spateo.tools.CCI_effects_modeling.distributions¶
Defining the types of distributions that the dependent variable can be assumed to take.
Attributes¶
Classes¶
Parent class for transformations of the dependent variable. The link function is used to transform the mean of |
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The logit link function to transform the probability of a binary response variable to the scale of a linear |
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Transform by raising to a power to transform the mean parameter to the scale of the linear predictor. |
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Identity transform. |
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Inverse power transform. |
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Square root transform. |
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Transform by taking the logarithm. |
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Relates the variance of a random variable to its mean. |
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Variance function that is a power of the mean. |
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Variance function for binomial distribution. |
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Variance function for the negative binomial distribution. |
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Parent class for one-parameter exponential distributions that can be used with Spateo's modeling core. Some of |
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Poisson distribution for modeling count data. |
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Gaussian distribution for modeling continuous data. |
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Gamma distribution for modeling continuous data. |
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Binomial distribution for modeling binary data. |
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Negative binomial distribution for modeling count data. |
Module Contents¶
- class spateo.tools.CCI_effects_modeling.distributions.Link[source]¶
Bases:
object
Parent class for transformations of the dependent variable. The link function is used to transform the mean of the response variable, which may have a different distributional form than the linear predictor, to the scale of the linear predictor.
For example, the probability returned by a logistic regressor and the mean parameters are related through this link function.
Does nothing, but includes the expected methods for transformations.
- inverse(z: numpy.ndarray) numpy.ndarray [source]¶
Inverse of the transformation.
- Parameters:
- z
The prediction of the transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
The value of the inverse transform function (converting from values to probabilities)
- Return type:
g^(-1)(z)
- deriv(fitted: numpy.ndarray) numpy.ndarray [source]¶
Derivative of the logit transformation evaluated at the fitted mean response variable and with respect to the linear predictor.
- Parameters:
- fitted
The fitted mean response variable
- Returns:
The value of the derivative of the logit function evaluated at the fitted mean response variable
- Return type:
deriv
- second_deriv(p: numpy.ndarray) numpy.ndarray [source]¶
Second derivative of the transformation.
- Parameters:
- p
Logits to model the probability of an event, given predictor variables with specified values
- Returns:
The value of the second derivative of the link function
- Return type:
g’’(p)
- inverse_deriv(z: numpy.ndarray)[source]¶
Derivative of the inverse transformation g^(-1)(z).
- Parameters:
- z
The prediction of the transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
The value of the derivative of the fitted mean response variable (link function
- Return type:
g^(-1)’(p)
- class spateo.tools.CCI_effects_modeling.distributions.Logit[source]¶
Bases:
Link
The logit link function to transform the probability of a binary response variable to the scale of a linear predictor.
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- __call__(p: numpy.ndarray)[source]¶
Transforms the probabilities to logits.
- Parameters:
- p
Probabilities of an event, given predictor variables with specified values
- Returns:
The transformed logits
- Return type:
z
- inverse(z: numpy.ndarray) numpy.ndarray [source]¶
Inverse of the transformation, transforms the linear predictor to the scale of the response variable.
- Parameters:
- z
The prediction of the logit-transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
Transformed linear predictor
- Return type:
inv
- inverse_deriv(z: numpy.ndarray)[source]¶
Derivative of the inverse transformation g^(-1)(z).
- Parameters:
- z
The prediction of the transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
The value of the derivative of the inverse of the logit function
- Return type:
inv_deriv
- deriv(fitted: numpy.ndarray) numpy.ndarray [source]¶
Derivative of the logit transformation evaluated at the fitted mean response variable and with respect to the linear predictor.
- Parameters:
- fitted
The fitted mean response variable
- Returns:
The value of the derivative of the logit function evaluated at the fitted mean response variable
- Return type:
deriv
- second_deriv(p: numpy.ndarray) numpy.ndarray [source]¶
Second derivative of the logit transformation.
- Parameters:
- p
Logits to model the probability of an event, given predictor variables with specified values
- Returns:
The value of the second derivative of the logit function at “p”
- Return type:
second_deriv
- class spateo.tools.CCI_effects_modeling.distributions.Power(power: float)[source]¶
Bases:
Link
Transform by raising to a power to transform the mean parameter to the scale of the linear predictor.
