Package 'LKT'

Search for an LKT model specification

Description

Runs forward and/or backward stepwise search over candidate component-feature pairs, tracking nonlinear parameters and common fit metrics. This is a legacy public model-selection helper used by the vignette examples.

Usage

buildLKTModel(
  data,
  usefolds = NA,
  allcomponents,
  allfeatures,
  currentcomponents = c(),
  specialcomponents = c(),
  specialfeatures = c(),
  forv,
  bacv,
  preset = NA,
  presetint = T,
  currentfeatures = c(),
  verbose = FALSE,
  currentfixedpars = c(),
  maxitv = 10,
  interc = FALSE,
  forward = TRUE,
  backward = TRUE,
  metric = "BIC",
  removefeat = c(),
  removecomp = c()
)

Arguments

data	Data frame or data table containing Anon.Student.Id, CF..ansbin., component columns, and optional fold.
usefolds	Numeric vector of folds passed to LKT() for fitting.
allcomponents	Character vector of candidate component columns.
allfeatures	Character vector of candidate feature names.
currentcomponents	Character vector of component columns in the starting model.
specialcomponents	Character vector of components paired one-to-one with specialfeatures and included outside the crossed search grid.
specialfeatures	Character vector of special feature names paired with specialcomponents.
forv	Minimum improvement required to add a term.
bacv	Maximum loss tolerated when removing a term.
preset	Optional preset model family: "static", "AFM", "PFA", "advanced", "AFMLLTM", "PFALLTM", or "advancedLLTM".
presetint	Logical; include preset intercept terms when TRUE.
currentfeatures	Character vector of feature names in the starting model.
verbose	Logical passed to LKT().
currentfixedpars	Numeric vector of fixed parameter values for the starting model.
maxitv	Maximum nonlinear optimizer iterations passed to LKT().
interc	Logical passed to LKT() to include a global intercept.
forward	Logical; allow forward additions.
backward	Logical; allow backward removals.
metric	Selection metric. One of "BIC", "AUC", "AIC", "RMSE", or "R2".
removefeat	Character vector of feature names to exclude from the crossed candidate list.
removecomp	Character vector of component names paired with removefeat to exclude from the crossed candidate list.

Value

A list containing tracetable search history and the final currentfit LKT model.

Examples

data(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
searched <- buildLKTModel(
  data = samplelkt,
  allcomponents = "KC..Default.",
  allfeatures = "lineafm",
  forv = 0,
  bacv = 0,
  interc = TRUE,
  verbose = FALSE
)
names(searched)

---

Compute an LKT feature vector

Description

Computes one feature vector for a prepared LKT component context. This is a legacy public helper used by examples and advanced workflows; most users should call LKT() instead.

Usage

computefeatures(data, feat, par1, par2, index, index2, par3, par4, par5, fcomp)

Arguments

data	Data frame or data table after LKT component preparation.
feat	Feature name to compute.
par1	First nonlinear feature parameter.
par2	Second nonlinear feature parameter.
index	Student-by-component index vector.
index2	Component-level index vector.
par3	Third nonlinear feature parameter.
par4	Fourth nonlinear feature parameter.
par5	Fifth nonlinear feature parameter.
fcomp	Component column name used by features that read component-level spacing or numeric data.

Value

A vector suitable for use as one model-matrix input column.

Examples

data(samplelkt)
data.table::setDT(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
prepared <- computeSpacingPredictors(samplelkt, "KC..Default.")
prepared$history_index <- paste(prepared$KC..Default., prepared$Anon.Student.Id)
prepared$index <- prepared$history_index
prepared$indexcomp <- prepared$KC..Default.
prepared$cor <- countOutcomeold(prepared, "history_index", "CORRECT")
prepared$icor <- countOutcomeold(prepared, "history_index", "INCORRECT")
head(computefeatures(
  prepared, "lineafm", 0, 0,
  prepared$index, prepared$indexcomp, 0, 0, 0, "KC..Default."
))

---

Compute spacing predictors for LKT features

Description

Adds repetition-spacing history columns for one or more component columns. These columns are required by recency, spacing, and forgetting features in LKT(). If CF..reltime. or CF..Time. is missing, the function derives it from Duration..sec. when possible.

