Package 'spmodel'

Description

Compute AICc for one or several fitted model objects for which a log-likelihood value can be obtained.

Usage

AICc(object, ..., k = 2)

Arguments

Details

When comparing models fit by maximum or restricted maximum likelihood, the smaller the AICc, the better the fit. The AICc contains a correction to AIC for small sample sizes. The theory of AICc requires that the log-likelihood has been maximized, and hence, no AICc methods exist for models where estmethod is not "ml" or "reml". Additionally, AICc comparisons between "ml" and "reml" models are meaningless – comparisons should only be made within a set of models estimated using "ml" or a set of models estimated using "reml". AICc comparisons for "reml" must use the same fixed effects. To vary the covariance parameters and fixed effects simultaneously, use "ml".

Hoeting et al. (2006) study AIC and AICc in a spatial context, using the AIC definition $-2loglik + 2(estparams)$ and the AICc definition as $-2loglik + 2n(estparams) / (n - estparams - 1)$, where $n$ is the sample size and $estparams$ is the number of estimated parameters. For "ml", $estparams$ is the number of estimated covariance parameters plus the number of estimated fixed effects. For "reml", $estparams$ is the number of estimated covariance parameters.

Value

If just one object is provided, a numeric value with the corresponding AICc.

If multiple objects are provided, a data.frame with rows corresponding to the objects and columns representing the number of parameters estimated (df) and the AICc.

See Also

stats::AIC() stats::BIC()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
AICc(spmod)
AIC(spmod)
BIC(spmod)

Description

Compute analysis of variance tables for a fitted model object or a likelihood ratio test for two fitted model objects.

Usage

## S3 method for class 'splm'
anova(object, ..., test = TRUE, Terms, L, ddf)

## S3 method for class 'spautor'
anova(object, ..., test = TRUE, Terms, L, ddf)

## S3 method for class 'spglm'
anova(object, ..., test = TRUE, Terms, L, ddf)

## S3 method for class 'spgautor'
anova(object, ..., test = TRUE, Terms, L, ddf)

## S3 method for class 'anova.splm'
tidy(x, ...)

## S3 method for class 'anova.spautor'
tidy(x, ...)

## S3 method for class 'anova.spglm'
tidy(x, ...)

## S3 method for class 'anova.spgautor'
tidy(x, ...)

Arguments

Details

When one fitted model object is present, anova() performs a general linear hypothesis test corresponding to some hypothesis specified by a matrix of constraints. If Terms and L are not specified, each model term is tested against zero (which correspond to type III or marginal hypothesis tests from classical ANOVA). If Terms is specified and L is not specified, all terms are tested jointly against zero. When L is specified, the linear combinations of terms specified by L are jointly tested against zero.

When two fitted model objects are present, one must be a "reduced" model nested in a "full" model. Then anova() performs a likelihood ratio test.

Value

When ddf is "asymptotic", anova() returns a data frame with degrees of freedom (Df), test statistics (Chi2), and p-values (Pr(>Chi2) if test = TRUE) corresponding to asymptotic Chi-squared hypothesis tests for each model term. When ddf is "satterthwaite", anova() instead numerator degrees of freedom (NumDF), denominator degrees of freedom (DenDF), $F$ statistics (F value), and p-values (Pr(>F) if test = TRUE) for each model term.

When two fitted model objects are present, anova() returns a data frame with the difference in degrees of freedom between the full and reduced model (Df), a test statistic (Chi2), and a p-value corresponding to the likelihood ratio test (Pr(>Chi2) if test = TRUE).

Whether one or two fitted model objects are provided, tidy() can be used to obtain tidy tibbles of the anova(object) output.

See Also

satterthwaite()

Examples

# one-model anova
spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
anova(spmod)
tidy(anova(spmod))
# see terms
tidy(anova(spmod))$effects
tidy(anova(spmod, Terms = c("water", "tarp")))
# same as
tidy(anova(spmod, Terms = c(2, 3)))
# likelihood ratio test
lmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "none"
)
tidy(anova(spmod, lmod))

Description

Augment accepts a fitted model object and a data set and adds information about each observation in the data set. New columns always begin with a . prefix to avoid overwriting columns in the original data set.

Augment behaves differently depending on whether the original data or new data requires augmenting. Typically, when augmenting the original data, only the fitted model object is specified, and when augmenting new data, the fitted model object and newdata is specified. When augmenting the original data, diagnostic statistics are augmented to each row in the data set. When augmenting new data, predictions and optional intervals or standard errors are augmented to each row in the new data set.

Usage

## S3 method for class 'splm'
augment(
  x,
  drop = TRUE,
  newdata = NULL,
  se_fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  local,
  ...
)

## S3 method for class 'spautor'
augment(
  x,
  drop = TRUE,
  newdata = NULL,
  se_fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  local,
  ...
)

## S3 method for class 'spglm'
augment(
  x,
  drop = TRUE,
  newdata = NULL,
  type.predict = c("link", "response"),
  type.residuals = c("deviance", "pearson", "response"),
  se_fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  newdata_size,
  level = 0.95,
  local = local,
  var_correct = TRUE,
  ...
)

## S3 method for class 'spgautor'
augment(
  x,
  drop = TRUE,
  newdata = NULL,
  type.predict = c("link", "response"),
  type.residuals = c("deviance", "pearson", "response"),
  se_fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  newdata_size,
  level = 0.95,
  local,
  var_correct = TRUE,
  ...
)

Arguments

Details

augment() returns a tibble with the same class as data. That is, if data is an sf object, then the augmented object (obtained via augment(x)) will be an sf object as well. When augmenting newdata, the augmented object has the same class as data.

Missing response values from the original data can be augmented as if they were a newdata object by providing x$newdata to the newdata argument (where x is the name of the fitted model object). This is the only way to compute predictions for spautor() and spgautor() fitted model objects.

Value

When augmenting the original data set, a tibble with additional columns

• .fitted Fitted value

• .resid Response residual (the difference between observed and fitted values)

• .hat Leverage (diagonal of the hat matrix)

• .cooksd Cook's distance

• .std.resid Standardized residuals

• .se.fit Standard error of the fitted value.

When augmenting a new data set, a tibble with additional columns

• .fitted Predicted (or fitted) value

• .lower Lower bound on interval

• .upper Upper bound on interval

• .se.fit Standard error of the predicted (or fitted) value

Autoregressive models and prediction quantities

For spautor() and spgautor() model objects the prediction locations are part of the model: they determine the neighbor structure and hence the covariance of the observed data itself. se_fit and interval are therefore only defined at those locations, and object$newdata is automatically used when se_fit or interval is requested (and hence the rows returned by augment()) correspond to object$newdata. splm() and spglm() model objects have no such restriction, as their covariance does not depend on where predictions are made.

