BAQM: Babson Analytics and Quantitative Methods Tools

Description

Instructor-developed tools for Analytics and Quantitative Methods (AQM) courses at Babson College. Included are compact descriptive statistics for data frames and lists, expanded reporting and graphics for linear regressions, and formatted reports for best subsets analyses.

Author(s)

Maintainer: Peter Lert plert@babson.edu [copyright holder]

See Also

Useful links:

• https://github.com/CPA-wrk/BAQM

• https://cpa-wrk.github.io/BAQM/

• Report bugs at https://github.com/CPA-wrk/BAQM/issues

Create a Four-Panel Regression Assumptions Plot

Description

Generates a 4-panel diagnostic plot for a multiple regression model, including: 1) Fitted values vs. observed values (check for non-linearity), 2) Quantile–Quantile plot of residuals (check for non-normality), 3) Residuals vs. fitted values (check for heteroskedasticity), 4) Autocorrelation for time series otherwise influence plot (leverage also available).

Usage

lm_plot.4way(
  mdl,
  ...,
  is.ts = FALSE,
  pred.intvl = TRUE,
  pval.SW = FALSE,
  pval.BP = FALSE,
  pval.DW = FALSE,
  cook.loess = FALSE,
  rtn.all = FALSE,
  plt.nms = c("fit", "var", "qq", ifelse(is.ts, "ac", "infl")),
  parms = list()
)

Arguments

Details

This function is a high-level wrapper that calls internal plotting functions (lm_plot.fit, lm_plot.var, lm_plot.qq, and either lm_plot.ac or lm_plot.infl) and assembles their outputs into a combined plot_grid.

Value

A ggplot object representing the 4-way diagnostic panel. Optionally invisibly returns a list containing:

• p_4way – the combined plot,

• other elements passed through from the individual plot functions.

Examples

fit <- lm(mpg ~ wt + hp, data = mtcars)
lm_plot.4way(fit, is.ts = FALSE, pval.SW = TRUE)
fit <- lm(Employed ~ ., data = longley)
lm_plot.4way(fit, is.ts = TRUE, pval.DW = TRUE)

Plot Residuals vs. Observation Order (Autocorrelation Check)

Description

Creates a plot of residuals against the sequence/order of observations to visually assess independence and detect autocorrelation. Outliers are labeled by default. Optionally includes p-value result from the Durbin–Watson test for autocorrelation.

Usage

lm_plot.ac(
  mdl,
  ...,
  pval.DW = FALSE,
  parms = lm_plot.parms(mdl),
  df = lm_plot.df(mdl, parms = parms)
)

Arguments

Details

Points are colored and shaped according to whether they are residual outliers (as determined by Tukey's boxplot rule). The function can label points using ggrepel if parm$pts$id$outl or parm$pts$id$reg are set to TRUE.

Value

A ggplot object representing the residuals vs. order plot. Included as an attribute "parm" is a list containing:

• lim Plotted limits on x and y axes,

• pval.DW Option to show Durbin-Watson p-value,

• DW The htest object with Durbin-Watson test results.

See Also

dwtest, lm_plot.df, lm_plot.parms

Examples

fit <- lm(res ~ ., data = data.frame(time = time(austres), res = austres))
lm_plot.ac(fit, pval.DW = TRUE)

Augment Model Data for Diagnostic Plots

Description

Generates an augmented data frame from a linear model object, including fitted values, residuals, leverage, Cook's distance, prediction intervals, and outlier/influence flags. This function prepares model diagnostics for plotting.

Usage

lm_plot.df(mdl, parms = lm_plot.parms(mdl))

Arguments

Details

The returned data frame contains key statistics for each observation:

• .id: Observation identifier

• .sequence: Sequence index

• .obs: Observed values

• .fits: Fitted/predicted values

• .resid: Residuals

• .se.fit: Estimated standard error of fitted (mean) value

• .lower.pi: Lower bound on 95% prediction interval of fitted value

• .upper.pi: Upper bound on 95% prediction interval of fitted value

• .std.resid: Standardized residuals

• .stud.resid: Studentized residuals

• .cooksd: Cook's distance

• .hat: Leverage (diagonal of the hat matrix)

• .quantile: Theoretical normal quantile of residuals

• .is.outl: Flag for residual outlier ("outl" or "reg")

• .is.infl: Flag for influential point ("infl" or "outl" or "reg")

• .is.lev: Flag for high leverage point ("lev" or "infl" or "reg")

Value

A data frame with augmented diagnostic variables, one row per observation.

See Also

influence, influence.measures, rstandard, rstudent, outlier

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
df <- lm_plot.df(mdl)
head(df)

Plot Observed vs. Fitted Values to Check Linearity

Description

Generates a scatter plot of fitted values versus observed values from a linear model, with identification of outlier points and optional prediction interval. The plot includes a reference line y = x for assessing linearity.