- Aliases of Power:
identity = Power(power=1) squared = Power(power=2) sqrt = Power(power=0.5) inverse = Power(power=-1) inverse_squared = Power(power=-2)
- Parameters:
- power
The exponent of the power transform
- __call__(fitted: numpy.ndarray)[source]¶
Raises parameters to power.
- Parameters:
- fitted
Mean parameter values
- Returns:
The transformed logits
- Return type:
z
- inverse(z: numpy.ndarray) numpy.ndarray [source]¶
Inverse of the transformation, transforms the linear predictor to the scale of the response variable.
- Parameters:
- z
The prediction of the power-transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
Transformed linear predictor
- Return type:
inv
- inverse_deriv(z: numpy.ndarray)[source]¶
Derivative of the inverse transformation g^(-1)(z).
- Parameters:
- z
The prediction of the transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
The value of the derivative of the inverse of the power transform
- Return type:
inv_deriv
- deriv(fitted: numpy.ndarray) numpy.ndarray [source]¶
Derivative of the logit transformation evaluated at the fitted mean response variable and with respect to the linear predictor.
- Parameters:
- fitted
The fitted mean response variable
- Returns:
The value of the derivative of the logit function evaluated at the fitted mean response variable
- Return type:
deriv
- second_deriv(p: numpy.ndarray) numpy.ndarray [source]¶
Second derivative of the power transformation.
- Parameters:
- p
(non-transformed) logits to model the probability of an event, given predictor variables with specified values
- Returns:
The value of the second derivative of the logit function at “p”
- Return type:
second_deriv
- class spateo.tools.CCI_effects_modeling.distributions.identity[source]¶
Bases:
Power
Identity transform.
g(p) = p
Alias of Power(power=1.)
- class spateo.tools.CCI_effects_modeling.distributions.inverse_power[source]¶
Bases:
Power
Inverse power transform.
g(p) = 1 / p
Alias of Power(power=-1.)
- class spateo.tools.CCI_effects_modeling.distributions.sqrt[source]¶
Bases:
Power
Square root transform.
g(p) = sqrt(p)
Alias of Power(power=0.5)
- class spateo.tools.CCI_effects_modeling.distributions.Log[source]¶
Bases:
Link
Transform by taking the logarithm.
g(p) = log(p)
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- __call__(p: numpy.ndarray)[source]¶
Transforms the probabilities to logits.
- Parameters:
- p
Probabilities of an event, given predictor variables with specified values
- Returns:
The transformed logits
- Return type:
z
- inverse(z: numpy.ndarray) numpy.ndarray [source]¶
Inverse of the transformation, transforms the linear predictor to the scale of the response variable.
- Parameters:
- z
The prediction of the log-transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
Transformed linear predictor
- Return type:
inv
- inverse_deriv(z: numpy.ndarray)[source]¶
Derivative of the inverse transformation g^(-1)(z).
- Parameters:
- z
The prediction of the transformed dependent variable from the IRLS algorithm as applied with a generalized linear model
- Returns:
The value of the derivative of the inverse of the power transform
- Return type:
inv_deriv
- deriv(fitted: numpy.ndarray) numpy.ndarray [source]¶
Derivative of the log transformation evaluated at the fitted mean response variable and with respect to the linear predictor.
- Parameters:
- fitted
The fitted mean response variable
- Returns:
The value of the derivative of the logit function evaluated at the fitted mean response variable
- Return type:
deriv
- second_deriv(y: numpy.ndarray) numpy.ndarray [source]¶
Second derivative of the logit transformation evaluated at the mean response variable and with respect to the linear predictor.
- Parameters:
- y
The mean response variable
- Returns:
The value of the second derivative of the logit function at “p”
- Return type:
second_deriv
- class spateo.tools.CCI_effects_modeling.distributions.VarianceFunction[source]¶
Bases:
object
Relates the variance of a random variable to its mean.
- class spateo.tools.CCI_effects_modeling.distributions.Power_Variance(power=1.0)[source]¶
Bases:
object
Variance function that is a power of the mean.
- Alias for Power_Variance:
fitted = Power_Variance() fitted_squared = Power_Variance(power=2) fitted_cubed = Power_Variance(power=3)
- Parameters:
- power
Exponent used in the variance function
- class spateo.tools.CCI_effects_modeling.distributions.Binomial_Variance(n=1)[source]¶
Bases:
object
Variance function for binomial distribution.
- Equations:
V(fitted) = p * (1 - p) * n, where p = mu / n
- Parameters:
- n
The number of trials. The default is 1, under which the assumption is that each observation is an independent trial with a binary outcome.