See Also

tidy.spmodel() glance.spmodel() predict.spmodel()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
augment(spmod)
spmod_sulf <- splm(sulfate ~ 1, data = sulfate, spcov_type = "exponential")
augment(spmod_sulf)
augment(spmod_sulf, newdata = sulfate_preds)
# missingness in original data
spmod_seal <- spautor(log_trend ~ 1, data = seal, spcov_type = "car")
augment(spmod_seal)
augment(spmod_seal, newdata = spmod_seal$newdata)

Description

Compare area under the receiver operating characteristic curve (AUROC) for binary (e.g., logistic) models. The area under the ROC curve provides a measure of the model's classification accuracy averaged over all possible threshold values.

Usage

AUROC(object, ...)

## S3 method for class 'spglm'
AUROC(object, ...)

## S3 method for class 'spgautor'
AUROC(object, ...)

Arguments

Value

The area under the receiver operating characteristic curve.

References

Robin, X., Turck, N., Hainard, A., Tiberti, N., Lisacek, F., Sanchez, J. C., & Müller, M. (2011). pROC: an open-source package for R and S+ to analyze and compare ROC curves. BMC bioinformatics, 12, 1-8.

Examples

spgmod <- spglm(presence ~ elev,
  family = "binomial", data = moose,
  spcov_type = "exponential"
)
AUROC(spgmod)

Description

A caribou forage experiment.

Usage

caribou

Format

A tibble with 30 rows and 5 columns:

• water: A factor representing whether water was added. Takes values N (no water added) and Y (water added).

• tarp: A factor representing tarp cover. Takes values clear (a clear tarp), shade (a shade tarp), and none (no tarp).

• z: The percentage of nitrogen.

• x: The x-coordinate.

• y: The y-coordinate.

Source

These data were provided by Elizabeth Lenart of the Alaska Department of Fish and Game. The data were used in the publication listed in References.

References

Lenart, E.A., Bowyer, R.T., Ver Hoef, J.M. and Ruess, R.W. 2002. Climate Change and Caribou: Effects of Summer Weather on Forage. Canadian Journal of Zoology 80: 664-678.

Description

coef extracts fitted model coefficients from fitted model objects. coefficients is an alias for it.

Usage

## S3 method for class 'splm'
coef(object, type = "fixed", ...)

## S3 method for class 'splm'
coefficients(object, type = "fixed", ...)

## S3 method for class 'spautor'
coef(object, type = "fixed", ...)

## S3 method for class 'spautor'
coefficients(object, type = "fixed", ...)

## S3 method for class 'spglm'
coef(object, type = "fixed", ...)

## S3 method for class 'spglm'
coefficients(object, type = "fixed", ...)

## S3 method for class 'spgautor'
coef(object, type = "fixed", ...)

## S3 method for class 'spgautor'
coefficients(object, type = "fixed", ...)

Arguments

Value

A named vector of coefficients.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
coef(spmod)
coefficients(spmod)
coef(spmod, type = "spcov")

Description

Conditionally simulate prediction data from a model object.

Usage

conditional(object, ...)

## S3 method for class 'splm'
conditional(
  object,
  newdata,
  output = "newdata",
  samples = 1000,
  simulate_covparams = FALSE,
  ...
)

## S3 method for class 'spglm'
conditional(
  object,
  newdata,
  output = "newdata",
  type = c("link", "response", "new"),
  samples = 1000,
  newdata_size,
  ...
)

Arguments

Details

If "newdata" is in output, conditional simulations are returned for each row of newdata. If "beta" is in output, conditional simulations are returned for each fixed effect (i.e., element of coef(object). If "object" is in output, the observed data from object is returned once for each row of newdata. For example, c("newdata", "beta") returns the conditional simulations both for newdata and for the fixed effects. If "cov"/"spcov"/"randcov" is in output (only available when simulate_covparams = TRUE), the simulated covariance parameter draws themselves are returned.

Value

If output = "newdata", an a x b matrix of conditional simulations for each row in newdata, where a is the number of rows in newdata and b is the number of samples. If output = "beta", an p x b matrix of conditional simulations for each element in coef(object), where p is the number of fixed effects and b is the number of samples. If output = "object", an n x b matrix of observed data values, where n is the number of rows in data and b is the number of samples. If output = "cov"/"spcov"/"randcov" (simulate_covparams = TRUE only), a (covariance parameter) x b matrix of the of conditoinal simulations for each covariance parameter, where b is the number of samples. "cov" returns every covariance parameter, while "spcov"/"randcov" return just the spatial/random-effect covariance parameters, respectively.

If output has more than one element, a list is returned with the respetive elements named according to the relevant output. For example output = c("newdata", "beta") returns a list with elements "newdata" and "beta", each containing the relevant output for output = "newdata" and output = "beta", respectively.

Examples

set.seed(0)
spmod <- splm(sulfate ~ 1, data = sulfate, spcov_type = "exponential")
cond <- conditional(spmod, newdata = sulfate_preds)
predict(spmod, sulfate_preds[20, ], se.fit = TRUE)
c("fit_cond" = mean(cond[20, ]), "se.fit_cond" = sd(cond[20, ]))
hist(cond[20, ])

Description

Computes confidence intervals for one or more parameters in a fitted model object.

Usage

## S3 method for class 'splm'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'spautor'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'spglm'
confint(object, parm, level = 0.95, ...)

## S3 method for class 'spgautor'
confint(object, parm, level = 0.95, ...)

Arguments

Value

Confidence intervals (two-sided and equal-tailed) for the fixed effect coefficients based on the confidence level specified by level. For spglm() or spgautor() fitted model objects, confidence intervals are on the link scale.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
confint(spmod)
confint(spmod, parm = "waterY", level = 0.90)

Description

Compute the Cook's distance for each observation from a fitted model object.

Usage

## S3 method for class 'splm'
cooks.distance(model, ...)

## S3 method for class 'spautor'
cooks.distance(model, ...)

## S3 method for class 'spglm'
cooks.distance(model, ...)

## S3 method for class 'spgautor'
cooks.distance(model, ...)

Arguments

Details

Cook's distance measures the influence of an observation on a fitted model object. If an observation is influential, its omission from the data noticeably impacts parameter estimates. The larger the Cook's distance, the larger the influence.

Value

A vector of Cook's distance values for each observation from the fitted model object.

See Also

augment.spmodel() hatvalues.spmodel() influence.spmodel() residuals.spmodel()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
cooks.distance(spmod)

Description

Create a covariance matrix from a fitted model object.

Usage

covmatrix(object, newdata, ...)

## S3 method for class 'splm'
covmatrix(object, newdata, cov_type, ...)

## S3 method for class 'spautor'
covmatrix(object, newdata, cov_type, ...)

## S3 method for class 'spglm'
covmatrix(object, newdata, cov_type, ...)

## S3 method for class 'spgautor'
covmatrix(object, newdata, cov_type, ...)

Arguments

Value

If newdata is omitted, the covariance matrix of the observed data, which has dimension n x n, where n is the sample size used to fit object. If newdata is provided, the covariance matrix between the unobserved (new) data and the observed data, which has dimension m x n, where m is the number of new observations and n is the sample size used to fit object.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
covmatrix(spmod)

Description

Apply the spatial decorrelation transformation for point-referenced data, allowing for random effects, anisotropy, partition factors, and big data methods.

