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CovarianceEstimatorFunction
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CovarianceEstimatorFunction

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is an option for generalized linear model fitting functions that specifies the estimator for the parameter covariance matrix.

Details

Examples

open allclose all

Basic Examples  (1)Summary of the most common use cases

Fit a generalized linear model:

In[1]:=1
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-cpmdpa
In[2]:=2
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-e6g1ik
Out[2]=2

Compute the covariance matrix using the expected information matrix:

In[3]:=3
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-imv9d3
Out[3]=3

Use the observed information matrix instead:

In[4]:=4
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-dpvhsq
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-fosnc8
Out[5]=5

Scope  (2)Survey of the scope of standard use cases

Specify the covariance estimate within the FittedModel:

In[1]:=1
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-c27jh
In[2]:=2
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-gmpx1f
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-b3dnk0
Out[3]=3

Use with LogitModelFit:

In[1]:=1
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-zth78
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-b81s7a
Out[2]=2
In[3]:=3
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-gc1tux
Out[3]=3
In[4]:=4
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-mu46v9
Out[4]=4

Use with ProbitModelFit:

In[5]:=5
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-gg1run
Out[5]=5
In[6]:=6
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-bcghvd
Out[6]=6
In[7]:=7
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-ehqon5
Out[7]=7

Properties & Relations  (2)Properties of the function, and connections to other functions

Error estimates and confidence intervals involve covariance estimates:

In[1]:=1
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-y5pru
In[2]:=2
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-g6i71g
Out[2]=2

Estimate errors and intervals using expected information:

In[3]:=3
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-oa8f
Out[3]=3

Use observed information:

In[4]:=4
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-qyo15
Out[4]=4

CovarianceEstimatorFunction controls the general structure of the covariance:

In[1]:=1
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-g52c7q
Out[1]=1
In[2]:=2
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-jngjdb
Out[2]=2

DispersionEstimatorFunction affects the scale:

In[3]:=3
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-cfgtk7
Out[3]=3

The ratio of the errors squared is the ratio of the dispersion estimates:

In[4]:=4
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-l9s7ne
Out[4]=4
In[5]:=5
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https://wolfram.com/xid/0tgql0xsgps7uks9sei6-mtdhki
Out[5]=5
Wolfram Research (2008), CovarianceEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html.
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Wolfram Research (2008), CovarianceEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html.

Text

Wolfram Research (2008), CovarianceEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html.

✖
Wolfram Research (2008), CovarianceEstimatorFunction, Wolfram Language function, https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html.

CMS

Wolfram Language. 2008. "CovarianceEstimatorFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html.

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Wolfram Language. 2008. "CovarianceEstimatorFunction." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html.

APA

Wolfram Language. (2008). CovarianceEstimatorFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html

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Wolfram Language. (2008). CovarianceEstimatorFunction. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html

BibTeX

@misc{reference.wolfram_2025_covarianceestimatorfunction, author="Wolfram Research", title="{CovarianceEstimatorFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html}", note=[Accessed: 26-March-2025 ]}

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@misc{reference.wolfram_2025_covarianceestimatorfunction, author="Wolfram Research", title="{CovarianceEstimatorFunction}", year="2008", howpublished="\url{https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html}", note=[Accessed: 26-March-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_covarianceestimatorfunction, organization={Wolfram Research}, title={CovarianceEstimatorFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html}, note=[Accessed: 26-March-2025 ]}

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@online{reference.wolfram_2025_covarianceestimatorfunction, organization={Wolfram Research}, title={CovarianceEstimatorFunction}, year={2008}, url={https://reference.wolfram.com/language/ref/CovarianceEstimatorFunction.html}, note=[Accessed: 26-March-2025 ]}