This document is designed to be a reference. We strongly encourage the reader
to first consult Bierlaire (2015), where the syntax of a first model is analyzed in
details, as well as the many examples provided online. This document has been
written using BisonBiogeme 2.4, but should be valid for future versions, as no
major release if foreseen.
The sections of this file have to be specified as described below. Note that comments
can be included using //. All characters after this command, up to the end of the
current line, are ignored.
Note that only relevant sections must be specified. Morevover, the order of the
section is irrelevant. However, we suggest to comply to the order as described
below.

[ModelDescription]
 Type here any text that describes the model. It may
contain several lines. Each line must be within doublequotes, like
this
[ModelDescription]
"This is the first line of the model description"
"This is the second line of the model description"
Note that it will be copied verbatim in the output files. Note that, if it
contains special characters which are interpreted by LATEX, such as $ or &,
you may need to edit the LATEX output file before processing
it.

[Choice]
 Provide here the formula to compute the identifier of the chosen
alternative from the data file. Typically, a “choice” entry will be available
directly in the file, but any formula can be used to compute it. Assume for
example that, in your model, you have numbered alternatives 100, 200 and
300. But in the data file, they are numbered 1, 2 and 3. In this case, you
must write
[Choice]
100 * choice
Any expression described in Section [Expressions] is valid here.

[Weight]
 Provide here the formula to compute the weight associated with each
observation. The weight of an observation will be multiplied to the
corresponding term in the log likelihood function. Ideally, the sum of
the weights should be equal to the total number of observations,
although it is not required. The file reporting the statistics contains a
recommendation to adjust the weights in order to comply with this
convention.
Important: do not use the weight section in Biosim.

[Beta]
 Each line of this section corresponds to a parameter of the utility
functions. Five entries must be provided for each parameter:
 Name: the first character must be a letter (any case) or an
underscore (_), followed by a sequence of letters, digits, underscore
(_) or dashes (), and terminated by a white space. Note that
case sensitivity is enforced. Therefore varname and Varname would
represent two different variables.
 Default value that will be used as a starting point for the
estimation, or used directly for the simulation in BIOSIM.
 Lower bound on the valid values ;
 Upper bound on the valid values;
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given default value.
Note that this section is independent of the specific model to be estimated,
as it captures the deterministic part of the utility function.
[Beta]
// Name Value LowerBound UpperBound status
ASC1 0 10000 10000 1
ASC2 0.159016 10000 10000 0
ASC3 0.0869287 10000 10000 0
ASC4 0.51122 10000 10000 0
ASC5 0.718513 10000 10000 0
ASC6 1.39177 10000 10000 0
BETA1 0.778982 10000 10000 0
BETA2 0.809772 10000 10000 0

[Mu]
 μ is the homogeneity parameter of the MEV model. Usually, it is
constrained to be one. However, BisonBiogeme enables to estimate it if
requested (see the Swissmetro example 10nestedBottom.mod for a nested
logit model normalized from the bottom, so that μ is estimated). Four
entries are specified here:
 Default value that will be used as a starting point for the
estimation (common value: 1.0);
 Lower bound on the valid values (common value: 1.0e5);
 Upper bound on the valid values (common value: 1.0);
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given value.