Usage

decorrelate(
  formula,
  data,
  spcov_type,
  spcov_params,
  xcoord,
  ycoord,
  algorithm = "ranger",
  statistic = "RMSPE",
  training,
  evaluate_test,
  anisotropy = FALSE,
  random,
  randcov_params,
  partition_factor,
  ordering,
  local,
  grid,
  dense_grid,
  ...
)

## S3 method for class 'decorrelate_grid'
tidy(x, sort_by, decreasing, ...)

Arguments

Details

The spatial decorrelation transformation is a preprocessing transformation that reduces the impacts of spatial dependence (i.e., covariance, correlation) on machine learning models. Predictions are made on the decorrelated scale and then recorrelated to account for spatial dependence. See Heaton et al., 2025 for details.

spcov_type Details: The correlation matrix $R$ controls the spatial dependence structure among observations. Parametric forms for $R$ are given below, where $\eta = h / range$ for $h$ distance between observations:

• exponential: $exp(- \eta )$

• spherical: $(1 - 1.5\eta + 0.5\eta^3) * I(h <= range)$

• gaussian: $exp(- \eta^2 )$

• triangular: $(1 - \eta) * I(h <= range)$

• circular: $(1 - (2 / \pi) * (m * sqrt(1 - m^2) + sin^{-1}(m))) * I(h <= range), m = min(\eta, 1)$

• cubic: $(1 - 7\eta^2 + 8.75\eta^3 - 3.5\eta^5 + 0.75\eta^7) * I(h <= range)$

• pentaspherical: $(1 - 1.875\eta + 1.25\eta^3 - 0.375\eta^5) * I(h <= range)$

• cosine: $cos(\eta)$

• wave: $sin(\eta) / \eta * I(h > 0) + I(h = 0)$

• jbessel: $Bj(h * range)$, Bj is Bessel-J function

• gravity: $(1 + \eta^2)^{-0.5}$

• rquad: $(1 + \eta^2)^{-1}$

• magnetic: $(1 + \eta^2)^{-1.5}$

• matern: $2^{1 - extra}/ \Gamma(extra) * \alpha^{extra} * Bk(\alpha, extra)$, $\alpha = (2extra)^{0.5} * \eta$, Bk is Bessel-K function with order $1/5 \le extra \le 5$

• cauchy: $(1 + \eta^2)^{-extra}$, $extra > 0$

• pexponential: $exp(h^{extra}/range)$, $0 < extra \le 2$

• none: $0$

All spatial covariance functions are valid in one spatial dimension. All spatial covariance functions except triangular and cosine are valid in two dimensions. An alias for none is ie.

anisotropy Details: By default, all spatial covariance parameters except rotate and scale as well as all random effect variance parameters are assumed unknown, requiring estimation. If either rotate or scale are given initial values other than 0 and 1 (respectively) in spcov_params(), anisotropy is implicitly set to TRUE. (Geometric) Anisotropy is modeled by transforming a covariance function that decays differently in different directions to one that decays equally in all directions via rotation and scaling of the original coordinates. The rotation is controlled by the rotate parameter in $[0, \pi]$ radians. The scaling is controlled by the scale parameter in $[0, 1]$. The anisotropy correction involves first a rotation of the coordinates clockwise by rotate and then a scaling of the coordinates' minor axis by the reciprocal of scale. The spatial covariance is then computed using these transformed coordinates.

random Details: If random effects are used (the estimation method must be "reml" or "ml"), the model can be written as $y = X \beta + Z1u1 + ... Zjuj + \tau + \epsilon$, where each Z is a random effects design matrix and each u is a random effect.

partition_factor Details: The partition factor can be represented in matrix form as $P$, where elements of $P$ equal one for observations in the same level of the partition factor and zero otherwise. The covariance matrix involving only the spatial and random effects components is then multiplied element-wise (Hadmard product) by $P$, yielding the final covariance matrix.

training Details: When replicate or the number of cross validation folds is at least two, there are separate grids evaluated for each replication (or fold). Statistics in each grid are averaged across replications (or folds) to determine a final grid ranked by statistic.

local Details: The big data approximation works by leveraging the conditional nature of the spatial decorrelation transformation via the Vecchia approximation. The Vecchia approximation enables efficient computation of the conditional distribution by considering only the size most relevant observations in the ordering (rather than using all the observations).

Observations with NA response values are removed for model fitting, but their values can be predicted afterwards by running predict(object).

Value

A list with many elements that store information about the fitted model object:

• algorithm: The machine learning algorithm used.

• decorrelate_data: The output of decorrelate_data() applied to data.

• fit: The fitted machine learning model object applied to the decorrelated data.

• grid: If used, the grid of spatial decorrelation parameters evaluated and their corresponding metrics when applied to the test data.

• newdata: The rows of data that have NA response values and are stored as prediction data.

• training: If used, the observations assigned to each training and test data set.

• test: If used, a list with the lowest (absolute) mean bias (bias), mean-squared-prediction error (MSPE), root-mean-squared-prediction error (RMSPE), and predictive R-squared (cor2).

References

Matthew J. Heaton, Andrew Millane, and Jake S. Rhodes. 2025. A Scalable Spatial Decorrelation Preprocessing Approach for Machine and Deep Learning. Journal of Data Science. 1-15, DOI 10.6339/25-JDS1210

Examples

decorr <- decorrelate(log_cond ~ temp, data = lake, spcov_type = "exponential")
tidy(decorr$grid)

Description

Apply the spatial decorrelation transformation to a data object. This object contains the transformed explanatory and response variables which can be used to fit a machine learning model. This object also contains information needed to decorrelate prediction data.

Usage

decorrelate_data(
  formula,
  data,
  spcov_params,
  xcoord,
  ycoord,
  randcov_params,
  partition_factor,
  ordering,
  local,
  ...
)

Arguments

Details

The spatial decorrelation transformation is a preprocessing transformation that reduces the impacts of spatial dependence (i.e., covariance, correlation) on machine learning models. See decorrelate() and Heaton et al., 2025 for more details.

Value

A list with many elements that store information about the fitted model object. Importantly, the list contains the following elements:

• X: The original fixed effects design matrix (of explanatory variables)

• y: The original response variable

• tX: The spatially decorrelated transformed fixed effects design matrix

• ty: The spatially decorrelated transformed response variable

References

Matthew J. Heaton, Andrew Millane, and Jake S. Rhodes. 2025. A Scalable Spatial Decorrelation Preprocessing Approach for Machine and Deep Learning. Journal of Data Science. 1-15, DOI 10.6339/25-JDS1210

See Also

decorrelate() spcov_params() randcov_params()

Examples

params <- spcov_params("exponential", de = 1, ie = 0.2, range = 1e5)
decorr <- decorrelate_data(log_cond ~ temp, data = lake, spcov_params = params)
head(cbind(decorr$X, decorr$tX))
head(cbind(decorr$y, decorr$ty))

Description

Create a spatial decorrelation transformation grid of initial parameters to be evaluated via a grid search.

