Demonstration of NLOGIT Software
• • • • • • •
Preparation of Data set Reading Data Various data analysis commands Input for MNL model Interpretation of MNL output Input file for Nested logit model Interpretation of NL output
NLOGIT • Extension of LIMited DEPendent Variable Models (LIMDEP) • Nested LOGIT Models (NLOGIT) – Descriptive statistics – Linear regressions – Developing Models like • • • •
Multinomial Logit models Nested Logit models Random parameter logit models Probit models etc.
Choice twTT
tTT
bTT
cTT
twTC
tTC
bTC
cTC Hhinc Hhsiz
2
35
24
38
30
15
7
10
23
50
4
3
30
20
32
25
13
6
8
22
40
3
1
50
35
59
45
23
13
15
40
70
2
ALOGIT Choices: 1-TW, 2-Train, 3-Bus,
4-Car
NLOGIT Choice
TT
TC
Hhinc
Hhsiz
0
35
15
50
4
1
24
7
50
4
0
38
10
50
4
0
30
23
50
4
0
30
13
40
3
0
20
6
40
3
1
32
8
40
3
0
25
22
40
3
1
50
23
70
2
0
35
13
70
2
0
59
15
70
2
0
45
40
70
2
Data set TW Train Bus Car TW Train Bus Car TW Train Bus Car TW Train Bus Car
Cset 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
AltID 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Choice 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0
TT 20 15 45 60 15 12 42 70 34 30 80 100 55 42 100 150
TC 27 22 52 70 22 19 49 100 41 37 87 140 62 49 107 200
Reading Data • Manual entry • Spread sheet file program (Microsoft Excel) • Data file (.dat) • By using “Read” command • By using project file (.lpj)
Reading data • Text;_ _ _ _ _ _ _ $ • Read ;File=E:\Nlogit.prn ;Nobs=1000 ;Nvar=7 ;Names=Choice,TT,TC,GC,WT,HHInc,Hhsize $
Instructions to NLOGIT • Two methods of giving instructions to NLOGIT – Dialog boxes – Self documenting Command lines
Data analysis commands • REGRESS; Lhs = dependent variable; Rhs = independent variable $ • HISTOGRAM; Rhs = a variable $ • DSTATS; RHS = the list of variables $ ? For descriptive statistics. • CREATE; name = expression; name = expression . . . $ • CROSSTAB; Lhs = variable; RHS = Variable $ • SHOW • Simulation ;Scenario: TC(Rail)=[*]2 ;Scenario: TT(Bus)=[+]4
Types of data on the choice variable • Individual data The Lhs variable consists of zeros and a single which indicates the choice that the individual made • Proportions data Lhs variable consists of a set of sample proportions ranges from zero to one • Frequency data Lhs variable consists of a set of frequency counts for the outcomes (non negative integers) • Ranks data Lhs variable consists of a complete set of ranks of the alternatives in the individual’s choice set • [0,1,0,0,0] ----- unranked • [4,1,3,2,5] ------ ranked
Multinomial Logit model • The choice variable, Choice=1,2,3,4 for tw, train, bus and car • For each mode, TT, TC, GC, WT --- Differ by choices • For the individual, Hhinc, Hhsize --- Does not differ by choice • NLOGIT ; Lhs= Choice ; Choices = tw, train, bus, car ; Rhs = TT, TC, GC, WT ;Rh2 = One, hhinc, hhsiz $
Multinomial choice model (MNL) NLOGIT ;lhs = choice ;choices = ;Model: U(alternative 1 name) = / U(alternative 2 name) = / -------U(alternative i name) = $
Multinomial choice model (MNL) NLOGIT ;lhs = choice ;choices =Metro,Rail,Bus,Car ;Model: U(Metro) = a_metro+tt*TT+tc*TC+wt*WT+gc*GC+a_hhinc*HHInc / U(Rail) =b_rail+ tt*TT+tc*TC+wt*WT+gc*GC+b_hhinc*HHInc / U(Bus) = c_bus+tt*TT+tc*TC+wt*WT+gc*GC+c_hhinc*HHInc/ U(Car)=d_car+tt*TT+tc*TC+wt*WT+gc*GC+d_hhinc*HHInc $