[Utilities]
 Each row of this section corresponds to an alternative. Four entries
are specified:
 The identifier of the alternative, with a numbering convention
consistent with the choice definition;
 The name of the alternative: the first character must be a letter
(any case) or an underscore (_), followed by a sequence of letters,
digits, underscore (_) or dashes (), and terminated by a white
space;
 The availability condition: this must be a direct reference to an
entry in the data file, or to an expression defined in the Section
[Expressions];
 The linearinparameter utility function is composed of a list of
terms, separated by a +. Each term is composed of the name of
a parameter and the name of an attribute, separated by a
*. The parameter must be listed in Section [Beta], if it is a
regular parameter. If it is a random parameter, the syntax
is
nameParam [ nameParam ]
in the case of the normal distribution, or :
nameParam { nameParam }
to get a random parameter that comes from a uniform distribution.
For example, in the case of the normal:
BETA [ SIGMA ]
Note that the blank after each name parameter is required. Also,
parameters BETA and SIGMA have to be listed in Section [Beta]. In the
context of an independent random parameter, BETA represents the
mean while SIGMA corresponds to the standard deviation. With
correlated random parameters, SIGMA technically corresponds to the
appropriate term in the Cholesky decomposition matrix that captures
the variancecovariance structure among the random parameters. An
attribute must be an entry of the data file, or an expression defined in
Section [Expressions]. In order to comply with this syntax, the
Alternative Specific Constants must appear in a term like ASC * one,
where one is defined in the Section [Expressions]. Here is an
example:
[Utilities]
// Id Name Avail linearinparameter expression
1 Alt1 av1 ASC1 * one + BETA1 [SIGMA] * x11 + BETA2 * x12
2 Alt2 av2 ASC2 * one + BETA1 [SIGMA] * x21 + BETA2 * x22
3 Alt3 av3 ASC3 * one + BETA1 [SIGMA] * x31 + BETA2 * x32
4 Alt4 av4 ASC4 * one + BETA1 [SIGMA] * x41 + BETA2 * x42
5 Alt5 av5 ASC5 * one + BETA1 [SIGMA] * x51 + BETA2 * x52
6 Alt6 av6 ASC6 * one + BETA1 [SIGMA] * x61 + BETA2 * x62
If the utility function does not contain any part which is
linearinparameters, then the keyword $NONE must be written. For
example:
[Utilities]
// Id Name Avail linearinparameter expression
1 Alt1 av1 $NONE

[GeneralizedUtilities]
 This section enables the user to add nonlinear terms
to the utility function. For each alternative, the syntax is simply the
identifier of the alternative, followed by the expression. For example, if the
utility of alternative 1 is
the syntax is
[Utilities]
1 Alt1 av1 BETA_1 * X11
[GeneralizedUtilities]
1 BETA_2 * (X21 ^ LAMBDA  1) / LAMBDA
Another example where a nonlinear part is required is when specifying a log
normal random coefficient.

[ParameterCovariances]
 BisonBiogeme allows normally distributed random
parameters to be correlated, and can estimate their covariance. By
default, the variancecovariance matrix of the random parameters is
supposed to be diagonal, and no covariance is estimated. If some
covariances must be estimated, each pair of correlated random coefficients
must be identified in this section. Each entry of the section should
contain:
 The name of the first random parameter in the given pair. If it
appears in the utility function as BETA [ SIGMA ], its name must
be typed BETA_SIGMA.
 The name of the second random parameter involved in the pair,
using the same naming convention.
 The default value that will be used as a starting point for the
estimation;
 The lower bound on the valid values;
 The upper bound on the valid values;
 The status, which is 0 if the parameter must be estimated, or 1 if
the parameter has to be maintained at the given value.
If no covariance is to be estimated, you must either entirely remove the
section, or specify $NONE as follows:
[ParameterCovariances]
$NONE

[Draws]
 Number of draws to be used in Maximum Simulated Likelihood
estimation.