Usage

lm_plot.fit(
  mdl,
  ...,
  pred.intvl = TRUE,
  parms = lm_plot.parms(mdl),
  df = lm_plot.df(mdl, parms = parms)
)

Arguments

Details

The plot visualizes fitted versus observed values, includes a diagonal reference line, marks outliers, and can optionally display prediction intervals. Outlier and regular points can be labeled. This plot is useful for visually assessing linearity and model fit quality.

Value

A ggplot object representing the fitted vs. observed plot. Included as an attribute "parm" is a list containing:

• lim Plotted limits on x and y axes,

• pred.intvl Option to show prediction interval,

See Also

lm_plot.df, lm_plot.parms

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
lm_plot.fit(mdl)

Plot Leverage vs. Fitted Values to Visualize Inflential Observations

Description

Creates a plot of leverage values versus the linear fitted values, including an identification of points with a large Cook's distance, to visualize high-leverage and influential observations.

Usage

lm_plot.infl(
  mdl,
  ...,
  parms = lm_plot.parms(mdl),
  df = lm_plot.df(mdl, parms = parms)
)

Arguments

Details

The plot visualizes the calculated leverage of individual data points, defined as the diagonal element of the 'hat' matrix, as a function of the fitted values and implicitly relative to their location in the field of predictor variables, and the threshold value of high leverage is indicated. In addition, Cook's distance can be used to label influential points, along with outlier and regular points.

Value

A ggplot object representing the comb plot of residuals vs sequence, indicating influential points. Included as an attribute "parms" is a list containing:

• lim Plotted limits on x and y axes.

See Also

lm_plot.df, lm_plot.parms, outlier

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
result <- lm_plot.infl(mdl)

Plot Standard Residuals vs. Leverage with Cook's Distance Contours

Description

Creates a plot of standard residuals versus leverage values, including Cook's distance contours to visualize influential observations.

Usage

lm_plot.lev(
  mdl,
  ...,
  cook.loess = FALSE,
  parms = lm_plot.parms(mdl),
  df = lm_plot.df(mdl, parms = parms)
)

Arguments

Details

The plot displays standardized residuals against leverage, overlays Cook's distance contours, and marks outliers based on residuals and Cook's distance. Outlier and influential points can be labeled, and a loess fit line is optionally added.

Value

A ggplot object representing the standardized residuals vs leverage plot. Included as an attribute "parms" is a list containing:

• lim Plotted limits on x and y axes,

• cook.loess Option to show loess curve for Cook's distances.

See Also

lm_plot.df, lm_plot.parms

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
lm_plot.lev(mdl)

Set or Retrieve Default Plot Parameters for Model Diagnostic Plots

Description

Initializes or updates a list of plot element parameters for use in model diagnostic plotting functions. If any required parameter is missing or invalid, a default value will be supplied.

Usage

lm_plot.parms(mdl, parms = list())

Arguments

Details

The returned list contains parameters for points (size, color, shape), lines (type, color, size), options for plot features, Cook's distance/Influence contours, and seed values for sampling functions. These are used by other lm_plot.* functions to control plot appearance and annotation. Key defaults include:

• pts: Properties for points (size, color, shape, outlier flags)

• lins: Properties for lines (type, color, size)

• cook: Cook's distance contour settings (points, levels, line type)

• infl: Influence line settings (line type)

See function code for full list of available settings and default values.

Value

A list of plot element parameters with defaults filled in for any missing or invalid entries.

See Also

lm_plot.fit, lm_plot.lev, lm_plot.infl outlier

Examples

# Retrieve default parameters
parms <- lm_plot.parms(mdl = lm(Sepal.Length ~ Sepal.Width, data = iris))
# Set custom color for regular points
parms <- lm_plot.parms(mdl = lm(Sepal.Length ~ Sepal.Width, data = iris),
                       parms = list(pts = list(colr = list(reg = "blue"))))

Q-Q Plot of Residuals to Assess Normality

Description

Produces a Q-Q plot of residuals from a linear model to test for normality, optionally annotating outlier points and adding the Shapiro-Wilk test p-value.

Usage

lm_plot.qq(
  mdl,
  ...,
  pval.SW = FALSE,
  parms = lm_plot.parms(mdl),
  df = lm_plot.df(mdl, parms = parms)
)

Arguments

Details

The plot visualizes the distribution of residuals against theoretical normal quantiles. Points are colored and shaped by outlier status, and a reference Q-Q line is added. Optionally, outlier and regular points can be labeled. If enabled, the Shapiro-Wilk normality test p-value is displayed.

Value

A ggplot object representing the quantile-quantile plot. Included as an attribute "parm" is a list containing:

• lim Plotted limits on x and y axes,

• pval.SW Option to show Shapiro-Wilk p-value,

• DW The htest object with Shapiro-Wilk test results.