Maximum Likelihood Estimation • LL = (n!/h!(n − h)!)p^h(1 − p)^(n−h) • Searching for the value of “p” which will maximize the likelihood
• −2(LLbase model − LLestimated model)∼ Chi squared(number of new parameters estimated in the estimated model) • Prob [ chi squared > value ] = .00000
Interpretation To Determine whether an explanatory variable is statistically significant or not • Logical sign of the parameter • Wald statistic (model) > critical wald value (1.96) [at 95 percent confidence level (i.e. alpha=0.05)] • P-value < 0.05 (alpha) [ Null hypothesis: Estimated model is no better than base model Alternate hypothesis: Estimated model is better than base model]
Nested Logit Model Limb
Travel
Branch Twig
Public Bus
Private Rail
Car
• U(Bus)=β0+ β1*Var1+ β2*Var2 • U(Public)=Σ α*Z + Ф*EMU • EMU (Bus,Rail) = ln {expV(bus) + expV(Rail)}
TW
• In defining the tree structure, the following NLOGIT conventions apply: • {} specifies a trunk (level 4) • [] specifies a limb within a trunk (level 3) • () specifies a branch within a limb within a trunk (level 2). Travel Public Bus
Private Rail
Car
TW
• NLOGIT may have up to a maximum of five trunks, 10 limbs, 25 branches, and 100 alternatives • NLOGIT can estimate upto 4 level nested structure
Scale Parameter • The mean and variance of the Gumbel distribution are: Mean = η + (0.577/ λ) Variance= (π^2/6 λ^2) Where, λ is the scale parameter (inverse function of variance) and η is the location or mode parameter • U(Bus)=λβ0+ λ β1Var1+ λ β2Var2
Travel Ø2
Ø1
Public λ1Bus
λ2 Rail
Private Car λ3
λ4 TW
• Parameter of Inclusive value at level 2 = Ratio of the scale parameter at level 2 to scale parameter at level 1 = (Ø/λ) • Normalization at lower level = RU1 = Ø • Normalization at higher level = RU2
Range of IV parameter • Must lie within 0-1 range • Scale parameter at upper level must be lower than scale parameter of lower level Travel Public Bus
Private Rail
Car
TW
Consistency of IV parameter • The structural parameter should satisfy the condition: 0 < Ø≤1 • If Ø < 0, an increase in the utility of an alternative in the nest, which should increase the value of EMU, would actually diminish the probability of selecting the nest • If Ø = 0, such an increase would not effect the nest’s probability of being selected, as EMU would not effect the choice between car and PT. • If Ø >1, an increase in the utility of an alternative in the nest would tend to increase not only its selection probability but also those of the rest of the options in the nest. • If Ø = 1, the model becomes equivalent to MNL.
Travel Public Bus
Private Rail
Car CarD
TW CarP TWD
TWP
Tree = Travel{Public[Bus,Rail],Private[Car(CarD,CarP),TW (TWD,TWP)]}
Command Line for NL • Nlogit ;Lhs=CHOICE ;Choices=Bus,Rail,BR,TW,IPT,CarD,CarP,WNMT ;Tree=Private(CarD,CarP,TW),Public(Bus,Rail,BR),Others(I PT,WNMT) ;ias=Carp ;Show Tree ;start=logit ;Maxit=100 ;Model: Utility functions
Interpretation • FIML: Nested Multinomial Logit Model • Nested logit models can be estimated: sequentially or simultaneously • Sequential estimation (known as limited information maximum likelihood estimators or LIML) involves the estimation of separate levels of the NL tree in sequential order from the lowest level of the tree to the highest level. • The simultaneous estimation of the branches, limbs, and trunks of an NL model is achieved using FIML