[Expressions]
 In this section are defined all expressions appearing either in the
availability conditions or in the utility functions of the alternatives defined
in Section [Utilities]. If the expression is readily available from the data
file, it can be omitted in the list. It is good practice to generate
new variables from this section especially when one objective is to
compute market shares or to evaluate effects of policies with the help of
Biosim.
We now summarize the syntax that can be used for generating new
variables. Variables which form an expression might be of type float or of
type integer. You can use numerical values or the name of a numerical
variable. New variables can be created using unary and binary expression
operators.
Unary expressions:
 y = sqrt(x) // y is square root of x.
 y = log(x) // y is natural log of x.
 y = exp(x) // y is exponential of x.
 y = abs(x) // y is absolute value of x.
binary expression: (Numerical)
 y = x + z // y is sum of variables x and z
 y = x  z // y is difference of variables x and z
 y = x * z // y is product of variables x by z
 y = x / z // y is division of variable x by z
 y = x ^ z // y is x to power of z (square would be y = x ^ 2)
 y = x % z // y is x modulo z, i.e. rest of x/z
binary expression: (Logical)
 y = x == z // y is 1 if x equals z, 0 otherwise
 y = x != z // y is 1 if x not equal to z, 0 otherwise
 y = x  z // y is 1 if x != 0 OR z != 0, 0 otherwise
 y = x && z // y is 1 if x != 0 AND z != 0, 0 otherwise
 y = x < z // y is 1 if x < z (note: also > )
 y = x <= z // y is 1 if x <= z (note: also >= )
 y = max(x,z) // y is max of x and z (note: also min)
Note that an expression is considered to be TRUE if it is non zero, and
FALSE if it is zero. For a full description of these expressions and
alternative syntaxes, please look at the files patSpecParser.y and
patSpecScanner.l in the BIOGEME distribution.
Loops can be defined if several expressions have almost the same syntax.
The idea is to replace all occurrences of a string, say xx, by numbers. The
numbers are generated within a loop, defined by 3 numbers: the start of the
loop (a), the end of the loop (b) and the step (c) with the following
syntax:
$LOOP {xx a b c}
The expression
$LOOP {xx 1 5 2} my_expression_xx =
other_expression_xx * term_xx_first
is equivalent to
my_expression_1 = other_expression_1 * term_1_first
my_expression_3 = other_expression_3 * term_3_first
my_expression_5 = other_expression_5 * term_5_first
Warning: make sure that the string is awkward enough so that it cannot
match any other instance by mistake. For example, the loop
{xp 1 5 2} my_expression_xp = other_expression_xp * term_xp_first
is equivalent to
my_e1ression_1 = other_e1ression_1 * term_1_first
my_e3ression_3 = other_e3ression_3 * term_3_first
my_e5ression_5 = other_e5ression_5 * term_5_first
which is probably not the desired effect.

[Group]
 Provide here the formula to compute the group ID of the observed
individual. Typically, a “group” entry will be available directly
from the data file, but any formula can be used to compute it. Any
expression described in Section [Expressions] is valid here. A
different scale parameter will be estimated for the utility of each
group.

[Exclude]
 Define an expression (see Section [Expressions]) which identifies
entries of the data file to be excluded. If the result of the expression is not
zero, the entry will be discarded.

[Model]
 Specifies which MEV model is to be used. Valid entries are $BP for
Binary Probit, $MNL for Multinomial Logit model, $NL for single level Nested
Logit model, $CNL for CrossNested Logit model and $NGEV for Network
GEV model.

[PanelData]
 Used to specify the name of the variable (ex: userID) in the dataset
identifying the observations belonging to a given individual and to specify
the name of the random parameters that are invariant within the
observation of a given individual userID.

[Scale]
 A scale parameter is associated with each group. The utility function of
each member of a group is multiplied by the associated scale parameter. A
typical application is the joined estimation of revealed and stated
preferences. It is therefore possible to estimate a logit model combining
both data sources, without playing around with dummy nested
structures as proposed by Bradley and Daly (1991). Each row of
this section corresponds to a group. Five entries are required per
row:
 Group number: the numbering must be consistent with the group
definition;
 Default value that will be used as a starting point for the
estimation (1.0 is a good guess);
 Lower bound on the valid values;
 Upper bound on the valid values;
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given value.
Clearly, one of the groups must have a fixed scale parameter.

[SelectionBias]
 Identifies the parameters capturing the selection bias, using the
estimator proposed by Bierlaire et al. (2008). Each of them has to
be listed in Section [Beta]. The section must contain a row per
alternative for which a selection bias has to be estimated. Each
row contains the number of the alternative and the name of the
associated parameter. Note that these parameters play a similar role
as the alternative specific constants, and must not be used with
logit.
[SelectionBias]
1 SB_1
4 SB_4
6 SB_6

