random
Description
Examples
Generate Random Responses from Data
Load the fisheriris
sample data set.
load fisheriris
The column vector species
contains three iris flower species: setosa, versicolor, and virginica. The matrix meas
contains four types of measurements for the flowers: the length and width of sepals and petals in centimeters.
Fit a multinomial regression model using the measurements as the predictor data and the iris species as the response data.
mdl = fitmnr(meas,species);
mdl
is a multinomial regression model object that contains the results of fitting a nominal multinomial regression model to the data.
Use the rand
function to generate new predictor data by adding uniformly distributed random noise to the measurements data.
rng("default") % Set the random seed for reproducibility sz = size(meas); measNew = meas + rand(sz);
Each row of measNew
corresponds to predictor data for a unique data point.
Generate random response values sampled from the multinomial distributions generated by passing measNew
to the fitted model.
speciesPred = random(mdl,measNew)
speciesPred = 150x1 cell
{'versicolor'}
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'versicolor'}
{'setosa' }
{'versicolor'}
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'versicolor'}
{'setosa' }
{'versicolor'}
{'setosa' }
{'versicolor'}
{'setosa' }
{'versicolor'}
{'setosa' }
{'setosa' }
{'setosa' }
{'setosa' }
{'versicolor'}
{'setosa' }
{'setosa' }
{'versicolor'}
⋮
Display the original response data.
species
species = 150x1 cell
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
{'setosa'}
⋮
The outputs for speciesPred
and species
show that the majority of the randomly generated responses in speciesPred
match the original response labels in species
. The difference between measNew
and meas
contributes to the difference between speciesPred
and species
, as does the random nature of sampling the speciesPred
values from the multinomial distributions associated with the predictor data.
Sample Multiple Responses from Each Multinomial Distribution
Load the fisheriris
sample data set.
load fisheriris
The column vector species
contains three iris flower species: setosa, versicolor, and virginica. The matrix meas
contains four types of measurements for the flowers: the length and width of sepals and petals in centimeters.
Fit a multinomial regression model using the measurements as the predictor data and the iris species as the response data.
mdl = fitmnr(meas,species);
mdl
is a multinomial regression model object that contains the results of fitting a nominal multinomial regression model to the data.
Use the rand
function to generate new predictor data by adding uniformly distributed random noise to the measurements data.
rng("default") % Set the random seed for reproducibility sz = size(meas); measNew = meas + 5*rand(sz);
Each row of measNew
corresponds to predictor data for a unique data point.
Generate random response values sampled from the multinomial distributions generated by passing measNew
to the fitted model. For each data point in measNew
, generate 100 samples from the corresponding multinomial distribution, and return the results in a table of counts.
speciesPred = random(mdl,measNew,100,"counts")
speciesPred=150×3 table
setosa versicolor virginica
______ __________ _________
0 31 69
100 0 0
0 100 0
0 100 0
0 100 0
0 78 22
0 100 0
0 0 100
0 98 2
100 0 0
0 100 0
0 0 100
0 0 100
0 100 0
0 100 0
0 0 100
⋮
Each row of the speciesPred
table corresponds to a data point in measNew
, and each table variable corresponds to a response category. The elements of speciesPred
indicate how many times each species is sampled.
Input Arguments
mdl
— Multinomial regression model object
MultinomialRegression
model object
Multinomial regression model object, specified as a MultinomialRegression
model object created with the fitmnr
function.
XNew
— New predictor input values
table | n-by-p matrix
New predictor input values, specified as a table or an
n-by-p matrix, where n is the
number of new observations, and p is the number of predictor
variables used to fit mdl
.
If
XNew
is a table, it must contain all the names of the predictors used to fitmdl
. You can find the predictor names in themdl.PredictorNames
property.If
XNew
is a matrix, it must have the same number of columns as the number of estimated coefficients. You can find the number of estimated coefficients in themdl.NumPredictors
property. You can specifyXNew
as a matrix only when all names inmdl.PredictorNames
refer to numeric predictors.
Example: random(mdl,[5.8 2.7; 5.7 2.5])
generates a simulated
response from each multinomial distribution given by evaluating the two-predictor model
mdl
at the query points xq1 = [5.8 2.7]
and
xq2 = [5.7 2.5]
.
Data Types: single
| double
| table
NumTrials
— Number of trials to simulate
1 (default) | positive integer scalar
Number of trials to simulate for each data point in XNew
,
specified as a positive integer scalar.
Data Types: single
| double
type
— Type for returned simulated responses
"samples"
(default) | "counts"
Type for the returned simulated responses, specified as "samples"
or "counts"
. To return the simulated response values as a cell array
of class labels, specify type
as "samples"
. To
return the simulated response values as a table of counts for each response category,
specify type
as "counts"
.
Data Types: char
| string
Output Arguments
Ysim
— Simulated responses
r-by-m cell array of category labels | r-by-N table of counts
Simulated responses, returned as a cell array of category labels or a table of counts.
If you specify the input argument
type
as"samples"
,Ysim
is an r-by-m cell array of category labels. r is the number of data points inXNew
, and m is the number of trials specified inNumTrials
.If you specify the input argument
type
as"counts"
,Ysim
is an r-by-N table, where N is the number of response variable categories in the data used to fitmdl
.
Algorithms
The random
function uses the fitted multinomial regression model
object mdl
to calculate response category probabilities for each data
point in XNew
. Each set of probabilities defines a multinomial
distribution from which the function randomly samples response values for the corresponding
predictor data.
Version History
Introduced in R2023a
See Also
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