Usage

computeSpacingPredictors(data, KCs)

Arguments

data	Data frame or data table containing Anon.Student.Id, CF..ansbin., and each component named in KCs. Requires either CF..reltime. or Duration..sec..
KCs	Character vector of component columns for which spacing predictors should be computed.

Value

The input data with added spacing-history columns for each component: spacing, relspacing, prev, meanspacing, relmeanspacing, and spacinglagged suffixes.

Examples

data(samplelkt)
data.table::setDT(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
spacing_data <- computeSpacingPredictors(samplelkt, "KC..Default.")
head(spacing_data$KC..Default.spacing)

---

Count prior outcomes within an index

Description

Legacy exported helper that counts previous rows whose Outcome value equals response within each index group. It is retained for compatibility with older examples; new package code uses internal helpers.

Usage

countOutcomeold(data, index, response)

Arguments

data	Data frame or data table containing an Outcome column.
index	Grouping column name or data.table by expression that defines the history stream for each row.
response	Outcome value to count, such as "CORRECT" or "INCORRECT".

Value

Numeric vector of lagged cumulative counts, one value per row.

Examples

data(samplelkt)
data.table::setDT(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
samplelkt$history_index <- paste(samplelkt$KC..Default., samplelkt$Anon.Student.Id)
head(countOutcomeold(samplelkt, "history_index", "CORRECT"))

---

Raw Memphis DataShop sample

Description

A raw trial-level sample from the Memphis DataShop export used in examples.

Usage

largerawsample

Format

A data frame with the original exported DataShop columns.

Source

https://pslcdatashop.web.cmu.edu/Export?datasetId=5513

---

Build LASSO input data for LKT feature search

Description

Constructs the sparse design matrices used by LASSOLKTModel() by expanding nonlinear features across a grid of fixed parameter values. This legacy public helper is vignette-facing and returns the nosolve = TRUE form of LKT().

Usage

LASSOLKTData(
  data,
  gridpars,
  allcomponents,
  allfeatures,
  preset = NA,
  presetint = T,
  specialcomponents = c(),
  specialfeatures = c(),
  specialpars = c(),
  removefeat = c(),
  removecomp = c()
)

Arguments

data	Data frame or data table containing Anon.Student.Id, CF..ansbin., component columns, and optional fold.
gridpars	Numeric vector of parameter values used to materialize nonlinear feature candidates.
allcomponents	Character vector of candidate component columns.
allfeatures	Character vector of candidate feature names.
preset	Optional preset model family: "static", "AFM", "PFA", "advanced", "AFMLLTM", "PFALLTM", or "advancedLLTM".
presetint	Logical; include preset intercept terms when TRUE.
specialcomponents	Character vector of components paired one-to-one with specialfeatures.
specialfeatures	Character vector of special feature names paired with specialcomponents.
specialpars	Numeric vector of parameter values for specialfeatures.
removefeat	Character vector of feature names to exclude from the crossed candidate list.
removecomp	Character vector of component names paired with removefeat to exclude from the crossed candidate list.

Value

A list from LKT(nosolve = TRUE) containing LASSO feature names and sparse design data.

Examples

data(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
lasso_data <- LASSOLKTData(
  data = samplelkt,
  gridpars = c(0.25, 0.5),
  allcomponents = "KC..Default.",
  allfeatures = "lineafm"
)
names(lasso_data)

---

Fit a LASSO-selected LKT model

Description

Builds LKT feature matrices with LASSOLKTData() and fits a binomial glmnet path. This is a legacy public model-selection helper retained for vignette compatibility.