Usage

decorrelate_grid(
  formula,
  data,
  spcov_type,
  spcov_params,
  xcoord,
  ycoord,
  anisotropy = FALSE,
  random,
  randcov_params,
  dense_grid
)

Arguments

Value

A grid of spatial decorrelation parameters stored as a data.frame.

Examples

decorrelate_grid(log_cond ~ temp, data = lake, spcov_type = "exponential")

Description

Apply the spatial decorrelation transformation to a newdata object. This object contains explanatory variables that are transformed for prediction accoring to some spatial decorrelation transformation.

Usage

decorrelate_newdata(object, newdata, local, ...)

Arguments

Value

A list with many elements that store information about the fitted model object. Importantly, the list contains the following element:

• X_newdata: The original fixed effects design matrix (of explanatory variables) for the prediction data.

• tX_newdata: The spatially decorrelated fixed effects design matrix for the prediction data.

Examples

params <- spcov_params("exponential", de = 1, ie = 0.2, range = 1e5)
decorr <- decorrelate_data(log_cond ~ temp, data = lake, spcov_params = params)
decorr_newdata <- decorrelate_newdata(decorr, newdata = lake_preds)
head(decorr_newdata$tX_newdata)

Description

Returns the deviance of a fitted model object.

Usage

## S3 method for class 'splm'
deviance(object, ...)

## S3 method for class 'spautor'
deviance(object, ...)

## S3 method for class 'spglm'
deviance(object, ...)

## S3 method for class 'spgautor'
deviance(object, ...)

Arguments

Details

For objects estimated using "ml" or "reml", the deviance is twice the difference in log-likelihoods between the saturated (perfect-fit) model and the fitted model.

Value

The deviance.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
deviance(spmod)

Description

Create a dispersion parameter initial object that specifies initial and/or known values to use while estimating the dispersion parameter with spglm() or spgautor().

Usage

dispersion_initial(family, dispersion, known)

Arguments

Details

The dispersion_initial list is later passed to spglm() or spgautor().

The variance function of an individual $y$ (given $\mu$) for each generalized linear model family is given below:

• family: $Var(y)$

• poisson: $\mu \phi$

• nbinomial: $\mu + \mu^2 / \phi$

• binomial: $n \mu (1 - \mu) \phi$

• beta: $\mu (1 - \mu) / (1 + \phi)$

• Gamma: $\mu^2 / \phi$

• inverse.gaussian: $\mu^2 / \phi$

The parameter $\phi$ is a dispersion parameter that influences $Var(y)$. For the poisson and binomial families, $\phi$ is always one. Note that this inverse Gaussian parameterization is different than a standard inverse Gaussian parameterization, which has variance $\mu^3 / \lambda$. Setting $\phi = \lambda / \mu$ yields our parameterization, which is preferred for computational stability. Also note that the dispersion parameter is often defined in the literature as $V(\mu) \phi$, where $V(\mu)$ is the variance function of the mean. We do not use this parameterization, which is important to recognize while interpreting dispersion parameter estimates using spglm() or spgautor(). For more on generalized linear model constructions, see McCullagh and Nelder (1989).

Value

A list with two elements: initial and is_known. initial is a named numeric vector indicating the dispersion parameters with a specified initial and/or known value. is_known is a named numeric vector indicating whether the dispersion parameters in initial is known or not. The class of the list matches the value given to the family argument.

References

McCullagh P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.

Examples

# known dispersion value 1
dispersion_initial("nbinomial", dispersion = 1, known = "dispersion")

Description

Create a dispersion parameter object for use with other functions.

Usage

dispersion_params(family, dispersion)

Arguments

Details

The variance function of an individual $y$ (given $\mu$) for each generalized linear model family is given below:

• family: $Var(y)$

• poisson: $\mu \phi$

• nbinomial: $\mu + \mu^2 / \phi$

• binomial: $n \mu (1 - \mu) \phi$

• beta: $\mu (1 - \mu) / (1 + \phi)$

• Gamma: $\mu^2 / \phi$

• inverse.gaussian: $\mu^2 / \phi$

The parameter $\phi$ is a dispersion parameter that influences $Var(y)$. For the poisson and binomial families, $\phi$ is always one. Note that this inverse Gaussian parameterization is different than a standard inverse Gaussian parameterization, which has variance $\mu^3 / \lambda$. Setting $\phi = \lambda / \mu$ yields our parameterization, which is preferred for computational stability. Also note that the dispersion parameter is often defined in the literature as $V(\mu) \phi$, where $V(\mu)$ is the variance function of the mean. We do not use this parameterization, which is important to recognize while interpreting dispersion parameter estimates using spglm() or spgautor(). For more on generalized linear model constructions, see McCullagh and Nelder (1989).

Value

A named numeric vector with class family containing the dispersion.

References

McCullagh P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.

Examples

dispersion_params("beta", dispersion = 1)

Description

Compute the empirical autocovariance (i.e., empirical covariance) for varying bin sizes and cutoff values.

Usage

eacf(
  formula,
  data,
  xcoord,
  ycoord,
  cloud = FALSE,
  bins = 15,
  cutoff,
  dist_matrix,
  partition_factor
)

## S3 method for class 'eacf'
plot(x, ...)

Arguments

Details

The empirical autocovariance (i.e., empirical covariance) is a tool used to visualize and model spatial dependence by estimating the semivariance of a process at varying distances. For a constant-mean process, the autocovariance at distance $h$ is denoted $Cov(h)$ and defined as $Cov(z1, z2)$. Under second-order stationarity, $Cov(h) = Cov(0) - \gamma(h)$, where $gamma(h)$ is the semivariance function at distance h. Typically the residuals from an ordinary least squares fit defined by formula are second-order stationary with mean zero. These residuals are used to compute the empirical autocovariance At a distance h, the empirical autocovariance is $1/N(h) \sum (r1 \times r2)$, where $N(h)$ is the number of (unique) pairs in the set of observations whose distance separation is h and r1 and r2 are residuals corresponding to observations whose distance separation is h. In spmodel, these distance bins actually contain observations whose distance separation is h +- c, where c is a constant determined implicitly by bins. Typically, only observations whose distance separation is below some cutoff are used to compute the empirical semivariogram (this cutoff is determined by cutoff).

Value

If cloud = FALSE, a tibble (data.frame) with distance bins (bins), the average distance (dist), the average autocovariance (acov), and the number of (unique) pairs (np). If cloud = TRUE, a tibble (data.frame) with distance (dist) and autocovariance (acov) for each unique pair.

Examples

eacf(sulfate ~ 1, sulfate)
plot(eacf(sulfate ~ 1, sulfate))

Description

Compute the empirical semivariogram for varying bin sizes and cutoff values.