• −2(LLbase model − LLestimated model)∼ Chi squared(difference in number of parameters estimated between two models) • Prob [ chi squared > value ] = .00000
Normalizing IV parameters • Constraining IV parameters ;ivset:(private,public) • Normalizing to fixed value ;ivset:(private)=[0.8]/(public)=[0.9] • Trail and Error process
• IV parameters closer to 1.0 not only indicate a smaller difference in the variance between adjoining levels, but also smaller correlation structures between the utility functions of alternatives present within the lower level of the nest corr (bus, train) = 1 − (IV)2
• • • • • • • • • • • •
Nlogit ;Lhs=CHOICE ;Choices=Bus,Rail,BR,TW,IPT,CarD,CarP,WNMT ;Tree=Private(CarD,CarP,TW),Public(Bus,Rail,BR),Others(IPT, WNMT) ;Start=logit ;ivset: (Car)=[1.0] ;Maxit=100 ;Model: U(private)= numbvehs*numbvehs / U(public) = asc1 / U(Others) = asc2/ U(carD) = /; U(carP) =/; U(TW) = /; U(train) = /;U(bus) = /; U(BR) =/; U(IPT)=; U(WNMT)= $
• If there is two degenerate alternatives, both the scale parameters are normalized to 1 , which is equivalent to treating both the alternatives are in the same nest Travel
Travel
Ø1
Bus
Ø1
Rail
Ø3
TW
Car
Bus
Rail
TW
Car
Converting Data set Choice twTT
tTT
bTT
cTT
twTC
tTC
bTC
cTC Hhinc Hhsiz
2
35
24
38
30
15
7
10
23
50
4
3
30
20
32
25
13
6
8
22
40
3
1
50
35
59
45
23
13
15
40
70
2
ALOGIT
NLOGIT Choice
TT
TC
Hhinc
Hhsiz
0
35
15
50
4
1
24
7
50
4
0
38
10
50
4
0
30
23
50
4
0
30
13
40
3
0
20
6
40
3
1
32
8
40
3
0
25
22
40
3
1
50
23
70
2
0
35
13
70
2
0
59
15
70
2
0
45
40
70
2
Converting the data set to multiple line format • The choice variable, Choice=1,2,3,4 for tw, train, bus and car • For each mode, TT, TC --- Differ by choices • For the individual, Hhinc, Hhsize --- Does not differ by choice • NLCONVERT ; Lhs= Choice ; Choices = tw, train, bus, car ; Rhs = twTT, tTT, bTT, cTT, twTC, tTC, bTC, cTC ;Rh2 = hhinc, hhsiz ;Names = choice, TT, TC, Hhinc, HHsiz
Data set Bus Train Car Walk Bus Train Car Walk Bus Train Car Walk Bus Train Car Walk
Cset 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4
AltID 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4
Choice 0 0 0 1 0 1 0 0 0 0 0 1 0 0 1 0
TT 20 15 45 60 15 12 42 70 34 30 80 100 55 42 100 150
TC 27 22 52 0 22 19 49 0 41 37 87 0 62 49 107 0
Variable choice set • Number of choices is not constant from one observation to next – Universal choice set (Tw, bus, car, train, metro) – Non availability of alternatives
• NLOGIT ;Lhs = choice, cset, altij ;Choices = tw, train, bus, car, metro ;Rhs = TT, TC $
Choice
Cset
AltID
TT
TC
Hhinc
Hhsiz
0
3
1 (TW)
35
15
50
4
1
3
2 (Train)
24
7
50
4
0
3
4 (Car)
38
10
50
4
0
4
1 (TW)
30
13
40
3
0
4
2 (Train)
20
6
40
3
1
4
3 (Bus)
32
8
40
3
0
4
4 (Car)
25
22
40
3
1
2
3 (Bus)
50
23
70
2
0
2
4 (Car)
35
13
70
2
Restricting the choice set • IIA test is performed by fitting the model to a restricted choice set • Comparing the two sets of parameter estimates
• NLOGIT ;Lhs = choice, cset, altij ;Choices = tw, (bus), train, car ;Rhs = TT, TC $
• In out put, restricted choices are marked with “*”
Generalized Nested Logit Model • Extension of Nested logit model • Alternatives may appear in more than one branch • GNLOGIT ;Lhs = Mode ;Choices=tw, train, bus, car ;Rhs=one,tt,tc,gc ;Tree=private(car,plane),ground(car,train,bus) $
