Multinomial, Ordered and Multivariate Models
Multinomial, ordered and multivariate models allow us to use various types of categorical data for
our dependent variable.
What type of dependent variable do you have?
Dependent Variable
Model
Interval or ratio scale
Ordinary Least Squares
Binary: 0,1
Logit or Probit
st
nd
rd
Ordered Logit or Probit
Ordinal: 1 , 2 , 3 (mutually
exclusive)
Nominal: gender (mutually
exclusive)
Multiple Binary:
y1: 0, 1
Multinomial Model
Multivariate Model
y2 : 0, 1 ….
Should you use Logit or Probit?
Logit
Probit
 Coefficients affect the
 Coefficients affect the
log odds ratio
probability
 k Pi (1  Pi )
  k  Z i 
 Odds = (P)/(1-P)
 Based off the normal
distribution model
 Logistic distribution
tails are fatter
Deciding between a Multinomial and an Ordered Model
This choice depends on what type of data you are working with.
Nominal Data: Categorical data where the categories have an arbitrary order.
Ordinal Data: Categorical data where categories have a meaningful rank. However, ordinal data may
not describe relative size of each category or the amount of difference between categories.
Multinomial Models
When to use a multinomial model? When the
dependent variable has more than two
discrete categorical outcomes, a multinomial
model can estimate effects for the explanatory
variables for each category of the dependent
variable.
Variable 1a
Variable 2a
Variable 3a
Variable 1b
Variable 2b
Variable 3b
Variable 1c
Variable 2c
Variable 3c
Dependent Variable:
Multiple Categories
Example: Land Use
2. Farming
Dependent Variable:
Multiple Categories
Example: Land Use
1. Housing
Dependent Variable:
Multiple Categories
Example: Land Use
3. Forest Land
Ordered Models
When to use an ordered model? If the
dependent variable is both categorical and
ordinal, use an ordered model to estimate the
effects of explanatory variables on the
probability that an observation will fall within
one of the categories of the dependent variable.
Ordinal models assume that the independent
variables have the same effect when moving
between categories.
Explanatory
Variable 1
Explanatory
Variable 2
Explanatory
Variable 3
Dependent Variable:
Multiple Ordered
Categories
Example: Rank
1. Gold
2. Silver
3. Bronze
Multivariate Models
When is a multivariate approach necessary?
Multivariate models simultaneously estimate
multiple dependent variables. These
dependent variables can be binary or
continuous. Since we are addressing logit
and probit models here we will focus on
binary responses.
Explanatory
Variable 1
Explanatory
Variable 2
Explanatory
Variable 3
Dependent Variable #1
Example: Male has
bank account
Dependent Variable #2
Example: Female has
bank account
Multivariate models can be particularly helpful when two dependent variables are correlated.
Multivariate commands take an extra step of calculating the correlation of the two y variables and
including that in the estimation of coefficients. By estimating them together efficiency is improved.
There is no gain in efficiency if the two dependent variables are not correlated. In that case it would
be better to just estimate them separately.
How the Multivariate analysis is set up: (Bivariate example)
Typical set up of the
dependent variables
(here shown as binary).
The only addition is
that we have more
than one.
This added step of
estimating ρ is what
allows us to use
variables that may be
highly correlated.
Example of a Multivariate and Bivariate Analysis
Marieka Klawitter, ‘Who Is Banked in Low Income Families? The Effects of Gender and Bargaining Power.’, Social Science
Research, 40 (2011), 50.
Data: Survey that includes data on which families have bank accounts, which bank accounts are
jointly or individually owned.
Models: Probit, bivariate and multivariate models were each specified with bank account ownership
as the dependent variable and various socioeconomic factors as explanatory variables.
Analysis: By using a multivariate method the study is able to show how intrahousehold dynamics
influence whether a family and an individual has a bank account. The probit model on its own does
not give the richness of data that we see from the multivariate approach.
Stata Code for Reference
Model
Ordinary Least Squares
Binary
Binary Logit
Binary Probit
Ordinal
Ordered Logit
Generalized Logit
Ordered Probit
Nominal
Multinomial Logit
Conditional Logit
Multinomial Probit
Multivariate Bivariate
Multivariate
Stata
Command
.regress
.logit, .logistic
.probit
.ologit
.gologit2
.oprobit
.mlogit
.clogit
.mprobit
.bvariate
Many, search
STATA for options
Resources:
Multinomial and Ordinal Models: http://www.indiana.edu/~statmath/stat/all/cdvm/cdvm1.html#s11
Multinomial Logit: http://en.wikipedia.org/wiki/Multinomial_logit
Intro to Multivariate: http://www.pisces-conservation.com/pdf/mvstats-lecture1.pdf