Usage

esv(
  formula,
  data,
  xcoord,
  ycoord,
  cloud = FALSE,
  robust = FALSE,
  bins = 15,
  cutoff,
  dist_matrix,
  partition_factor
)

## S3 method for class 'esv'
plot(x, ...)

Arguments

Details

The empirical semivariogram is a tool used to visualize and model spatial dependence by estimating the semivariance of a process at varying distances. For a constant-mean process, the semivariance at distance $h$ is denoted $\gamma(h)$ and defined as $0.5 * Var(z1 - z2)$. Under second-order stationarity, $\gamma(h) = Cov(0) - Cov(h)$, where $Cov(h)$ is the covariance function at distance h. Typically the residuals from an ordinary least squares fit defined by formula are second-order stationary with mean zero. These residuals are used to compute the empirical semivariogram. At a distance h, the empirical semivariance is $1/N(h) \sum (r1 - r2)^2$, where $N(h)$ is the number of (unique) pairs in the set of observations whose distance separation is h and r1 and r2 are residuals corresponding to observations whose distance separation is h. The robust version is described by Cressie and Hawkins (1980). In spmodel, these distance bins actually contain observations whose distance separation is h +- c, where c is a constant determined implicitly by bins. Typically, only observations whose distance separation is below some cutoff are used to compute the empirical semivariogram (this cutoff is determined by cutoff).

When using splm() with estmethod as "sv-wls", the empirical semivariogram is calculated internally and used to estimate spatial covariance parameters.

Value

If cloud = FALSE, a tibble (data.frame) with distance bins (bins), the average distance (dist), the average semivariance (gamma), and the number of (unique) pairs (np). If cloud = TRUE, a tibble (data.frame) with distance (dist) and semivariance (gamma) for each unique pair.

References

Cressie, N & Hawkins, D.M. 1980. Robust estimation of the variogram. Journal of the International Association for Mathematical Geology, 12, 115-125.

Examples

esv(sulfate ~ 1, sulfate)
plot(esv(sulfate ~ 1, sulfate))

Description

State borders for the four corners states in the United States: Arizona, Colorado, New Mexico, Utah.

Usage

fc_borders

Format

An sf object with 4 rows and 4 columns:

• NAME: State name.

• STUSPS: State postal code.

• GEO.ID: State GEO.ID from the United States Census Bureau.

• geometry: POINT geometry representing coordinates in a NAD83 projection (EPSG: 5070). Distances between points are in meters.

Source

The data source is the United States Census Bureau TIGER/Line Shapefiles.

Description

Extract fitted values from fitted model objects. fitted.values is an alias.

Usage

## S3 method for class 'splm'
fitted(object, type = "response", ...)

## S3 method for class 'splm'
fitted.values(object, type = "response", ...)

## S3 method for class 'spautor'
fitted(object, type = "response", ...)

## S3 method for class 'spautor'
fitted.values(object, type = "response", ...)

## S3 method for class 'spglm'
fitted(object, type = "response", ...)

## S3 method for class 'spglm'
fitted.values(object, type = "response", ...)

## S3 method for class 'spgautor'
fitted(object, type = "response", ...)

## S3 method for class 'spgautor'
fitted.values(object, type = "response", ...)

Arguments

Details

When type is "response", the fitted values for each observation are the standard fitted values $X \hat{\beta}$. When type is "spcov" the fitted values for each observation are (generally) the best linear unbiased predictors of the spatial dependent and spatial independent random error. When type is "randcov", the fitted values for each level of each random effect are (generally) the best linear unbiased predictors of the corresponding random effect. The fitted values for type "spcov" and "randcov" can generally be used to check assumptions for each component of the fitted model object (e.g., check a Gaussian assumption).

Value

The fitted values according to type.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
fitted(spmod)
fitted.values(spmod)
fitted(spmod, type = "spcov")

Description

Return formula used by a fitted model object.

Usage

## S3 method for class 'splm'
formula(x, ...)

## S3 method for class 'spautor'
formula(x, ...)

## S3 method for class 'spglm'
formula(x, ...)

## S3 method for class 'spgautor'
formula(x, ...)

Arguments

Value

The formula used by a fitted model object.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
formula(spmod)

Description

Returns a row of model summaries from a fitted model object. Glance returns the same number of columns for all models and estimation methods. If a particular summary is undefined for a model or estimation method (e.g., likelihood statistics for estimation methods "sv-wls" or "sv-cl" of splm() objects), NA is returned for that summary.

Usage

## S3 method for class 'splm'
glance(x, ...)

## S3 method for class 'spautor'
glance(x, ...)

## S3 method for class 'spglm'
glance(x, ...)

## S3 method for class 'spgautor'
glance(x, ...)

Arguments

Value

A single-row tibble with columns

• n The sample size.

• p The number of fixed effects.

• npar The number of estimated covariance parameters.

• value The optimized value of the fitting function.

• AIC The AIC.

• AICc The AICc.

• BIC The BIC.

• logLik The log-likelihood.

• deviance The deviance.

• pseudo.r.squared The pseudo r-squared.

See Also

stats::AIC() AICc() stats::BIC() logLik.spmodel() deviance.spmodel() pseudoR2() tidy.spmodel() augment.spmodel()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
glance(spmod)

Description

glances() repeatedly calls glance() on several fitted model objects and binds the output together, sorted by a column of interest.

Usage

glances(object, ...)

## S3 method for class 'splm'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

## S3 method for class 'spautor'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

## S3 method for class 'splm_list'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

## S3 method for class 'spautor_list'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

## S3 method for class 'spglm'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

## S3 method for class 'spgautor'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

## S3 method for class 'spglm_list'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

## S3 method for class 'spgautor_list'
glances(object, ..., sort_by = "AICc", decreasing = FALSE, warning = TRUE)

Arguments

Value

A tibble where each row represents the output of glance() for each fitted model object.

Examples

lmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "none"
)
spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
glances(lmod, spmod)
glances(lmod, spmod, sort_by = "logLik", decreasing = TRUE)

Description

Compute the leverage (hat) value for each observation from a fitted model object.

Usage

## S3 method for class 'splm'
hatvalues(model, ...)

## S3 method for class 'spautor'
hatvalues(model, ...)

## S3 method for class 'spglm'
hatvalues(model, ...)

## S3 method for class 'spgautor'
hatvalues(model, ...)

Arguments

Details

Leverage values measure how far an observation's explanatory variables are relative to the average of the explanatory variables. In other words, observations with high leverage are typically considered to have an extreme or unusual combination of explanatory variables. Leverage values are the diagonal of the hat (projection) matrix. The larger the hat value, the larger the leverage.

Value

A vector of leverage (hat) values for each observation from the fitted model object.

See Also

augment.spmodel() cooks.distance.spmodel() influence.spmodel() residuals.spmodel()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
hatvalues(spmod)

Description

Provides basic quantities which are used in forming a wide variety of diagnostics for checking the quality of fitted model objects.

Usage

## S3 method for class 'splm'
influence(model, ...)

## S3 method for class 'spautor'
influence(model, ...)

## S3 method for class 'spglm'
influence(model, ...)

## S3 method for class 'spgautor'
influence(model, ...)

Arguments

Details

This function calls residuals.spmodel(), hatvalues.spmodel(), and cooks.distance.spmodel() and puts the results into a tibble. It is primarily used when calling augment.spmodel().

