Fitting kDGLM models

Fit a model given its structure and the observed data. This function can be used for any supported family (see vignette).

Usage

fit_model(
  ...,
  smooth = TRUE,
  p.monit = NA,
  condition = "TRUE",
  metric = "log.like",
  lag = 1,
  pred.cred = 0.95,
  metric.cutoff = NA,
  save.models = FALSE,
  silent = FALSE
)

Arguments

...: dlm_block or dlm_distr objects or named values: The structural blocks of the model (dlm_block objects), alongside the model outcomes (dlm_distr object). If at least one block is undefined, the user must also provide its value in this argument (see last example).
smooth: boolean: A flag indicating if the smoothed distribution for the latent states should be calculated.
p.monit: numeric (optional): The prior probability of changes in the latent space variables that are not part of its dynamic. Only used when performing sensitivity analysis.
condition: character: A character defining which combinations of undefined hyper parameter should be tested. See example for details. Only used when performing sensitivity analysis.
metric: character: The name of the metric to use for model selection. One of log-likelihood for the one-step-ahead prediction ("log.like"), Mean Absolute Scaled Error ("mase") (Hyndman and Koehler 2006) or Interval Score ("interval.score") (Bracher et al. 2021) . Only used when performing sensitivity analysis.
lag: integer: The number of steps ahead used for the prediction when calculating the metrics. If lag<0, predictions are made using the smoothed distribution of the latent states. Only used when performing sensitivity analysis.
pred.cred: numeric: A number between 0 and 1 (not included) indicating the credibility interval for predictions. If not within the valid range of values, 0.95 will be used. Only used when performing sensitivity analysis.
metric.cutoff: integer: The number of observations to ignore when calculating the metrics. Default is 1/10 of the number of observations (rounded down). Only used when performing sensitivity analysis.
save.models: boolean: A flag indicating if all evaluated models should be saved. If FALSE, only the best model (according to the chosen metric) will be saved. Only used when performing sensitivity analysis.
silent: boolean: A flag indicating if a progress bar should be printed. Only used when performing sensitivity analysis.

Value

A fitted_dlm object.

Details

This is the main function of the kDGLM package, as it is used to fit all models.

For the details about the implementation see dos Santos et al. (2024) .

For the details about the methodology see Alves et al. (2024) .

For the details about the Dynamic Linear Models see West and Harrison (1997) and Petris et al. (2009) .

Examples


# Poisson case
data <- c(AirPassengers)

level <- polynomial_block(rate = 1, order = 2, D = 0.95)
season <- harmonic_block(rate = 1, order = 2, period = 12, D = 0.975)

outcome <- Poisson(lambda = "rate", data = data)

fitted.data <- fit_model(level, season,
  AirPassengers = outcome
)
summary(fitted.data)
#> Fitted DGLM with 1 outcomes.
#> 
#> distributions:
#>     AirPassengers: Poisson
#> 
#> ---
#> No static coeficients.
#> ---
#> See the coef.fitted_dlm for the coeficients with temporal dynamic.
#> 
#> One-step-ahead prediction
#> Log-likelihood        : -580.2514
#> Interval Score        : 129.48462
#> Mean Abs. Scaled Error:   0.47013
#> ---

plot(fitted.data, plot.pkg = "base")


##################################################################

# Multinomial case
structure <- (
  polynomial_block(p = 1, order = 2, D = 0.95) +
    harmonic_block(p = 1, period = 12, D = 0.975) +
    noise_block(p = 1, R1 = 0.1) +
    regression_block(p = chickenPox$date >= as.Date("2013-09-01"))
  # Vaccine was introduced in September of 2013
) * 4