Usage

LASSOLKTModel(
  data,
  gridpars,
  allcomponents,
  preset = NA,
  presetint = T,
  allfeatures,
  specialcomponents = c(),
  specialfeatures = c(),
  specialpars = c(),
  target_n,
  removefeat = c(),
  removecomp = c(),
  test_fold = 1
)

Arguments

data	Data frame or data table containing Anon.Student.Id, CF..ansbin., component columns, and a fold column.
gridpars	Numeric vector of parameter values used to materialize nonlinear feature candidates.
allcomponents	Character vector of candidate component columns.
preset	Optional preset model family: "static", "AFM", "PFA", "advanced", "AFMLLTM", "PFALLTM", or "advancedLLTM".
presetint	Logical; include preset intercept terms when TRUE.
allfeatures	Character vector of candidate feature names.
specialcomponents	Character vector of components paired one-to-one with specialfeatures.
specialfeatures	Character vector of special feature names paired with specialcomponents.
specialpars	Numeric vector of parameter values for specialfeatures.
target_n	Desired number of nonzero model features used to choose a lambda from the fitted path.
removefeat	Character vector of feature names to exclude from the crossed candidate list.
removecomp	Character vector of component names paired with removefeat to exclude from the crossed candidate list.
test_fold	Fold value used as the held-out test fold.

Value

A list containing training and test matrices, response vectors, the fitted glmnet object, AUC/RMSE/BIC by lambda, selected lambda index, predictions, selected coefficients, and selected feature summary.

Examples

## Not run: 
data(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
samplelkt$fold <- rep(1:2, length.out = nrow(samplelkt))
lasso_model <- LASSOLKTModel(
  data = samplelkt,
  gridpars = c(0.25, 0.5),
  allcomponents = "KC..Default.",
  allfeatures = "lineafm",
  target_n = 2,
  test_fold = 1
)
names(lasso_model)

## End(Not run)

---

Define the default LibLinear LKT model

Description

Creates the default LKT model adapter backed by LiblineaR. This model uses the shared LKT feature input and returns the common LKTModelFit() shape.

Usage

LibLinearModel()

Value

A model adapter suitable for LKT(model = ...).

Examples

adapter <- LibLinearModel()
adapter$name

---

Fit a logistic knowledge tracing model

Description

Computes LKT features from trial-level learning data and fits a logistic model that predicts CF..ansbin.. The default model adapter uses LiblineaR; custom adapters can be supplied with LKTCustomModel().

Usage

LKT(
  data,
  usefolds = NA,
  components,
  features,
  fixedpars = NA,
  seedpars = NA,
  interacts = NA,
  curvefeats = NA,
  dualfit = FALSE,
  interc = FALSE,
  verbose = TRUE,
  epsilon = 1e-04,
  cost = 512,
  lowb = 1e-05,
  highb = 0.99999,
  type = 0,
  maketimes = FALSE,
  bias = 0,
  maxitv = 100,
  factrv = 1e+12,
  nosolve = FALSE,
  autoKC = rep(0, length(components)),
  autoKCcont = rep("NA", length(components)),
  connectors = rep("+", max(1, length(components) - 1)),
  distribution = "exp",
  weibull_mse_weight = 0,
  weibull_t0_fixed = NULL,
  model = LibLinearModel(),
  model_options = list()
)

Arguments

data	Data frame or data table containing one row per trial. Must include Anon.Student.Id, CF..ansbin., and every component column named in components. Some features also require timing columns such as CF..Time., CF..reltime., or Duration..sec..
usefolds	Numeric vector of fold values to use for fitting. Features are still computed over all rows so held-out rows can be evaluated later. NA fits on all rows.
components	Character vector naming component columns or component specifications used to build feature histories.
features	Character vector of LKT feature names, parallel to components.
fixedpars	Numeric vector of nonlinear feature parameters. Use NA entries to optimize corresponding parameters.
seedpars	Numeric vector of starting values for nonlinear parameter optimization. NA uses default starts.
interacts	Optional vector of interaction terms added to component feature terms. Use NA for no interaction.
curvefeats	Optional vector of columns used by legacy difficulty curve features.
dualfit	Logical; if TRUE, also fit a response-time model. Requires Duration..sec..
interc	Logical; if TRUE, include a global intercept.
verbose	Logical; if TRUE, print progress and fit diagnostics.
epsilon	Numeric stopping tolerance passed to LiblineaR.
cost	Numeric regularization cost passed to LiblineaR.
lowb	Lower bound for nonlinear parameter optimization.
highb	Upper bound for nonlinear parameter optimization.
type	Integer LiblineaR solver type.
maketimes	Logical; if TRUE, create missing time columns from Duration..sec. where possible.
bias	Numeric bias term passed to LiblineaR.
maxitv	Maximum iteration count for nonlinear optimization.
factrv	Factr control value passed to optim() for nonlinear optimization.
nosolve	Logical; if TRUE, return the constructed sparse design data instead of fitting a model. This is a legacy public interface used by LASSO search helpers.
autoKC	Integer vector controlling automatic KC clustering. 0 disables clustering for the corresponding component; positive values are cluster counts.
autoKCcont	Character vector controlling automatic KC randomization. Use "rand" to randomize cluster assignment for comparison runs.
connectors	Character vector of formula operators ("+", ":", or "*") between model terms. Defaults to additive terms.
distribution	Latency model distribution. Supported values are "exp" and "Weibull" when dualfit = TRUE.
weibull_mse_weight	Numeric weight in ⁠[0, 1]⁠ for the point-prediction component of Weibull latency fitting.
weibull_t0_fixed	Optional fixed minimum response time, in seconds, for Weibull latency fitting.
model	LKT model adapter. Defaults to LibLinearModel().
model_options	Optional list of adapter-specific model options.