Value

A tibble with residuals (.resid), leverage values (.hat), cook's distance (.cooksd), and standardized residuals (.std.resid).

See Also

augment.spmodel() cooks.distance.spmodel() hatvalues.spmodel() residuals.spmodel()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
influence(spmod)

Description

Perform k-fold cross validation with options for computationally efficient approximations for big data. Generalizes loocv() (leave-one-out cross validation) to leaving out k folds of (approximately) equal size instead of single observations.

Usage

kcv(object, ...)

## S3 method for class 'splm'
kcv(
  object,
  k = 5,
  cv_predict = FALSE,
  se.fit = FALSE,
  local,
  interval = c("none", "prediction"),
  level = 0.95,
  folds_index,
  ...
)

## S3 method for class 'spautor'
kcv(
  object,
  k = 5,
  cv_predict = FALSE,
  se.fit = FALSE,
  local,
  interval = c("none", "prediction"),
  level = 0.95,
  folds_index,
  ...
)

## S3 method for class 'spglm'
kcv(
  object,
  k = 5,
  cv_predict = FALSE,
  type = c("link", "response"),
  se.fit = FALSE,
  delta = FALSE,
  local,
  folds_index,
  ...
)

## S3 method for class 'spgautor'
kcv(
  object,
  k,
  cv_predict = FALSE,
  type = c("link", "response"),
  se.fit = FALSE,
  delta = FALSE,
  local,
  folds_index,
  ...
)

Arguments

Details

Observations are randomly partitioned into k folds of (approximately) equal size. Each fold is held out from the data set in turn and the remaining data are used to make predictions for the held-out fold. This is compared to the true values of the held-out observations and several fit statistics are (sometimes optionally) computed: bias, mean-squared-prediction error (MSPE), root-mean-squared-prediction error (RMSPE), and the squared correlation (cor2) between the observed data and k-fold cross validation predictions (regarded as a prediction version of r-squared appropriate for comparing across spatial and nonspatial models), , and prediction interval coverage (cover.XX). Generally, bias should be near zero and prediction interval coverage at the intended level for well-fitting models. The lower the MSPE and RMSPE, the better the model fit (according to the k-fold cross validation criterion). The higher the cor2, the better the model fit (according to the k-fold cross validation criterion). cor2 and cover.XX are not returned when object was fit using spglm() or spgautor() because we do not observe the underlying latent mean.

When object is from splm() or spautor(), setting interval = "prediction" additionally reports the empirical coverage of the level (e.g. 95\ the proportion of held-out observations whose true value falls within fit +/- qnorm(1 - (1 - level) / 2) * se.fit (the same normal-quantile interval predict.spmodel() uses by default). This is only available for splm()/spautor() objects, since spglm()/spgautor() have no observed-scale latent mean to compare against.

Value

If cv_predict = FALSE and se.fit = FALSE, a fit statistics tibble (with bias, MSPE, RMSPE, and cor2; see Details). If cv_predict = TRUE or se.fit = TRUE, a list with elements: stats, a fit statistics tibble (with bias, MSPE, RMSPE, and cor2; see Details); cv_predict, a numeric vector with k-fold cross validation predictions for each observation (if cv_predict = TRUE); and se.fit, a numeric vector with k-fold cross validation prediction standard errors for each observation (if se.fit = TRUE). When object is from splm() or spautor() and interval = "prediction", the fit statistics tibble also has a cover.XX column (e.g. cover.95 for level = 0.95; see Details).

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
kcv(spmod)
kcv(spmod, k = 10, cv_predict = TRUE, se.fit = TRUE)

Description

Find a suitable set of labels from a fitted model object.

Usage

## S3 method for class 'splm'
labels(object, ...)

## S3 method for class 'spautor'
labels(object, ...)

## S3 method for class 'spglm'
labels(object, ...)

## S3 method for class 'spgautor'
labels(object, ...)

Arguments

Value

A character vector containing the terms used for the fixed effects from a fitted model object.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
labels(spmod)

Description

Lake data collected as part of the United States Environmental Protection Agency's 2012 and 2017 National Lakes Assessment and LakeCat.

Usage

lake

Format

An sf object with 102 rows and 10 columns:

• comid: A common identifier from NHDPlusV2.

• log_cond: The natural logarithm of lake conductivity.

• cond: The lake conductivity.

• state: The US state: One of Arizona (AZ), Colorado (CO), Nevada (NV), Utah (UT).

• temp: Lake catchment 30-year average temperature (in degrees Celsius).

• precip: Lake watershed 30-year average precipitation (in centimeters).

• elev: Lake elevation (in meters).

• origin: Lake origin (human-made or natural).

• year: A factor representing year (2012 or 2017).

• geometry: POINT geometry representing coordinates in a NAD83 projection (EPSG: 5070). Distances between points are in meters.

Description

Lake prediction data collected as part of the United States Environmental Protection Agency's 2012 and 2017 National Lakes Assessment and LakeCat.

Usage

lake_preds

Format

An sf object with 10 rows and 8 columns:

• comid: A common identifier from NHDPlusV2.

• state: The US state: One of Arizona (AZ), Nevada (NV), Utah (UT).

• temp: Lake catchment 30-year average temperature (in degrees Celsius).

• precip: Lake watershed 30-year average precipitation (in centimeters).

• elev: Lake elevation (in meters).

• origin: Lake origin (human-made or natural).

• year: A factor representing year (2012 or 2017).

• geometry: POINT geometry representing coordinates in a NAD83 projection (EPSG: 5070). Distances between points are in meters.

Description

Find the log-likelihood of a fitted model when estmethod is "ml" or "reml".

Usage

## S3 method for class 'splm'
logLik(object, ...)

## S3 method for class 'spautor'
logLik(object, ...)

## S3 method for class 'spglm'
logLik(object, ...)

## S3 method for class 'spgautor'
logLik(object, ...)

Arguments

Value

The log-likelihood.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
logLik(spmod)

Description

Perform leave-one-out cross validation with options for computationally efficient approximations for big data.

Usage

loocv(object, ...)

## S3 method for class 'splm'
loocv(
  object,
  cv_predict = FALSE,
  se.fit = FALSE,
  local,
  interval = c("none", "prediction"),
  level = 0.95,
  ...
)

## S3 method for class 'spautor'
loocv(
  object,
  cv_predict = FALSE,
  se.fit = FALSE,
  local,
  interval = c("none", "prediction"),
  level = 0.95,
  ...
)

## S3 method for class 'spglm'
loocv(
  object,
  cv_predict = FALSE,
  type = c("link", "response"),
  se.fit = FALSE,
  delta = FALSE,
  local,
  ...
)

## S3 method for class 'spgautor'
loocv(
  object,
  cv_predict = FALSE,
  type = c("link", "response"),
  se.fit = FALSE,
  delta = FALSE,
  local,
  ...
)

Arguments

Details

Each observation is held-out from the data set and the remaining data are used to make a prediction for the held-out observation. This is compared to the true value of the observation and several fit statistics are (sometimes optionally) computed: bias, mean-squared-prediction error (MSPE), root-mean-squared-prediction error (RMSPE), and the squared correlation (cor2) between the observed data and leave-one-out predictions (regarded as a prediction version of r-squared appropriate for comparing across spatial and nonspatial models), and prediction interval coverage (cover.XX). Generally, bias should be near zero and prediction interval coverage at the intended level for well-fitting models. The lower the MSPE and RMSPE, the better the model fit (according to the leave-out-out criterion). The higher the cor2, the better the model fit (according to the leave-out-out criterion). cor2 and cover.XX are not returned when object was fit using spglm() or spgautor() because we do not observe the underlying latent mean.