outcome <- Multinom(p = structure$pred.names, data = chickenPox[, c(2, 3, 4, 6, 5)])
fitted.data <- fit_model(structure, chickenPox = outcome)
summary(fitted.data)
#> Fitted DGLM with 1 outcomes.
#> 
#> distributions:
#>     chickenPox: Multinomial
#> 
#> Static coeficients (smoothed):
#>                  Estimate Std. Error   t value Pr(>|t|)
#> Var.Reg.1         0.38672    0.25101  1.54061    0.123   
#> Var.Reg.2         0.46804    0.26503  1.76600    0.077   
#> Var.Reg.3         0.48480    0.28504  1.70080    0.089   
#> Var.Reg.4        -0.26821    0.24810 -1.08105    0.280   
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> ---
#> See the coef.fitted_dlm for the coeficients with temporal dynamic.
#> 
#> One-step-ahead prediction
#> Log-likelihood        : -1962.023
#> Interval Score        : 167.73519
#> Mean Abs. Scaled Error:   0.77385
#> ---
plot(fitted.data, plot.pkg = "base")


##################################################################

# Univariate Normal case
structure <- polynomial_block(mu = 1, D = 0.95) +
  polynomial_block(V = 1, D = 0.95)

outcome <- Normal(mu = "mu", V = "V", data = cornWheat$corn.log.return[1:500])
fitted.data <- fit_model(structure, corn = outcome)
summary(fitted.data)
#> Fitted DGLM with 1 outcomes.
#> 
#> distributions:
#>     corn: Normal
#> 
#> ---
#> No static coeficients.
#> ---
#> See the coef.fitted_dlm for the coeficients with temporal dynamic.
#> 
#> One-step-ahead prediction
#> Log-likelihood        : 1277.54
#> Interval Score        : 0.07564
#> Mean Abs. Scaled Error: 0.76327
#> ---
plot(fitted.data, plot.pkg = "base")


##################################################################

# Bivariate Normal case
structure <- (polynomial_block(mu = 1, D = 0.95) +
  polynomial_block(V = 1, D = 0.95)) * 2 +
  polynomial_block(rho = 1, D = 0.95)

outcome <- Normal(
  mu = c("mu.1", "mu.2"),
  V = matrix(c("V.1", "rho", "rho", "V.2"), 2, 2),
  data = cornWheat[1:500, c(4, 5)]
)
fitted.data <- fit_model(structure, cornWheat = outcome)
summary(fitted.data)
#> Fitted DGLM with 1 outcomes.
#> 
#> distributions:
#>     cornWheat: Normal
#> 
#> ---
#> No static coeficients.
#> ---
#> See the coef.fitted_dlm for the coeficients with temporal dynamic.
#> 
#> One-step-ahead prediction
#> Log-likelihood        : 2557.802
#> Interval Score        : 0.07505
#> Mean Abs. Scaled Error: 0.74750
#> ---
plot(fitted.data, plot.pkg = "base")


##################################################################

# Gamma case
structure <- polynomial_block(mu = 1, D = 0.95)

outcome <- Gamma(phi = 0.5, mu = "mu", data = cornWheat$corn.log.return[1:500]**2)
fitted.data <- fit_model(structure, corn = outcome)
summary(fitted.data)
#> Fitted DGLM with 1 outcomes.
#> 
#> distributions:
#>     corn: Gamma
#> 
#> ---
#> No static coeficients.
#> ---
#> See the coef.fitted_dlm for the coeficients with temporal dynamic.
#> 
#> One-step-ahead prediction
#> Log-likelihood        : -Inf
#> Interval Score        : 0.00199
#> Mean Abs. Scaled Error: 0.93924
#> ---
plot(fitted.data, plot.pkg = "base")


##################################################################
# \donttest{
# Sensitivity analysis
data <- c(AirPassengers)

level <- polynomial_block(rate = 1, order = 2, D = "D.level")
season <- harmonic_block(rate = "sazo.effect", order = 2, period = 12, D = "D.sazo")

outcome <- Poisson(lambda = "rate", data = data)

fit_model(level, season, outcome,
  sazo.effect = c(0, 1),
  D.level = c(seq.int(0.8, 1, l = 11)),
  D.sazo = c(seq.int(0.95, 1, l = 11)),
  condition = "sazo.effect==1 | D.sazo==1"
)
#> 
[==================================================] - 99.24% - ETA - NA
#> Error in rep(" ", 50 - n.bar): invalid 'times' argument
# }

Usage

Arguments

Value

Details

See also

Examples