[NLNests]
 This section is relevant only if the $NL option has been selected in
Section [Model]. If the model to estimate is not a Nested Logit
model, the section will simply be ignored. Note that multilevel Nested
Logit models must be modeled as Network MEV models. Each row
of this section corresponds to a nest. Six entries are required per
row:
 Nest name: the first character must be a letter (any case) or an
underscore (_), followed by a sequence of letters, digits, underscore
(_) or dashes (), and terminated by a white space;
 Default value of the nest parameter μ_{m} that will be used as a
starting point for the estimation (1.0 is a good guess);
 Lower bound on the valid values. It is usually 1.0, if μ is
constrained to be 1.0. Do not forget that, for each nest i, the
condition μ_{i} ≥ μ must be verified to be consistent with discrete
choice theory;
 Upper bound on the valid values;
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given value.
 The list of alternatives belonging to the nest, numbered as
specified in Section [Utilities]. Make sure that each alternative
belongs to exactly one nest, as no automatic verification is
implemented in BisonBiogeme.

[CNLNests]
 This section is relevant only if the $CNL option has been selected in
Section [Model]. If the model to estimate is not a CrossNested Logit
model, the section will simply be ignored. Note that multilevel CrossNested
Logit models must be modeled as Network MEV models. Each row of
this section corresponds to a nest. Five entries are required per
row:
 Nest name: the first character must be a letter (any case) or an
underscore (_), followed by a sequence of letters, digits, underscore
(_) or dashes (), and terminated by a white space;
 Default value of the nest parameter μ_{m} that will be used as a
starting point for the estimation;
 Lower bound on the valid values. It is usually 1.0, if μ is
constrained to be 1.0. Do not forget that, for each nest i, the
condition μ_{i} ≥ μ must be verified to be consistent with discrete
choice theory;
 Upper bound on the valid values;
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given value.

[CNLAlpha]
 This section is relevant only if the $CNL option has been selected in
Section [Model]. If the model to estimate is not a CrossNested Logit
model, the section will simply be ignored. Each row of this section
corresponds to a combination of a nest and an alternative. Six entries are
required per row:
 Alternative name, as defined in Section [Utilities];
 Nest name: the first character must be a letter (any case) or an
underscore (_), followed by a sequence of letters, digits, underscore
(_) or dashes (), and terminated by a white space;
 Default value of the parameter capturing the level at which an
alternative belongs to a nest that will be used as a starting point
for the estimation;
 Lower bound on the valid values (usually 0.0);
 Upper bound on the valid values (usually 1.0);
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given value.

[Ratios]
 It is sometimes useful to read the ratio of two estimated coefficients.
The most typical case is the valueoftime, being the ratio of the time
coefficient and the cost coefficient. This feature is only implemented for fixed
parameters. Computation of ratio of random parameters is not permitted.
Note that it is not straightforward to characterize the distribution of the
ratio of two random coefficients. BenAkiva et al. (1993) suggest a simple
approach that is directly implementable in BIOGEME to handle
ratio of random parameters. Each row in this section enables to
specify such ratios to be produced in the output file. Three entries are
required:
 The parameter (from Section [Beta]) being the numerator of the
ratio;
 The parameter (from Section [Beta]) being the denominator of
the ratio;
 The name of the ratio, to appear in the output file: the first
character must be a letter (any case) or an underscore (_), followed
by a sequence of letters, digits, underscore (_) or dashes (), and
terminated by a white space.

[ConstraintNestCoef]
 It is possible to constrain nests parameters to
be equal. This is achieved by adding to this section expressions
like
NEST_A = NEST_B
where NEST_A and NEST_B are names of nests defined in Section [NLNests],
Section [CNLNests] or Section [NetworkGEVNodes]. This section will
become obsolete in future releases, as there is now a section for linear
constraints on the parameters: (Section [LinearConstraints]).