Value

If cv_predict = FALSE and se.fit = FALSE, a fit statistics tibble (with bias, MSPE, RMSPE, and cor2; see Details). If cv_predict = TRUE or se.fit = TRUE, a list with elements: stats, a fit statistics tibble (with bias, MSPE, RMSPE, and cor2; see Details); cv_predict, a numeric vector with leave-one-out predictions for each observation (if cv_predict = TRUE); and se.fit, a numeric vector with leave-one-out prediction standard errors for each observation (if se.fit = TRUE). When object is from splm() or spautor() and interval = "prediction", the fit statistics tibble also has a cover.XX column (e.g. cover.95 for level = 0.95; see Details).

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
loocv(spmod)
loocv(spmod, cv_predict = TRUE, se.fit = TRUE)

Description

Extract the model frame from a fitted model object.

Usage

## S3 method for class 'splm'
model.frame(formula, ...)

## S3 method for class 'spautor'
model.frame(formula, ...)

## S3 method for class 'spglm'
model.frame(formula, ...)

## S3 method for class 'spgautor'
model.frame(formula, ...)

Arguments

Value

A model frame that contains the variables used by the formula for the fitted model object.

See Also

stats::model.frame()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
model.frame(spmod)

Description

Extract the model matrix (X) from a fitted model object.

Usage

## S3 method for class 'splm'
model.matrix(object, ...)

## S3 method for class 'spautor'
model.matrix(object, ...)

## S3 method for class 'spglm'
model.matrix(object, ...)

## S3 method for class 'spgautor'
model.matrix(object, ...)

Arguments

Value

The model matrix (of the fixed effects), whose rows represent observations and whose columns represent explanatory variables corresponding to each fixed effect.

See Also

stats::model.matrix()

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
model.matrix(spmod)

Description

Moose counts and presence in Alaska, USA.

Usage

moose

Format

An sf object with 218 rows and 5 columns.

• elev: The elevation.

• strat: A factor representing strata (used for sampling). Can take values L and M.

• count: The count (number) of moose observed.

• presence: A binary factor representing whether no moose were observed (value 0) or at least one moose was observed (value 1).

• geometry: POINT geometry representing coordinates in an Alaska Albers projection (EPSG: 3338). Distances between points are in meters.

Source

Alaska Department of Fish and Game, Division of Wildlife Conservation has released this data set under the CC0 license.

Description

Locations at which to predict moose counts and presence in Alaska, USA.

Usage

moose_preds

Format

An sf object with 100 rows and 3 columns.

• elev: The elevation.

• strat: A factor representing strata (used for sampling). Can take values L and M.

• geometry: POINT geometry representing coordinates in an Alaska Albers projection (EPSG: 3338). Distances between points are in meters.

Source

Alaska Department of Fish and Game, Division of Wildlife Conservation has released this data set under the CC0 license.

Description

Heavy metals in mosses near a mining road in Alaska, USA.

Usage

moss

Format

An sf object with 365 rows and 12 columns:

• sample: A factor with a sample identifier. Some samples were replicated in the field or laboratory. As a result, there are 318 unique sample identifiers.

• field_dup: A factor representing field duplicate. Takes values 1 and 2.

• lab_rep: A factor representing laboratory replicate. Takes values 1 and 2.

• year: A factor representing year. Takes values 2001 and 2006.

• sideroad: A factor representing direction relative to the haul road. Takes values N (north of the haul road) and S (south of the haul road).

• log_dist2road: The log of distance (in meters) to the haul road.

• dist2road: The distance (in meters) to the haul road.

• log_Zn: The log of zinc concentration in moss tissue (mg/kg).

• Zn: The zinc concentration in moss tissue (mg/kg).

• geometry: POINT geometry representing coordinates in an Alaska Albers projection (EPSG: 3338). Distances between points are in meters.

Source

Data were obtained from Peter Neitlich and Linda Hasselbach of the National Park Service. Data were used in the publications listed in References.

References

Neitlich, P.N., Ver Hoef, J.M., Berryman, S. D., Mines, A., Geiser, L.H., Hasselbach, L.M., and Shiel, A. E. 2017. Trends in Spatial Patterns of Heavy Metal Deposition on National Park Service Lands Along the Red Dog Mine Haul Road, Alaska, 2001-2006. PLOS ONE 12(5):e0177936 DOI:10.1371/journal.pone.0177936

Hasselbach, L., Ver Hoef, J.M., Ford, J., Neitlich, P., Berryman, S., Wolk B. and Bohle, T. 2005. Spatial Patterns of Cadmium, Lead and Zinc Deposition on National Park Service Lands in the Vicinity of Red Dog Mine, Alaska. Science of the Total Environment 348: 211-230.

Description

Plot fitted model diagnostics such as residuals vs fitted values, quantile-quantile, scale-location, Cook's distance, residuals vs leverage, Cook's distance vs leverage, a fitted spatial covariance function, and a fitted anisotropic level curve of equal correlation.

Usage

## S3 method for class 'splm'
plot(x, which, ...)

## S3 method for class 'spautor'
plot(x, which, ...)

## S3 method for class 'spglm'
plot(x, which, ...)

## S3 method for class 'spgautor'
plot(x, which, ...)

Arguments

Details

For all fitted model objects,, the values of which make the corresponding plot:

• 1: Standardized residuals vs fitted values (of the response)

• 2: Normal quantile-quantile plot of standardized residuals

• 3: Scale-location plot of standardized residuals

• 4: Cook's distance

• 5: Standardized residuals vs leverage

• 6: Cook's distance vs leverage

For splm() and spglm() fitted model objects, there are two additional values of which:

• 7: Fitted spatial covariance function vs distance

• 8: Fitted anisotropic (or isotropic) level curve of equal correlation

Value

No return value. Function called for plotting side effects.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
plot(spmod)
plot(spmod, which = c(1, 2, 4, 6))

Description

Predicted values and intervals based on a fitted model object.