Value

A list containing the fitted model, coefficients, predictions, fit statistics, processed data, feature metadata, and optional latency-model results. With nosolve = TRUE, returns the constructed sparse matrices and feature names for downstream legacy model-selection helpers.

Examples

data(samplelkt)
fit <- LKT(
  data = samplelkt,
  components = "KC..Default.",
  features = "intercept",
  interc = TRUE,
  verbose = FALSE
)
head(fit$prediction)

---

Estimate coefficient HDIs by bootstrap resampling

Description

Fits a full LKT model and repeated student-level bootstrap samples, then summarizes coefficient intervals with HDInterval. This helper is computation-heavy and is retained as a legacy public interpretation aid.

Usage

LKT_HDI(
  dat,
  n_boot,
  n_students,
  comps,
  feats,
  conns = rep("+", max(1, length(comps) - 1)),
  ints = NA,
  fixeds,
  get_hdi = TRUE,
  cred_mass = 0.95
)

Arguments

dat	Data frame or data table containing trial data for LKT().
n_boot	Number of bootstrap subsamples to fit.
n_students	Number of students per bootstrap subsample.
comps	Character vector of components passed to LKT().
feats	Character vector of features passed to LKT().
conns	Character vector of formula connectors passed to LKT().
ints	Optional interactions passed to LKT().
fixeds	Fixed nonlinear parameters passed to LKT().
get_hdi	Logical compatibility argument. The current implementation always returns coef_hdi.
cred_mass	Credibility mass used for HDI width.

Value

A list containing bootstrap coefficient replicates (par_reps), the full-data model (mod_full), and coefficient intervals (coef_hdi).

Examples

data(samplelkt)
hdi_result <- LKT_HDI(
  samplelkt,
  n_boot = 2,
  n_students = 2,
  comps = "KC..Default.",
  feats = "intercept",
  fixeds = numeric(0)
)
names(hdi_result)

---

Define a custom LKT model

Description

Creates a model adapter that can be passed to LKT(model = ...). Model fit functions receive one argument named request and may also accept verbose. The request contains the shared feature input (formula, data, response, feature_spec, and sparse design matrices) plus fit controls such as usefolds and model options.

Usage

LKTCustomModel(name, fit)

Arguments

name	Single model name used in returned LKT objects and errors.
fit	Function with signature like ⁠function(request, verbose = FALSE)⁠.

Value

A model adapter suitable for LKT(model = ...).

Examples

adapter <- LKTCustomModel(
  "constant",
  function(request, verbose = FALSE) {
    LKTModelFit(
      model = list(name = "constant"),
      pred = rep(0.5, length(request$response))
    )
  }
)
inherits(adapter, "LKTModel")

---

Create model-agnostic LKT feature input

Description

Builds the shared input consumed by LKT models. The feature input contains the fitted formula, processed data, response vector, feature specification, sparse design matrices, and design-matrix column names.

