?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

PART 1

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?
? 1.  Test for significance of squared term
?
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 $
CALC   ; L0 = logl $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Pricesq,Asc4 $
CALC   ; L1  = logl $
CALC   ; list ; chisq = 2*(l1 - l0) $
?
? 2.  Test for homogeneity. Are men the same as women ?
?
SAMPLE ; All $
CLOGIT ; For[Male = 0] ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 $
CALC   ; LoglF = LogL $
MATRIX ; db = b ; dv = varb $
CLOGIT ; For[ Male = 1] ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 $
CALC   ; LoglM = LogL $
MATRIX ; db = db - b ; dv = dv + varb $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 $
CALC   ; LoglMF = LogL $
? Likelihood Ratio Test
CALC   ; List ; Chisq = 2*(LoglM + LogLF - LOGLMF) ; Ctb(.95,8) $
? Wald test
MATRIX ; List ; Wald = db'<dv>db $
? A convenient way to compute all three models.
CLOGIT ; For[Male = *,1,0] ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 $

?
? 3.  Examine the marginal effect of price on brand choice
?
SAMPLE ; All $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 
       ; Effects : Price (*) $
?
? 4.  What would happen to the market shares of the three brands
?     If the price of Brand 1 of shoes rose by 50%.  What would
?     happen to the market shares if the prices of all three
?     brands rose by 50%?
?
SAMPLE ; All $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 
       ; Effects : Price (*) $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 
       ; Simulation = * 
       ; Scenario: Price (Brand1)  = [*] 1.5 $ 
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 
       ; Simulation = * 
       ; Scenario: Price (Brand1,Brand2,Brand3)  = [*] 1.5  $

?
?  5.  Testing for IIA
?
SAMPLE ; All $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4  $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4 ; IAS = Brand3  $
?
? 6.  Do men pay different attention to fashion than women?
?     Is the difference statistically significant?
?
Create ; MaleFash = Male*Fash $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4,MaleFash $
CLOGIT ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,Asc4,MaleFash 
       ; Simulation = * ; Scenario: MaleFash(*) = [*] 0 $

?
? 7.  Building heterogeneity into the model
?
NLOGIT (none)  ; Lhs = Choice ; Choices = Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4 
       ; Effects: Price(Brand1,Brand2,Brand3)  $
NLOGIT (het) ; Lhs = Choice ; Choices = Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4 
       ; Het  ; Effects: Price(Brand1,Brand2,Brand3)  $
NLOGIT (variance, het) ; Lhs = Choice ; Choices = Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4 
       ; Het ; Hfn = Male,age25,age39  ; Effects: Price(Brand1,Brand2,Brand3)  $

?
? 8.  Testing for homoscedasticity with a Wald test
?
NLOGIT (het) ; Lhs = Choice ; Choices = Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4 
       ; Het ; Par $
MATRIX ; c = b(5:7) ; vc = Varb(5:7,5:7)  ; List ; WaldStat = c'<vc>c $

?
? 9.  Testing for heterogeneity in the heteroscedasticity
?
NLOGIT (het) ; Lhs = Choice ; Choices = Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4 
       ; Het $
CALC   ; LogLR = LogL $
NLOGIT (variance, het) ; Lhs = Choice ; Choices = Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4 
       ; Het ; Hfn = Male,age25,age39 $
CALC  ; LoglU = LogL $
CALC  ; List ; LRTest = 2*(LogLU - LogLR) ; Ctb(.95,3) $


?************************************************************************
?************************************************************************
?************************************************************************
?
? These exercises are based on the travel model data, clogit.lpj

?
?************************************************************************
?************************************************************************
?************************************************************************


?
? 1.  Basic nested logit
?
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; Tree = Private(Air,Car),Public(Train,Bus)
        ; Show Tree $
CALC    ; LOGLU = LOGL $
?
? 2.  Different normalization
?
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; Tree = Private(Air,Car),Public(Train,Bus)
        ; RU2 
        ; CrossTab$
?
? 3.  Constrain IV parameters to produce MNL model
?
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; Tree = Private(Air,Car),Public(Train,Bus)
        ; IVSET:(Private,Public)=[1] $
CALC    ; LOGLR = LOGL $
CALC    ; List ; LRTEST = 2*(LOGLU - LOGLR) $
?
? 4.  Degenerate branch.  Two normalizations
?
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; Tree = Fly(Air),Ground(Car,Train,Bus) $
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; Tree = Fly(Air),Ground(Car,Train,Bus) ; RU2 $
?
? 5. Use nested logit to reveal scaling.
?
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; Tree = Fly(Air),Drive(Car),Rail(Train),Ride(Bus) 
        ; IVSET: (Ride) = [1] 
        ; Par $
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; HET ; SDV = SA,ST,1.0,SC $
?
? 6.  A Generalized Nested Logit Model
?
NLOGIT  ; Lhs = Mode ; Choices=Air,Train,Bus,Car
        ; Rhs = One,GC,TTME,INVT,INVC
        ; Tree = Fast(Air,Car,Train),Public(Train,Bus)
        ; GNL $