Usage

## S3 method for class 'splm'
predict(
  object,
  newdata,
  se.fit = FALSE,
  scale = NULL,
  df = Inf,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  type = c("response", "terms", "weight"),
  block = FALSE,
  local,
  terms = NULL,
  na.action = na.fail,
  ...
)

## S3 method for class 'spautor'
predict(
  object,
  newdata,
  se.fit = FALSE,
  scale = NULL,
  df = Inf,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  type = c("response", "terms", "weight"),
  local,
  terms = NULL,
  na.action = na.fail,
  ...
)

## S3 method for class 'splm_list'
predict(
  object,
  newdata,
  se.fit = FALSE,
  scale = NULL,
  df = Inf,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  type = c("response", "terms"),
  local,
  terms = NULL,
  na.action = na.fail,
  ...
)

## S3 method for class 'spautor_list'
predict(
  object,
  newdata,
  se.fit = FALSE,
  scale = NULL,
  df = Inf,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  type = c("response", "terms"),
  local,
  terms = NULL,
  na.action = na.fail,
  ...
)

## S3 method for class 'splmRF'
predict(object, newdata, local, ...)

## S3 method for class 'spautorRF'
predict(object, newdata, local, ...)

## S3 method for class 'splmRF_list'
predict(object, newdata, local, ...)

## S3 method for class 'spautorRF_list'
predict(object, newdata, local, ...)

## S3 method for class 'spglm'
predict(
  object,
  newdata,
  type = c("link", "response", "terms", "weight"),
  se.fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  dispersion = NULL,
  terms = NULL,
  local,
  var_correct = TRUE,
  delta = FALSE,
  newdata_size,
  na.action = na.fail,
  ...
)

## S3 method for class 'spgautor'
predict(
  object,
  newdata,
  type = c("link", "response", "terms", "weight"),
  se.fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  dispersion = NULL,
  terms = NULL,
  local,
  var_correct = TRUE,
  delta = FALSE,
  newdata_size,
  na.action = na.fail,
  ...
)

## S3 method for class 'spglm_list'
predict(
  object,
  newdata,
  type = c("link", "response", "terms"),
  se.fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  dispersion = NULL,
  terms = NULL,
  local,
  var_correct = TRUE,
  newdata_size,
  na.action = na.fail,
  ...
)

## S3 method for class 'spgautor_list'
predict(
  object,
  newdata,
  type = c("link", "response", "terms"),
  se.fit = FALSE,
  interval = c("none", "confidence", "prediction"),
  level = 0.95,
  dispersion = NULL,
  terms = NULL,
  local,
  var_correct = TRUE,
  newdata_size,
  na.action = na.fail,
  ...
)

## S3 method for class 'decorrelate'
predict(object, newdata, local, ...)

## S3 method for class 'decorrelate_list'
predict(object, newdata, local, ...)

Arguments

Details

For splm and spautor objects, the (empirical) best linear unbiased predictions (i.e., Kriging predictions) at each site are returned when interval is "none" or "prediction" alongside standard errors. Prediction intervals are also returned if interval is "prediction". When interval is "confidence", the estimated mean is returned alongside standard errors and confidence intervals for the mean. For splm_list and spautor_list objects, predictions and associated intervals and standard errors are returned for each list element.

For splmRF or spautorRF objects, random forest spatial residual model predictions are computed by combining the random forest prediction with the (empirical) best linear unbiased prediction for the residual. This approach is called random forest regression Kriging. For splmRF_list or spautorRF objects, predictions are returned for each list element.

For decorrelate objects, the spatial decorrelation transformation predictions recorrelated to the original scale. For decorrelate_list objects, predictions are returned for each list element.

Value

For splm or spautor objects, if se.fit is FALSE, predict() returns a vector of predictions or a matrix of predictions with column names fit, lwr, and upr if interval is "confidence" or "prediction". If se.fit is TRUE, a list with the following components is returned:

• fit: vector or matrix as above

• se.fit: standard error of each fit

For splm_list or spautor_list objects, a list that contains relevant quantities for each list element.

For splmRF or spautorRF objects, a vector of predictions. For splmRF_list or spautorRF_list objects, a list that contains relevant quantities for each list element.

For decorrelate objects, a vector of predictions. For decorrelate_list objects, a list that contains relevant quantities for each list element.

References

Fox, E.W., Ver Hoef, J. M., & Olsen, A. R. (2020). Comparing spatial regression to random forests for large environmental data sets. PloS one, 15(3), e0229509.

Examples

spmod <- splm(sulfate ~ 1, data = sulfate, spcov_type = "exponential")
predict(spmod, sulfate_preds)
predict(spmod, sulfate_preds, interval = "prediction")
augment(spmod, newdata = sulfate_preds, interval = "prediction")

sulfate$var <- rnorm(NROW(sulfate)) # add noise variable
sulfate_preds$var <- rnorm(NROW(sulfate_preds)) # add noise variable
sprfmod <- splmRF(sulfate ~ var, data = sulfate, spcov_type = "exponential")
predict(sprfmod, sulfate_preds)


spgmod <- spglm(presence ~ elev * strat,
  family = "binomial",
  data = moose,
  spcov_type = "exponential"
)
predict(spgmod, moose_preds)
predict(spgmod, moose_preds, interval = "prediction")
augment(spgmod, newdata = moose_preds, interval = "prediction")

decorr <- decorrelate(log_cond ~ temp, data = lake, spcov_type = "exponential")
predict(decorr, newdata = lake_preds)

Description

Print fitted model objects and summaries.

Usage

## S3 method for class 'splm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'spautor'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'summary.splm'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'summary.spautor'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'anova.splm'
print(
  x,
  digits = max(getOption("digits") - 2L, 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'anova.spautor'
print(
  x,
  digits = max(getOption("digits") - 2L, 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'decorrelate'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'spglm'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'spgautor'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'summary.spglm'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'summary.spgautor'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'anova.spglm'
print(
  x,
  digits = max(getOption("digits") - 2L, 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'anova.spgautor'
print(
  x,
  digits = max(getOption("digits") - 2L, 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'splmRF'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'summary.splmRF'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

## S3 method for class 'spautorRF'
print(x, digits = max(3L, getOption("digits") - 3L), ...)

## S3 method for class 'summary.spautorRF'
print(
  x,
  digits = max(3L, getOption("digits") - 3L),
  signif.stars = getOption("show.signif.stars"),
  ...
)

Arguments

Value

Printed fitted model objects and summaries with formatting.

Examples

spmod <- splm(z ~ water + tarp,
  data = caribou,
  spcov_type = "exponential", xcoord = x, ycoord = y
)
print(spmod)
print(summary(spmod))
print(anova(spmod))

sulfate$var <- rnorm(NROW(sulfate)) # add noise variable
sprfmod <- splmRF(sulfate ~ var, data = sulfate, spcov_type = "exponential")
print(sprfmod)


sprfmod <- spautorRF(log_trend ~ stock, data = seal, spcov_type = "car")
print(sprfmod)

Description

Compute a pseudo r-squared for a fitted model object.

Usage

pseudoR2(object, ...)

## S3 method for class 'splm'
pseudoR2(object, adjust = FALSE, ...)

## S3 method for class 'spautor'
pseudoR2(object, adjust = FALSE, ...)

## S3 method for class 'spglm'
pseudoR2(object, adjust = FALSE, ...)

## S3 method for class 'spgautor'
pseudoR2(object, adjust = FALSE, ...)

Arguments