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- __call__(fitted: numpy.ndarray)[source]¶
Computes variance for the mean parameters by modeling the output probabilities as a binomial distribution.
- Parameters:
- fitted
Mean parameter values
- Returns:
Variance
- Return type:
var
- deriv(fitted: numpy.ndarray) numpy.ndarray [source]¶
Returns the derivative of the variance function.
- Parameters:
- fitted
Mean parameter values
- Returns:
Derivative of the variance function
- Return type:
deriv
- class spateo.tools.CCI_effects_modeling.distributions.Negative_Binomial_Variance(disp: float = 0.5)[source]¶
Bases:
object
Variance function for the negative binomial distribution.
- Equations:
V(fitted) = fitted + disp * fitted ** 2
- Parameters:
- disp
The dispersion parameter for the negative binomial. Assumed to be nonstochastic, defaults to 0.5.
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- __call__(fitted: numpy.ndarray)[source]¶
Computes variance for the mean parameters by modeling the output probabilities as a negative binomial distribution.
- Parameters:
- fitted
Mean parameter values
- Returns:
Variance, given by fitted + disp * fitted ** 2
- Return type:
var
- class spateo.tools.CCI_effects_modeling.distributions.Distribution(link, variance)[source]¶
Bases:
object
Parent class for one-parameter exponential distributions that can be used with Spateo’s modeling core. Some of the methods do nothing, but provide skeletons for the expected methods for the distributions themselves .
- Parameters:
- link
The link function to use for the distribution, for performing transformation of the linear outputs. See the individual distributions for the default link.
- variance
Measures the variance as a function of the mean probabilities. See the individual families that inherit from this class for the default variance function.
- _setlink(link)[source]¶
Sets the link function for the distribution.
If the chosen link function is not valid for a particular distribution family, a ValueError exception will be raised.
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- initial_predictions(y: numpy.ndarray) numpy.ndarray [source]¶
Starting value for linear predictions in the IRLS algorithm.
- Parameters:
- y
The untransformed dependent variable
- Returns:
Array of shape [n_samples,]; the initial linear predictors.
- Return type:
y_hat_0
- weights(fitted: numpy.ndarray) numpy.ndarray [source]¶
Weights for the IRLS algorithm.
- Parameters:
- fitted
Array of shape [n_samples,]; transformed mean response variable
- Returns:
Weights for the IRLS steps
- Return type:
w
- predict(fitted: numpy.ndarray) numpy.ndarray [source]¶
Given the linear predictors, map back to the scale of the dependent variable.
- Parameters:
- fitted
Linear predictors
- Returns:
The predicted dependent variable values
- Return type:
y_hat
- get_predictors(outputs: numpy.ndarray) numpy.ndarray [source]¶
Given model fit (outputs obtained from applying the link function), map back to the scale of the linear predictors.
- Parameters:
- outputs
The predicted dependent variable values
- Returns:
The linear predictors
- Return type:
predictor
- abstract deviance(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) float [source]¶
Deviance function to measure goodness-of-fit of model fitting. Defined as twice the log-likelihood ratio.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the deviance function
- Return type:
dev
- abstract deviance_residuals(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Deviance residuals for the model, representing the difference between the observed and expected values of the dependent variable.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable- residuals will be divided by the scale
- Returns:
The deviance residuals
- Return type:
dev_res
- abstract log_likelihood(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Log-likelihood function for the model.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the log-likelihood function
- Return type:
ll
- class spateo.tools.CCI_effects_modeling.distributions.Poisson(link=Log)[source]¶
Bases:
Distribution
Poisson distribution for modeling count data.
- Parameters:
- link
The link function to use for the distribution, for performing transformation of the linear outputs. The default link is the log link, but available links are “log”, “identity”, and “sqrt”.
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- deviance(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) float [source]¶
Poisson deviance function.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
Array of shape [n_samples, ]; the value of the deviance function evaluated for each sample.
- Return type:
dev
- deviance_residuals(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Poisson deviance residuals.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- scale
Optional scale of the response variable- residuals will be divided by the scale
- Returns:
The deviance residuals
- Return type:
dev_resid
- log_likelihood(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Poisson log likelihood of the fitted mean response.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the log-likelihood function
- Return type:
ll
- class spateo.tools.CCI_effects_modeling.distributions.Gaussian(link=identity)[source]¶
Bases:
Distribution
Gaussian distribution for modeling continuous data.