Usage

LKTFeatureInput(formula, data, feature_spec, terms_cache = NULL)

Arguments

formula	Model formula after LKT feature construction.
data	Processed trial-level data used for fitting.
feature_spec	Per-feature metadata collected during feature construction.
terms_cache	Optional environment used to cache formula terms.

Value

An LKT feature input object consumed by model adapters.

Examples

data(samplelkt)
data.table::setDT(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
input <- LKTFeatureInput(
  CF..ansbin. ~ KC..Default.,
  samplelkt,
  feature_spec = data.frame(feature = "intercept", component = "KC..Default.")
)
input$column_names

---

Create an LKT model fit result

Description

Standardizes the fit-result object returned by LKT model adapters. model and pred are required. pred must be one finite probability per row in the shared feature input, strictly between 0 and 1. If modelvs, fitstat, or predictor matrices are omitted, LKT fills common defaults where possible.

Usage

LKTModelFit(
  model,
  pred,
  modelvs = NULL,
  fitstat = NULL,
  predictset = NULL,
  predictset2 = NULL
)

Arguments

model	Fitted model object.
pred	Numeric probability vector, one value per input row.
modelvs	Optional coefficient matrix/data frame with a coefficient column.
fitstat	Optional log likelihood or comparable fit statistic.
predictset	Optional sparse model matrix.
predictset2	Optional CSR model matrix used by existing LKT outputs.

Value

A model fit-result list.

Examples

fit_result <- LKTModelFit(
  model = list(name = "constant"),
  pred = c(0.5, 0.5)
)
names(fit_result)

---

Evaluate online simple-adaptive decay learning

Description

Replays the online simple-adaptive model while adapting the recency decay parameter within subject using d <- d - alpha_decay * error.

Usage

LKTOnlineSimpleAdaptiveDecayEval(
  par,
  input,
  clip_epsilon = 1e-06,
  denom_epsilon = 1e-06,
  decay_lower = 1e-05,
  decay_upper = 0.99999,
  return_details = FALSE,
  require_native = FALSE
)

Arguments

par	Numeric vector: intercept, recency beta, logsuc beta, logitdec beta, recency alpha, logsuc alpha, and recency-decay alpha.
input	Output from LKTOnlineSimpleAdaptiveInput().
clip_epsilon	Probability clipping value.
denom_epsilon	Denominator stabilizer for beta updates.
decay_lower	Lower bound for the within-subject recency decay state.
decay_upper	Upper bound for the within-subject recency decay state.
return_details	Logical; return predictions and final subject states.
require_native	Logical; stop if the compiled native evaluator is not loaded.

Value

Negative log likelihood, or details when requested.

---

Evaluate the fast online simple-adaptive objective

Description

Evaluate the fast online simple-adaptive objective

Usage

LKTOnlineSimpleAdaptiveEval(
  par,
  input,
  clip_epsilon = 1e-06,
  denom_epsilon = 1e-06,
  return_details = FALSE,
  require_native = FALSE
)

Arguments

par	Numeric vector: intercept, recency beta, logsuc beta, logitdec beta, recency alpha, logsuc alpha.
input	Output from LKTOnlineSimpleAdaptiveInput().
clip_epsilon	Probability clipping value.
denom_epsilon	Denominator stabilizer.
return_details	Logical; return predictions and final subject betas.
require_native	Logical; stop if the compiled native evaluator is not loaded.

Value

Negative log likelihood, or details when requested.

---

Gradient for the fast online simple-adaptive objective

Description

Gradient for the fast online simple-adaptive objective

Usage

LKTOnlineSimpleAdaptiveGradient(
  par,
  input,
  clip_epsilon = 1e-06,
  denom_epsilon = 1e-06,
  require_native = FALSE
)

Arguments

par	Numeric vector: intercept, recency beta, logsuc beta, logitdec beta, recency alpha, logsuc alpha.
input	Output from LKTOnlineSimpleAdaptiveInput().
clip_epsilon	Probability clipping value.
denom_epsilon	Denominator stabilizer.
require_native	Logical; stop if the compiled native evaluator is not loaded.

Value

Gradient of the negative log likelihood.

