance)(type = incFast incFancy kidFast kidFancy), group(family_id) nologNested Logit estimatesLevels = 2 Number of obs = 2100 Dependent variable = chosen LR chi2(10) = likelihood = Prob > chi2 = | Coef.

9 Std. Err. z P>|z| [95% Conf. Interval]-------------+----------------- ---------------------------------------- -------restaurant |cost | .03402 <-These are the alpha | .1793759 .126895 .4280855distance | .0433352 +--------------------------------------- -------------------------type |incFast | .0116242 <-WHY DO I HAVE THESE?incFancy | .0458373 .0089109 .0283722 .0633024 <-These are the beta | .1394359 .2028729kidFancy | .1171277 +--------------------------------------- -------------------------(incl.)

10 Value |parameters) |type |/fast | <-These are the tau | | .4169075 .6494642 test of homoskedasticity (iv = 1): chi2(3)= Prob > chi2 = 213: Research MethodsFor nlogit chosen (restaurant= cost rating distance) (type = incFastincFancy kidFast kidFancy), group(family_id)nolog ivc(fast=1, family=1, fancy=1) notree <---CONSTRAINING TAU TO 1 User-defined constraints:IV constraints:[fast]_cons = 1[family]_cons = 1[fancy]_cons = 1 Nested Logit regressionLevels = 2 Number of obs = 2100 Dependent variable = chosen LR chi2(7) = likelihood = Prob > chi2 = | Coef.