- Parameters:
- link
The link function to use for the distribution, for performing transformation of the linear outputs. The default link is the identity link, but available links are “log”, “identity”, and “inverse”.
- deviance(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) float [source]¶
Gaussian deviance function.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the deviance function
- Return type:
dev
- deviance_residuals(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Gaussian deviance residuals.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response- residuals will be divided by the scale
- Returns:
The deviance residuals
- Return type:
dev_resid
- log_likelihood(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0)[source]¶
Gaussian log likelihood of the fitted mean response.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the log-likelihood function
- Return type:
ll
- class spateo.tools.CCI_effects_modeling.distributions.Gamma(link=Log)[source]¶
Bases:
Distribution
Gamma distribution for modeling continuous data.
- Parameters:
- link
The link function to use for the distribution, for performing transformation of the linear outputs. The default link is the inverse link, but available links are “log”, “identity”, and “inverse”.
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- deviance(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) float [source]¶
Gamma deviance function.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the deviance function
- Return type:
dev
- deviance_residuals(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Gamma deviance residuals.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable- residuals will be divided by the scale
- Returns:
The deviance residuals
- Return type:
dev_resid
- log_likelihood(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Gamma log likelihood of the fitted mean response.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the log-likelihood function
- Return type:
ll
- class spateo.tools.CCI_effects_modeling.distributions.Binomial(link=Logit)[source]¶
Bases:
Distribution
Binomial distribution for modeling binary data.
- Parameters:
- link
The link function to use for the distribution, for performing transformation of the linear outputs. The default link is the logit link, but available links are “logit” and “log”.
- initial_predictions(y: numpy.ndarray) numpy.ndarray [source]¶
Initial predictions for the IRLS algorithm.
- Parameters:
- y
Array of shape [n_samples, ]; untransformed dependent variable
- Returns:
Array of shape [n_samples,]; the initial linear predictors.
- Return type:
y_hat_0
- deviance(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0, axis: int | None = None) float [source]¶
Binomial deviance function.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- axis
Axis along which the deviance is calculated
- Returns:
The value of the deviance function
- Return type:
dev
- deviance_residuals(endog: numpy.ndarray, fitted: numpy.ndarray, scale: float = 1.0) numpy.ndarray [source]¶
Binomial deviance residuals.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- scale
Optional scale of the response variable- residuals will be divided by the scale
- Returns:
The deviance residuals
- Return type:
dev_resid
- log_likelihood(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Binomial log likelihood of the fitted mean response.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated
- values) at the linear predicted
- freq_weights
Array of shape [n_samples, ]; optional 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the log-likelihood function
- Return type:
ll
- class spateo.tools.CCI_effects_modeling.distributions.NegativeBinomial(link=Log, disp: float | None = None)[source]¶
Bases:
Distribution
Negative binomial distribution for modeling count data.
- Parameters:
- link
The link function to use for the distribution, for performing transformation of the linear outputs. The default link is the inverse link, but available links are “log”, “identity”, and “inverse”.
- clip(vals: numpy.ndarray) numpy.ndarray [source]¶
Clips values to avoid numerical issues.
- Parameters:
- vals
Values to clip
- Returns:
The clipped values
- Return type:
vals
- deviance(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) float [source]¶
Negative binomial deviance function.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated at the linear predicted values)
- freq_weights
Array of shape [n_samples, ]; 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the deviance function
- Return type:
dev
- deviance_residuals(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Negative binomial deviance residuals.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated
- values) at the linear predicted
- scale
Optional scale of the response variable- residuals will be divided by the scale
- Returns:
The deviance residuals
- Return type:
dev_resid
- log_likelihood(endog: numpy.ndarray, fitted: numpy.ndarray, freq_weights: numpy.ndarray | None = None, scale: float = 1.0) numpy.ndarray [source]¶
Negative binomial log likelihood of the fitted mean response.
- Parameters:
- endog
Array of shape [n_samples, ]; untransformed dependent variable
- fitted
Array of shape [n_samples, ]; fitted mean response variable (link function evaluated
- values) at the linear predicted
- freq_weights
Array of shape [n_samples, ]; optional 1D array of frequency weights, used to e.g. adjust for unequal sampling frequencies
- scale
Optional scale of the response variable
- Returns:
The value of the log-likelihood function
- Return type:
ll