---

Fast online simple-adaptive objective input

Description

Builds compact numeric arrays for the fast compiled objective used by the simple-adaptive online recency/logsuc model.

Usage

LKTOnlineSimpleAdaptiveInput(
  modelob,
  data,
  subject_col = "Anon.Student.Id",
  response_col = "CF..ansbin.",
  recency_coef = "recencyKC..Default.",
  logsuc_coef = "logsucKC..Default.",
  logitdec_coef = "logitdecAnon.Student.Id",
  spacing_col = "KC..Default.spacing",
  recency_decay_start = NULL
)

Arguments

modelob	Fitted simple-adaptive LKT model with predictors and coefs.
data	Data used for the fit.
subject_col	Subject identifier column.
response_col	Binary response column.
recency_coef	Coefficient name for the recency feature.
logsuc_coef	Coefficient name for the log-success feature.
logitdec_coef	Coefficient name for the student logitdec feature.
spacing_col	Raw spacing column used to recompute recency when the recency decay parameter is adapted online.
recency_decay_start	Optional starting recency decay value. If NULL, the value is read from modelob$model_specification.

Value

A list of compact arrays and starting parameters.

---

Optimize the fast online simple-adaptive model

Description

Optimize the fast online simple-adaptive model

Usage

LKTOptimizeOnlineSimpleAdaptive(
  input,
  start = NULL,
  lower = c(-Inf, -Inf, -Inf, -Inf, 0, 0),
  upper = rep(Inf, 6),
  control = list(maxit = 100),
  require_native = FALSE,
  use_gradient = TRUE
)

Arguments

input	Output from LKTOnlineSimpleAdaptiveInput().
start	Optional six-parameter starting vector.
lower	Lower bounds for L-BFGS-B.
upper	Upper bounds for L-BFGS-B.
control	Optimizer control list.
require_native	Logical; stop if the compiled native evaluator is not loaded.
use_gradient	Logical; pass the propagated gradient to the optimizer.

Value

A list containing the optimizer result and fit details.

---

Optimize only the online learning rates

Description

Optimizes the recency and logsuc online learning rates while holding the global simple-adaptive coefficients fixed at their LibLinear optimum.

Usage

LKTOptimizeOnlineSimpleAdaptiveAlpha(
  input,
  start = c(alpha_recency = 0.03, alpha_logsuc = 0.05),
  lower = c(0, 0),
  upper = rep(Inf, 2),
  control = list(maxit = 100),
  require_native = FALSE,
  use_gradient = TRUE
)

Arguments

input	Output from LKTOnlineSimpleAdaptiveInput().
start	Optional two-parameter starting vector: recency alpha and logsuc alpha.
lower	Lower bounds for L-BFGS-B.
upper	Upper bounds for L-BFGS-B.
control	Optimizer control list.
require_native	Logical; stop if the compiled native evaluator is not loaded.
use_gradient	Logical; pass the propagated alpha gradient to the optimizer.

Value

A list containing the optimizer result and fit details.

---

Optimize online beta and decay learning rates

Description

Optimizes online learning rates while holding global coefficients and the global starting recency decay fixed.

Usage

LKTOptimizeOnlineSimpleAdaptiveDecayAlpha(
  input,
  start = c(alpha_recency = 0.03, alpha_logsuc = 0.05, alpha_decay = 0.01),
  lower = c(0, 0, 0),
  upper = rep(Inf, 3),
  control = list(maxit = 100),
  require_native = FALSE,
  use_gradient = FALSE,
  decay_lower = 1e-05,
  decay_upper = 0.99999
)

Arguments

input	Output from LKTOnlineSimpleAdaptiveInput().
start	Starting vector for recency beta alpha, logsuc beta alpha, and recency-decay alpha.
lower	Lower bounds for L-BFGS-B.
upper	Upper bounds for L-BFGS-B.
control	Optimizer control list.
require_native	Logical; stop if the compiled native evaluator is not loaded.
use_gradient	Reserved for future analytic-gradient support.
decay_lower	Lower bound for the within-subject recency decay state.
decay_upper	Upper bound for the within-subject recency decay state.

Value

A list containing the optimizer result and fit details.

