NLINResults

Estimation results object for nlinfit algorithm

Description

The NLINResults object contains estimation results from fitting a SimBiology^® model to data using sbiofit with nlinfit as a choice of estimation algorithm. See the sbiofit function for a list of other supported algorithms.

Creation

Use sbiofit with nlinfit estimation algorithm to create an NLINResults object.

Properties

expand all

`GroupName` — Name of the group associated with the results
categorical | empty array

Name of the group associated with the results, specified as a categorical. If the 'Pooled' name-value pair argument was set to true when you ran sbiofit, then GroupName is returned as an empty array or [].

`Beta` — Table of estimated parameters
table

Table of estimated parameters, specified as a table. The jth row of the table represents the jth estimated parameter β_j. It contains transformed values of parameter estimates if any parameter transform is specified. Standard errors of these parameter estimates (StandardError) are calculated as: sqrt(diag(COVB)).

It can also contain the following variables:

Bounds — the values of transformed parameter bounds that you specified during fitting
CategoryVariableName — the names of categories or groups that you specified during fitting
CategoryValue — the values of category variables specified by CategoryVariableName

This table contains one row per distinct parameter value.

`ParameterEstimates` — Table of estimated parameters
table

Table of estimated parameters, specified as a table. The jth row of the table represents the jth estimated parameter β_j. This table contains untransformed values of parameter estimates. Standard errors of these parameter estimates (StandardError) are calculated as: sqrt(diag(CovarianceMatrix)).

It can also contain the following variables:

Bounds — the values of transformed parameter bounds that you specified during fitting
CategoryVariableName — the names of categories or groups that you specified during fitting
CategoryValue — the values of category variables specified by CategoryVariableName

This table contains sets of parameter values that are identified for each individual or group.

`J` — Jacobian matrix of the model
array

Jacobian matrix of the model, specified as an array. The Jacobian matrix with respect to an estimated parameter is

$J (i, j, k) = {\frac{\partial y_{k}}{\partial β_{j}} |}_{t_{i}}$

where t_i is the ith time point, β_j is the jth estimated parameter in the transformed space, and y_k is the kth response in the group of data.

`COVB` — Estimated covariance matrix for `Beta`
matrix

Estimated covariance matrix for Beta, specified as a matrix. This matrix is calculated as: COVB = inv(J'*J)*MSE.

`CovarianceMatrix` — Estimated covariance matrix for `ParameterEstimates`
matrix

Estimated covariance matrix for ParameterEstimates, specified as a matrix. This matrix is calculated as: CovarianceMatrix = T'*COVB*T, where T = diag(JInvT(Beta)). JInvT(Beta) returns a Jacobian matrix of Beta which is inverse transformed accordingly if you specified any transform to estimated parameters.

For instance, suppose you specified the log-transform for an estimated parameter x when you ran sbiofit. The inverse transform is: InvT = exp(x), and its Jacobian is: JInvT = exp(x) since the derivative of exp is also exp.

`R` — Residuals matrix
matrix

Residuals matrix, specified as a matrix. R_ij is the residual for the ith time point and the jth response in the group of data.

`LogLikelihood` — Maximized loglikelihood for the fitted model
scalar

Maximized loglikelihood for the fitted model, specified as a scalar.

`AIC` — Akaike Information Criterion (AIC)
scalar

Akaike Information Criterion (AIC), specified as a scalar. The AIC is calculated as AIC = 2*(-LogLikelihood + P), where P is the number of parameters.

`BIC` — Bayes Information Criterion (BIC)
scalar

Bayes Information Criterion (BIC), specified as a scalar. The BIC is calculated as BIC = -2*LogLikelihood + P*log(N), where N is the number of observations, and P is the number of parameters.

`DFE` — Degrees of freedom for error
scalar

Degrees of freedom for error (DFE), specified as a scalar. The DFE is calculated as DFE = N-P, where N is the number of observations and P is the number of parameters.

`MSE` — Mean squared error
scalar

Mean squared error, specified as a scalar.

`SSE` — Sum of squared (weighted) errors or residuals
scalar

Sum of squared (weighted) errors or residuals, specified as a scalar.

`Weights` — Matrix of weights
matrix

Matrix of weights, specified as a matrix with one column per response and one row per observation.

`Data` — Data used for fitting
`groupedData` object

Data used for fitting, specified as a groupedData object.

In most cases, this Data property contains a copy of groupedData specified as the input data in the sbiofit call or the Data property of a fitproblem object. One exception is that the Data property of unpooled fit results objects contain only the subset of data for the individual group used for fitting.

`EstimatedParameterNames` — Estimated parameter names
cell array of character vectors

Estimated parameter names, specified as a cell array of character vectors.

`ErrorModelInfo` — Error models and estimated error model parameters
table

Error models and estimated error model parameters, specified as a table.

The table has one row per error model.
The ErrorModelInfo.Properties.RowsNames property identifies which responses the row applies to.
The table contains three variables: ErrorModel, a, and b. The ErrorModel variable is categorical. The variables a and b can be NaN when they do not apply to a particular error model.

There are four built-in error models. Each model defines the error using a standard mean-zero and unit-variance (Gaussian) variable e, the function value f, and one or two parameters a and b. In SimBiology, the function f represents simulation results from a SimBiology model.

'constant': $y = f + a e$
'proportional': $y = f + b | f | e$
'combined': $y = f + (a + b | f |) e$
'exponential': $y = f * \exp (a e)$

`EstimationFunction` — Name of the estimation function
character vector

Name of the estimation function, specified as a character vector.

`DependentFiles` — File names to include for deployment
cell array of character vectors

File names to include for deployment, specified as a cell array of character vectors.

Object Functions

`boxplot`	Create box plot showing the variation of estimated SimBiology model parameters
`fitted`	Return simulation results of SimBiology model fitted using least-squares regression
`plot`	Compare simulation results to the training data, creating a time-course subplot for each group
`plotActualVersusPredicted`	Compare predictions to actual data, creating a subplot for each response
`plotResidualDistribution`	Plot the distribution of the residuals
`plotResiduals`	Plot residuals for each response, using time, group, or prediction as x-axis
`predict`	Simulate and evaluate fitted SimBiology model
`random`	Simulate SimBiology model, adding variations by sampling error model
`summary`	Return structure array that contains estimated values and fit quality statistics

Version History

Introduced in R2014a

NLINResults

Description

Creation

Properties

GroupName — Name of the group associated with the results categorical | empty array

Beta — Table of estimated parameters table

ParameterEstimates — Table of estimated parameters table

J — Jacobian matrix of the model array

COVB — Estimated covariance matrix for Beta matrix

CovarianceMatrix — Estimated covariance matrix for ParameterEstimates matrix

R — Residuals matrix matrix

LogLikelihood — Maximized loglikelihood for the fitted model scalar

AIC — Akaike Information Criterion (AIC) scalar

BIC — Bayes Information Criterion (BIC) scalar

DFE — Degrees of freedom for error scalar

MSE — Mean squared error scalar

SSE — Sum of squared (weighted) errors or residuals scalar

Weights — Matrix of weights matrix

Data — Data used for fitting groupedData object

EstimatedParameterNames — Estimated parameter names cell array of character vectors

ErrorModelInfo — Error models and estimated error model parameters table

EstimationFunction — Name of the estimation function character vector

DependentFiles — File names to include for deployment cell array of character vectors