sclr: Fits the scaled logit model
In sclr: Scaled Logistic Regression

Description Usage Arguments Details Value References Examples

Used to fit the scaled logit model from Dunning (2006).

sclr(
  formula,
  data = NULL,
  ci_lvl = 0.95,
  tol = 10^(-7),
  algorithm = c("newton-raphson", "gradient-ascent"),
  nr_iter = 2000,
  ga_iter = 2000,
  n_conv = 3,
  conventional_names = FALSE,
  seed = NULL
)

`formula`	an object of class "formula": a symbolic description of the model to be fitted.
`data`	a data frame.
`ci_lvl`	Confidence interval level for the parameter estimates.
`tol`	Tolerance.
`algorithm`	Algorithms to run. "newton-raphson" or "gradient-ascent". If a character vector, the algorithms will be applied in the order they are present in the vector.
`nr_iter`	Maximum allowed iterations for Newton-Raphson.
`ga_iter`	Maximum allowed iterations for gradient ascent.
`n_conv`	Number of times the algorithm has to converge (to work around local maxima).
`conventional_names`	If `TRUE`, estimated parameter names will be (Baseline), (Intercept) and the column names in the model matrix. Otherwise - lambda, beta_0 and beta_ prefix in front of column names in the model matrix.
`seed`	Seed for the algorithms.

The model is logistic regression with an added parameter for the top asymptote. That parameter is reported as theta (or (Baseline) if conventional_names = TRUE). Note that it is reported on the logit scale. See vignette("sclr-math") for model specification, log-likelihood, scores and second derivatives. The main default optimisation algorithm is Newton-Raphson. Gradient ascent is used as a fallback by default. Computing engine behind the fitting is sclr_fit.

An object of class sclr. This is a list with the following elements:

`parameters`	Maximum likelihood estimates of the parameter values.
`covariance_mat`	The variance-covariance matrix of the parameter estimates.
`algorithm`	Algorithm used.
`algorithm_return`	Everything the algorithm returned.
`n_converge`	The number of Newton-Raphson iterations (including resets) that were required for convergence.
`x`	Model matrix derived from `formula` and `data`.
`y`	Response matrix derived from `formula` and `data`.
`call`	The original call to `sclr`.
`model`	Model frame object derived from `formula` and `data`.
`terms`	Terms object derived from model frame.
`ci`	Confidence intervals of the parameter estimates.
`log_likelihood`	Value of log-likelihood calculated at the ML estimates of parameters.
`formula`	Passed formula.
`data`	Passed data.

Methods supported: print, vcov, coef, model.frame, model.matrix, summary, predict, tidy (broom package), logLik.

Dunning AJ (2006). "A model for immunological correlates of protection." Statistics in Medicine, 25(9), 1485-1497. https://doi.org/10.1002/sim.2282.

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library(sclr)
fit1 <- sclr(status ~ logHI, one_titre_data)
summary(fit1)

Call: status ~ logHI

Parameter estimates
      theta      beta_0  beta_logHI 
-0.03497876 -5.42535734  2.14877741 

95% confidence intervals
                2.5 %      97.5 %
theta      -0.1350572  0.06509969
beta_0     -6.4417802 -4.40893450
beta_logHI  1.8146909  2.48286389

Log likelihood: -2469.765