---

Define the online adaptive LKT model

Description

Creates an LKT model adapter that first fits the standard LibLinear model, then applies an online parameter-adaptation layer.

Usage

OnlineAdaptiveModel(
  alpha_recency_start = 0.03,
  alpha_logsuc_start = 0.05,
  alpha_decay_start = 0.01,
  online_mode = "alpha_only",
  beta_alpha_terms = NULL,
  nonlinear_alpha_terms = character(0),
  alpha_start = NULL,
  alpha_lower = -1,
  alpha_upper = 1,
  nonlinear_lower = 1e-05,
  nonlinear_upper = 0.99999,
  maxit = 100,
  factr = 1e+07,
  optim_trace = 0,
  optim_report = 1,
  require_native = FALSE,
  use_gradient = TRUE
)

FastOnlineSimpleAdaptiveModel(
  alpha_recency_start = 0.03,
  alpha_logsuc_start = 0.05,
  alpha_decay_start = 0.01,
  online_mode = "alpha_only",
  beta_alpha_terms = NULL,
  nonlinear_alpha_terms = character(0),
  alpha_start = NULL,
  alpha_lower = -1,
  alpha_upper = 1,
  nonlinear_lower = 1e-05,
  nonlinear_upper = 0.99999,
  maxit = 100,
  factr = 1e+07,
  optim_trace = 0,
  optim_report = 1,
  require_native = FALSE,
  use_gradient = TRUE
)

Arguments

alpha_recency_start	Starting value for the recency learning rate.
alpha_logsuc_start	Starting value for the logsuc learning rate.
alpha_decay_start	Legacy starting value for the recency decay learning rate.
online_mode	Online optimizer mode. "alpha_only" uses the generalized adaptive alpha layer. "six_parameter" and "decay_alpha" retain the named historical model behaviors.
beta_alpha_terms	Coefficient names whose beta values are updated online.
nonlinear_alpha_terms	Nonlinear parameter keys formatted as feature|component|slot.
alpha_start	Optional numeric starting vector for selected beta and nonlinear learning rates.
alpha_lower	Scalar or vector lower bounds for learning-rate optimization.
alpha_upper	Scalar or vector upper bounds for learning-rate optimization.
nonlinear_lower	Lower clamp for online nonlinear parameter states.
nonlinear_upper	Upper clamp for online nonlinear parameter states.
maxit	Maximum optimizer iterations.
factr	Optimizer factr control value.
optim_trace	Optimizer trace level passed to stats::optim().
optim_report	Optimizer reporting interval passed to stats::optim().
require_native	Logical; stop if the compiled native evaluator is not loaded.
use_gradient	Logical; pass the propagated gradient to the optimizer.

Value

A model adapter suitable for LKT(model = ...).

---

Define the online calibration LKT model

Description

Creates an LKT model adapter that first solves global feature weights with the standard static LKT/LibLinear model, then uses those weights as the starting beta vector for every subject. Within each subject, the full beta vector is updated online after each observed response: beta[j, t + 1] = beta[j, t] + alpha * x[j, t] * (y[t] - p[t]) / (x[j, t]^2 + denom_epsilon) for each online-updated coefficient j. With alpha = 0, this model reproduces the static global-beta predictions.

Usage

OnlineCalibrationModel(
  alpha_start = 0,
  alpha_lower = 0,
  alpha_upper = 10,
  beta_start = "liblinear",
  beta_lower = -Inf,
  beta_upper = Inf,
  optimize_alpha = TRUE,
  optimize_beta = FALSE,
  clip_epsilon = 1e-06,
  denom_epsilon = clip_epsilon,
  subject_col = "Anon.Student.Id",
  fixed_online_coefficients = c("(Intercept)", "intercept"),
  update_strategy = c("all", "best_loss"),
  maxit = 100,
  factr = 1e+07
)