[NetworkGEVNodes]
 This section is relevant only if the $NGEV option has been
selected in Section [Model]. If the model to estimate is not a Network GEV
model, the section will be simply ignored. Each row of this section
corresponds to a node of the Network GEV model. All nodes of the Network
GEV model except the root and the alternatives must be listed
here, with their associated parameter. Five entries are required per
row:
 Node name: the first character must be a letter (any case) or an
underscore (_), followed by a sequence of letters, digits, underscore
(_) or dashes (), and terminated by a white space;
 Default value of the node parameter μ_{j} that will be used as a
starting point for the estimation;
 Lower bound on the valid values. It is usually 1.0. Check the
condition on the parameters for the model to be consistent with
the theory in Bierlaire (2002);
 Upper bound on the valid values;
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given value.

[NetworkGEVLinks]
 This section is relevant only if the $NGEV option has been
selected in Section [Model]. If the model to estimate is not a Network GEV
model, the section will be simply ignored. Each row of this section
corresponds to a link of the Network GEV model, starting from the anode
to the bnode. The root node is denoted by __ROOT. All other nodes must be
either an alternative or a node listed in the section [NetworkGEVNodes].
Note that an alternative cannot be the anode of any link, and the root
node cannot be the bnode of any link. Six entries are required per
row:
 Name of the anode: it must be either __ROOT or a node listed in
the section [NetworkGEVNodes].
 Name of the bnode: it must be either a node listed in the section
[NetworkGEVNodes], or the name of an alternative.
 Default value of the link parameter that will be used as a starting
point for the estimation;
 Lower bound on the valid values.
 Upper bound on the valid values;
 Status, which is 0 if the parameter must be estimated, or 1 if the
parameter has to be maintained at the given value.

[LinearConstraints]
 In this section, the user can define a list of linear
constraints, in one of the following syntaxes:
 Formula = number,
 Formula ≤ number,
 Formula ≥ number.
The syntax is formally defined as follows:
oneConstraint : equation <= numberParam 
equation = numberParam 
equation >= numberParam
equation: eqTerm 
 eqTerm 
equation + eqTerm 
equation  eqTerm
eqTerm: parameter  numberParam * parameter
For example, the constraint
is written
ASC1 + ASC2 + ASC3 + ASC4 + ASC5 + ASC6 = 0.0
and the constraint
is written
MU  MUJ <= 0.0
or
MUJ  MU >= 0.0

[NonLinearEqualityConstraints]
 In this section, the user can define a list of
nonlinear equality constraints of the form
The section must contain a list of functions h(x). For example, the
constraint
is written
[NonLinearEqualityConstraints]
ALPHA_A1 ^ MU_A + ALPHA_B1 ^ MU_B  1.0

[NonLinearInequalityConstraints]
 BisonBiogeme is not able to handle
nonlinear inequality constraints yet. Note that the constraint
is equivalent to
where z is an additional variable (called slack variable).

[DiscreteDistributions]
 Provide here the list of random parameters with a
discrete distribution, or $NONE if there are none in the model. Each discrete
parameter is described using the following syntax:
nameDiscreteParam < listOfDiscreteTerms >
where nameDiscreteParam is the name of the random parameter, and
listOfDiscreteTerms is recursively defined as
oneDiscreteTerm 
listOfDiscreteTerms oneDiscreteTerm
where oneDiscreteTerm is defined as
nameValueParam ( nameProbaParam )
where nameValueParam is the name of the parameter capturing the discrete
value of the random parameter, and nameProbaParam is the name of the
parameter capturing the associated probability. Both must be defined in
Section [Beta]. As an example,
[DiscreteDistributions]
BETA1 < B1 ( W1 ) B2 ( W2 ) >
defines a random parameter BETA1, which takes the value B1 with
probability (or weight) W1, and the value B2 with probability W2. Note that
for this to make sense, the constraint W1 + W2 = 1.0 should be imposed
(Section [LinearConstraints]). Note also that the parameter BETA1 must
not appear in Section [Beta].

[AggregateLast]
 This section is relevant when the observation corresponds to a
latent choice (see Bierlaire and Frejinger, 2008 and next section). It
contains a boolean which, for each row in the sample file, identifies if it is
the last observation in an aggregate. Make sure that the value for the last
row is nonzero. As all booleans in BisonBiogeme, a numerical value of
0 means “FALSE” and a numerical value different from 0 means
“TRUE”. Any expression described in Section [Expressions] is valid
here.