?
? 7.  Homoscedastic vs. Heteroscedastic Extreme Value
?
NLOGIT		; Lhs = Mode
	    	; Choices = Air,Train,Bus,Car
                 	; Rhs = TTME,INVC,INVT,GC,One
          		; Effects: INVT(*) $
CALC      	; LR = LogL $
NLOGIT    	; Lhs = Mode
	    	; Choices = Air,Train,Bus,Car
          		; Rhs = TTME,INVC,INVT,GC,One
          		; Het 
          		; Effects: INVT(*) $
CALC      	; LU = LogL $
CALC      	; List ; LRTEST = 2*(LU - LR); Ctb(.95,3) $


?
? 8.Heterogeneous.  Does Income affect the means or the variances?
?
SAMPLE	; All $
NLOGIT    	; Lhs = Mode
	    	; Choices = Air,Train,Bus,Car
          		; Rhs = TTME,INVC,INVT,GC; Rh2=One,Hinc $
CREATE    	; LOGLMean = Logl_Obs $
NLOGIT    	; Lhs = Mode
	    	; Choices = Air,Train,Bus,Car
          		; Rhs = TTME,INVC,INVT,GC,one
          		; Het ; Hfn = HINC $
CREATE    	; LoglVar = Logl_Obs $
CREATE    	; V = LoglMean - LogLVar $
REJECT    	; CASC = 0 $
CALC      	; List ; Vuong = sqr(n) * xbr(v) / sdv(v) $



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?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

PART 2

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? Using the clogit.lpj data
?
? 1. Multinomial Probit Model
?
NLOGIT  ; Lhs = Mode ; output=ic
	  ; Choices = Air,Train,Bus,Car
        ; Rhs = TTME,INVC,INVT,GC; Rh2=One,Hinc 
        ; Effects:GC(*) $
NLOGIT  ; Lhs = Mode ; MNP ; PTS = 10 ; Maxit = 10 ; Halton
	  ; Choices = Air,Train,Bus,Car
        ; Rhs = TTME,INVC,INVT,GC; Rh2=One,Hinc 
        ; Effects:GC(*) $
?
? Using Brand Choices Data, brandchoicesSP.lpj
?
?(1) Basic 3 class model
?
Nlogit ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4
       ; LCM ; Pds = 8 ; Pts = 3 $
?
? (2) 3 class model. Class probabilities depend on covariates
?
Nlogit ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4
       ; LCM=Male,Age25,Age39 ; Pds = 8 ; Pts = 3 $
?
? (3) Overspecified model.  4 class model.  The true model
?     underlying the data has three classes
Nlogit ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4
       ; LCM ; Pds = 8 ; Pts = 4 $
?
? (4) Random parameters model
?
Nlogit ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4
       ; RPL  ; Fcn= Fash(n),Price(n) 
       ; Pds = 8 ; Pts = 25 $
?
? (5) Correlated parameters
?
Nlogit ; Lhs = Choice ; Choices=Brand1,Brand2,Brand3,None
       ; Rhs = Fash,Qual,Price,ASC4
       ; RPL  ; Fcn= Fash(n),Price(n) ; Correlated
       ; Pds = 8 ; Pts = 25 $
?
? (6).  An Error Components Logit model
?
ECLOGIT ; Lhs = Choice ; Choices = Brand1,Brand2,Brand3,None
        ; Rhs = Fash,Qual,Price,ASC4 
        ; Pts = 10 ; Pds = 8
        ; ECM = (Brand1,Brand2,Brand3),(none) $

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?&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

PART 3

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/* ?
? Data for this application are in SPRP.LPJ
?
? Application of revealed/stated preference data
? Uses nested logit to handle scaling.
? Sample is also choice based, as shown by weights.
?
? Documented in several Hensher papers from ITS in Sydney.
?
? Choice variable is CHOSEN
? Number of choices in choice set is CSET
? Specific choices from master set given by ALTIJ
? FCOST = fuel cost
? AUTOTIME = time spent commuting by car.
? Numerous other variables in the data set.
?
*/
NLOGIT
 ;lhs=chosen,cset,altij
 ;choices=RPDA,RPRS,RPBS,RPTN,SPDA,SPRS,SPBS,SPTN,SPLR,SPBW
         /.592,.208,.089,.111, 1.0, 1.0, 1.0, 1.0,1.0,1.0
 ;tree=Commute [  rp  (RPDA,RPRS,RPBS,RPTN),
   spda(SPDA), sprs(SPRS),spbs(SPBS),sptn(SPTN),
               splr(SPLR),spbw(SPBW)]
    ;ivset: (rp)=[1.0]  ;ru1 ;maxit=150
    ;model:
U(RPDA) = rdasc  + invc*fcost+tmrs*autotime /
U(RPRS) = rrsasc + invc*fcost+tmrs*autotime /
U(RPBS) = rbsasc + invc*mptrfare+mtpt*mptrtime/
U(RPTN) =          cstrs*mptrfare+mtpt*mptrtime/
U(SPDA) = sdasc  + invc*fueld  + tmrs*time+cavda*carav /
U(SPRS) = srsasc + invc*fueld + tmrs*time/? cavrs*carav/
U(SPBS) =          invc*fared + mtpt*time +acegt*spacegtm/
U(SPTN) = stnasc + invc*fared + mtpt*time+acegt*spacegtm/
U(SPLR) = slrasc + invc*fared + mtpt*time+acegt*spacegtm/
U(SPBW) = sbwasc + invc*fared + mtpt*time+acegt*spacegtm$