Arguments

alpha_start	Initial learning-rate value.
alpha_lower	Lower bound for the learning rate.
alpha_upper	Upper bound for the learning rate.
beta_start	Initial value for feature weights. Use "liblinear" to initialize from the standard static LKT fit. Numeric scalars are recycled.
beta_lower	Lower bound for feature weights. A scalar is recycled.
beta_upper	Upper bound for feature weights. A scalar is recycled.
optimize_alpha	Logical; optimize the learning rate when TRUE.
optimize_beta	Reserved for future joint optimization of the initial beta vector. The implemented model solves the initial beta vector globally before optimizing alpha.
clip_epsilon	Probability clipping value used before log likelihoods.
denom_epsilon	Small denominator stabilizer for online updates.
subject_col	Subject identifier column used for within-subject updates.
fixed_online_coefficients	Coefficients that remain fixed during within-subject online updates. By default, the global intercept is kept fixed when present.
update_strategy	Online update rule. "all" updates every eligible active coefficient on the trial. "best_loss" tries each eligible one-coefficient update and applies only the update that most reduces that trial's immediate logistic loss.
maxit	Maximum optimizer iterations.
factr	Optimizer factr control value.

Value

A model adapter suitable for LKT(model = ...).

Examples

adapter <- OnlineCalibrationModel(maxit = 5)
adapter$name

---

Predict with an LKT model object

Description

Generates predicted probabilities from a fitted LKT() object and, optionally, computes common evaluation statistics for selected folds.

Usage

predict_lkt(
  modelob,
  data,
  fold = NULL,
  return_stats = FALSE,
  min_pred_limit = 1e-05,
  max_pred_limit = 0.99999
)

Arguments

modelob	Fitted LKT model object containing coefficients and predictors.
data	Data frame or data table containing CF..ansbin. and, when fold filtering is requested, a fold column.
fold	Optional vector of fold values to include in the returned predictions and statistics. NULL or an empty vector uses all rows.
return_stats	Logical; if TRUE, return predictions plus log-likelihood, AUC, RMSE, and McFadden-style R-squared. If FALSE, return only predictions.
min_pred_limit	Minimum probability used to clamp predictions.
max_pred_limit	Maximum probability used to clamp predictions.

Value

If return_stats is FALSE, returns a list containing:

• predictions: The predicted probabilities for each observation in the specified fold(s).

If return_stats is TRUE, returns a list containing:

• predictions: The predicted probabilities for each observation in the specified fold(s).

• LL: Log-Likelihood of the model given the actual outcomes.

• AUC: Area Under the ROC Curve.

• RMSE: Root Mean Squared Error.

• R2: R-squared value, indicating the proportion of variance explained by the model.

Examples

data(samplelkt)
samplelkt$CF..ansbin. <- as.integer(samplelkt$Outcome == "CORRECT")
model <- LKT(
  data = samplelkt,
  components = "KC..Default.",
  features = "intercept",
  interc = TRUE,
  verbose = FALSE
)
preds <- predict_lkt(model, samplelkt)
head(preds$predictions)

---

Sample practice trial sequences

Description

A small trial-level dataset from a practice memory experiment.

Usage

samplelkt

Format

A data frame with 2074 rows and many variables:

Anon.Student.Id

unique identifier for each student

Duration..sec.

response duration in seconds

KC..Default.

default knowledge component label

Outcome

trial outcome label

Source

https://pslcdatashop.web.cmu.edu/DatasetInfo?datasetId=5508

---

Sample a subset of students

Description

Legacy exported helper that samples up to nSub students and returns all of their rows. It is retained because LKT_HDI() and older examples use it.

Usage

smallSet(data, nSub)

Arguments

data	Data frame or data table containing Anon.Student.Id.
nSub	Number of students to sample.

Value

A data frame containing all rows for the sampled students.

Examples

data(samplelkt)
subset_data <- smallSet(samplelkt, 2)
length(unique(subset_data$Anon.Student.Id))

---

Open a data frame in the system spreadsheet viewer

Description

Legacy exported convenience helper that writes a data frame to a temporary CSV file and opens it with the operating system's default application where supported. It is intended for interactive use, not package automation.

Usage

ViewExcel(df = .Last.value, file = tempfile(fileext = ".csv"))

Arguments

df	Data frame to write. Defaults to .Last.value.
file	File path for the temporary CSV output.

Value

The value returned by the operating-system file opener.

Examples

## Not run: 
ViewExcel(head(samplelkt))

## End(Not run)

---