[AggregateWeight]
 This section is relevant when the observation correspnds to a
latent choice. A choice is said to be “latent” when it is not directly observed.
This idea has been proposed by Bierlaire and Frejinger (2008) in a route
choice context where the actual chosen route was not directly observed.
Instead, the respondent reported a sequence of locations that they traversed.
In many cases, several routes in the network may have produced the same
reported locations.
Each observation consists of an aggregate, a set of actual alternatives that
may correspond to the observed situations. If _{}obs is the observed
aggregate, than the probability given by the choice model is
 (1) 
Equation P(_{}obsi) can be viewed as a measurement equation, and
represents the probability to observe _{}obs if i was the actual choice.
In BisonBiogeme, an aggregate observation is represented by a consecutive
sequence of elemental observations, associated with the probability
P(_{}obsi). Two additional sections in the model specification file are
used for the specification: section [AggregateLast] (see above) and
section [AggregateWeight], that associates a weight to elemental
observations of an aggregate. It corresponds to the term P(_{}obsi) in Eq.
(1). Any expression described in Section [Expressions] is valid
here.

[LaTeX]
 This section allows to define a description of each parameter to be used
in the LATEX file. For instance, the following section
[LaTeX]
ASC1 "Constant for alt. 1"
ASC2 "Constant for alt. 2"
ASC3 "Constant for alt. 3"
ASC4 "Constant for alt. 4"
ASC5 "Constant for alt. 5"
ASC6 "Constant for alt. 6"
BETA1 "$\beta_1$"
BETA2 "$\beta_2$"
will produce the following table:
   Robust  
Variable   Coeff.  Asympt.  
number  Description  estimate  std. error  tstat  pvalue











1  Constant for alt. 2  0.  159  0.  106  1.  49  0.  13 
2  Constant for alt. 3  0.  0869  0.  111  0.  78  0.  43 
3  Constant for alt. 4  0.  511  0.  172  2.  97  0.  00 
4  Constant for alt. 5  0.  719  0.  158  4.  54  0.  00 
5  Constant for alt. 6  1.  39  0.  195  7.  12  0.  00 
6  β_{1}  0.  779  0.  0301  25.  85  0.  00 
7  β_{2}  0.  810  0.  0307  26.  42  0.  00 












[Derivatives]

This section is for advanced users only. Use it at your own risk. If
you feel that you need it, you may seriously consider using
PythonBiogeme instead of BisonBiogeme.
When nonlinear utility functions are used, BisonBiogeme computes
automatically the derivatives needed by the maximum likelihood procedure.
However, this automatic derivation can significantly slow down the
estimation process, as no simplification is performed. This section allows the
user to provide BisonBiogeme with the analytical derivatives of the
utility function, in order to speed up the estimation process. In
some instances, half the estimation time was spared thanks to this
feature.
A row must be provided for each combination of nonlinear utilities (defined
in the Section Section [GeneralizedUtilities]) and parameters involved
in the formula. Each of these rows contains three items:
 the identifier of the alternative,
 the name of the parameter,
 the formula of the derivative.
For instance, assume that the systematic utility of alternative 1
is
so that
which is coded in BisonBiogeme as follows:
[Utilities]
// Id Name Avail linearinparameter expression (beta1*x1 + beta2*x2 + ... )
1 Alt1 av1 ASC1 * one
.
.
[GeneralizedUtilities]
1 BETA1 * ((x11 + 10 ) ^ LAMBDA11  1) / LAMBDA11 +
BETA2 * ((x12 + 10 ) ^ LAMBDA12  1) / LAMBDA12
[Derivatives]
1 BETA1 ((x11 + 10 ) ^ LAMBDA11  1) / LAMBDA11
1 BETA2 ((x12 + 10 ) ^ LAMBDA12  1) / LAMBDA12
1 LAMBDA11
BETA1 * ((x11 + 10) ^ LAMBDA11 * LN(x11 + 10) * LAMBDA11
 (x11 + 10) ^ LAMBDA11 + 1) / (LAMBDA11 * LAMBDA11 )
1 LAMBDA12
BETA2 * ((x12 + 10) ^ LAMBDA12 * LN(x12 + 10) * LAMBDA12
 (x12 + 10) ^ LAMBDA12 + 1) / (LAMBDA12 * LAMBDA12 )
In addition to usual expressions, the formula may contain the following
instruction:
$DERIV( formula , param )
which means that you ask BisonBiogeme to perform the derivation of the
formula for you. Although it may be useful to simplify the coding of the
derivatives, it is mandatory to use it for random parameters.
If BETA [ SIGMA ] is a random parameter, its derivative with respect to
BETA is 1, but its derivative with respect to SIGMA cannot be written by the
user, and must be coded
$DERIV( BETA [ SIGMA ] , SIGMA )
For instance, assume that the nonlinear utilities are defined as
1 exp( BETA1 [ SIGMA1 ] ) * x11
2 exp( BETA1 [ SIGMA1 ] ) * x21
The derivatives are coded as follows:
[Derivatives]
1 BETA1 exp( BETA1 [ SIGMA1 ] ) * x11
1 SIGMA1 exp( BETA1 [ SIGMA1 ] ) * x11
* $DERIV( BETA1 [ SIGMA1 ] , SIGMA1 )
2 BETA1 exp( BETA1 [ SIGMA1 ] ) * x21
2 SIGMA1 exp( BETA1 [ SIGMA1 ] ) * x21
* $DERIV( BETA1 [ SIGMA1 ] , SIGMA1 )
It is very easy to do an error in coding the analytical derivatives.
If there is an error, BisonBiogeme will not be able to estimate the
parameters, and will not even be able to detect that there is an
error. Therefore, we strongly suggest to set the parameter
gevCheckDerivatives to 1 and make sure that the numerical
derivatives match sufficiently well the analytical derivatives. Also,
estimate the model with few observations and few draws, once
with and once without this section. The results should be exactly
the same.

[SNP]
 This section allows to implement the test proposed by Fosgerau
and Bierlaire (2007) (read the paper first if you are not familiar with the
test). The section is composed of two things:
 The name of the random parameter to be tested. If this parameter
appears in the utility function as BETA [ SIGMA ], its name in
this section must be typed BETA_SIGMA.
 A list of positive integers associated with a parameter. The integer
is the degree of the Legendre polynomial, and the parameter the
associated coefficient in the development. Note that the name of
the parameter must appear in Section [Beta].
For instance, if parameter BETA [ SIGMA ] is tested using a seminonparametric
development defined by
the syntax in BisonBiogeme is
[Beta]
// Name Value LowerBound UpperBound status (0=variable, 1=fixed)
....
BETA 0 10000 10000 0
SIGMA 1 10000 10000 0
SMP1 0 10000 10000 0
SMP3 0 10000 10000 0
SMP4 0 10000 10000 0
[SNP]
// Define the coefficients of the series
// generated by the Legendre polynomials
BETA_SIGMA
1 SMP1
3 SMP3
4 SMP4
Note that only one random parameter can be transformed at a
time.

[OrdinalLogit]
 The parameters of ordinal binary logit models can be estimated.
However, this feature has not been fully tested, and should be
seen as a prototype. Thank you for reporting any bug. The segments
of the utility difference space must be numbered in a sequential way,
increasing from the leftmost to the rightmost. In this section, each segment
must be associated with its lower bound, except the first (because its lower
bound is ∞). For instance, if there are 4 segments the following syntax is
used:
[Beta]
....
tau1 0.3 1000 1000 1
tau2 0.4 1000 1000 0
tau3 0.5 1000 1000 0
[OrdinalLogit]
1 $NONE // infty > tau1
2 tau1 // tau1 > tau2
3 tau2 // tau2 > tau3
4 tau3 // tau3 > +infty
[LinearConstraints]
tau1  tau2 <= 0
tau2  tau3 <= 0
Note that the constraints impose that the segments are welldefined. Recall
also that the characters // represent a comment in the file and they are not
interpreted by BisonBiogeme, as well as all remaining characters on the
same line. Therefore, the following syntax for that section is completely
equivalent:
[OrdinalLogit]
1 $NONE
2 tau1
3 tau2
4 tau3
However, we strongly advise to use comments in order to clearly identify the
segments.

[SampleEnum]
 This section is ignored by BIOGEME. It is used by Biosim and
contains the number of simulations to perform in the sample enumeration
step.

[ZhengFosgerau]
 This section is ignored by BIOGEME. It is used by Biosim and
contains instructions to perform the ZhengFosgerau specification test and
residual analysis. Make sure to read the paper by Fosgerau (2008) before
using this section.
There is a line for each test, containing four items:
 The first item defines the function t introduced by Fosgerau (2008)
to reduce the dimensionality of the test. It is typically either
the probability of an alternative, or an expression involving
coefficients and attributes of the models, as soon as the expression is
continuous and not discrete. If it is a probability, the syntax
is
$P { AltName }
where AltName is the name of the alternative as defined in
Section [Utilities]. If it is a general expression, the syntax
is
$E { expr }
where expr is an expression complying with the syntax of
Section [Expressions]. However, it may also contain estimated
parameters.
 The second item is a parameter c used to define the bandwidth for the
nonparametric regression performed by the test (see end of Section 2.1
in Fosgerau, 2008). The bandwidth used by Biosim is defined as
c∕, where n is the sample size. Most users will use the value
c = 1.
 The third and the fourth item are lower and upper bounds (resp.)
Values of t outside of the bounds will not be used in the produced
pictures. It is good practice to use wide bounds first, and to adjust
them in order to obtain decent pictures. Note that if t is a
probability, it does not make sense to have bounds wider and
[0 : 1].
 The last item is the name of the function t, used in the report. Make
sure to put the name between doublequotes.
Here is an example of the syntax:
[ZhengFosgerau]
$P { Alt1 } 1 0 1 "P1"
$E { x31 } 1 1000 1000 "x31"

[IIATest]
 This section is ignored by BIOGEME. It is used to compute the
variables necessary to perform the McFadden omitted variables test on a
subset of alternatives:
 (2) 
The syntax is illustrated by the following example.
[IIATest]
// Description of the choice subsets to compute the new
// variable for McFadden’s IIA test
// Name list_of_alt
C123 1 2 3
C345 3 4 5
Each row corresponds to a new variable. It consists in the name of the
variable (it will appear as the column header in the output of Biosim),
followed by the list of alternatives to be included in the associated
subset.
BenAkiva, M., Bolduc, D. and Bradley, M. (1993). Estimation of
travel model choice models with randomly distributed values of time,
Transportation Research Record 1413: 88–97.
Bierlaire, M. (2002). The network GEV model, Proceedings of the 2nd
Swiss Transportation Research Conference, Ascona, Switzerland.
Bierlaire, M. (2015). BisonBiogeme 2.4: estimating a first model,
Series on Biogeme TRANSPOR 150720, Ecole Polytechnique Fédérale
de Lausanne.
biogeme.epfl.ch
Bierlaire, M., Bolduc, D. and McFadden, D. (2008). The estimation
of generalized extreme value models from choicebased samples,
Transportation Research Part B 42(4): 381–394.
Bierlaire, M. and Frejinger, E. (2008). Route choice modeling
with networkfree data, Transportation Research Part C: Emerging
Technologies 16(2): 187–198.
Bradley, M. A. and Daly, A. (1991). Estimation of logit choice
models using mixed stated preferences and revealed preferences
information, Methods for understanding travel behaviour in the 1990’s,
International Association for Travel Behaviour, Québec, pp. 116–133.
6th international conference on travel behaviour.
Fosgerau, M. (2008). Specification testing of discrete choice models:
a note on the use of a nonparametric test, Journal of Choice Modelling
1(1): 26–239.
Fosgerau, M. and Bierlaire, M. (2007). A practical test for the choice of
mixing distribution in discrete choice models, Transportation Research
Part B: Methodological 41(7): 784–794.