See Also

lm_plot.df, lm_plot.parms, shapiro.test

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
lm_plot.qq(mdl)

Plot Residuals vs. Fitted Values to Assess Homoskedasticity

Description

Produces a scatter plot of residuals against fitted values from a linear model, highlighting outlier points and optionally displaying the Breusch-Pagan test p-value for heteroskedasticity.

Usage

lm_plot.var(
  mdl,
  ...,
  pval.BP = FALSE,
  parms = lm_plot.parms(mdl),
  df = lm_plot.df(mdl, parms = parms)
)

Arguments

Details

The plot visualizes residuals versus fitted values to assess homoskedasticity (constant variance). Points are colored and shaped by outlier status, and outlier/regular points can be labeled. The Breusch-Pagan test for heteroskedasticity is run and, if enabled, its p-value annotates the plot.

Value

A ggplot object representing the residuals versus fitted values plot. Included as an attribute "parms" is a list containing:

• lim Plotted limits on x and y axes,

• pval.BP Option to show Breusch-Pagan p-value,

• BP The htest object with Breusch-Pagan test results.

See Also

lm_plot.df, lm_plot.parms, bptest

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
lm_plot.var(mdl, pval.BP = TRUE)

Identify Outliers Using Boxplot Heuristic

Description

Detects outliers in a numeric vector using the boxplot heuristic (default, outside 1.5 times the IQR from the 1st and 3rd quartiles). Handles missing values (NA) automatically.

Usage

outlier(x, coef = 1.5, rpt = FALSE)

Arguments

Value

If rpt = FALSE, returns a logical vector indicating outliers. If rpt = TRUE, returns a numeric vector of length 2 giving lower and upper limits for outlier detection

Examples

set.seed(1)
vals <- c(rnorm(100), 10, -10)
outlier(vals)
outlier(vals, rpt = TRUE)

Print a sumry Summarization for Linear Model Objects

Description

Prints a comprehensive summary for objects of class summary.lm or lm, including model statistics, ANOVA table, coefficients, and optional tables (correlations, covariance, fits), followed by a five-number summary of residuals and the model call.

Usage

## S3 method for class 'sumry.lm'
print(
  x,
  ...,
  digits = max(5, getOption("digits") - 2),
  symbolic.cor = NULL,
  signif.stars = getOption("show.signif.stars"),
  options = NULL,
  na.print = "",
  eps = .Machine$double.eps
)

Arguments

Details

The function prints summary statistics, ANOVA, and coefficients tables for a linear model in order, along with specified optional tables if provided. It concludes with a five-number-plus-mean summary of residuals and the model call.

Value

Invisibly return the unmodified object included in the call.

See Also

sumry.lm, print.table.sumry.lm

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
sumry(mdl)
sumry(mdl, options = c("correlation", "fits"))

Print Method for Best Subset Selection (regsubsets) Objects

Description

Prints a summary for objects of class summary.regsubsets or regsubsets (from the leaps package), showing model selection statistics for best subsets, including R-squared, adjusted R-squared, standard error of estimate, Mallows' Cp, and AIC.

Usage

## S3 method for class 'sumry.regsubsets'
print(x, ...)

Arguments

Details

The function prints the model call and a table summarizing the best models selected, including the number of predictors, R-squared, adjusted R-squared, standard error of estimate (SEE), Mallows' Cp, and included variables. If the input is a regsubsets object, it is converted with sumry(). If not, the object is returned unmodified.

Value

Invisibly return the object printed.

See Also

regsubsets, sumry.regsubsets

Examples

fit <- leaps::regsubsets(Fertility ~ ., data = swiss, nbest = 3)
print(sumry(fit))

Print a Table from Linear Model Summary

Description

Prints a formatted table from a sumry of a linear model, including coefficients, ANOVA, correlation matrices, or summary statistics. Significance stars and legends are added as appropriate.

Usage

## S3 method for class 'table.sumry.lm'
print(
  x,
  ...,
  digits = max(4, getOption("digits") - 2),
  quote = FALSE,
  na.print = "",
  zero.print = "0",
  right = TRUE,
  justify = "right",
  signif.stars = getOption("show.signif.stars"),
  eps = .Machine$double.eps,
  nsmall = 4,
  prnt.lgnd = c("coefficients"),
  dig.test = max(1, min(5, digits - 2))
)

Arguments

Details

This method handles tabular output from linear model sumry.lm, including coefficients, ANOVA, statistics, and correlation/covariance matrices. It formats p-values, adds significance stars, and prints appropriate legends for hypothesis tests.

Value

Invisibly returns the input table.

See Also

print.sumry.lm

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width, data = iris)
sum_mdl <- sumry(mdl)
print(sum_mdl$coefficients)

Summary Descriptive Statistics for BAQM

Description

sumry is a generic function for the BAQM package used to produce summaries of the results of certain model fitting functions.

Usage

sumry(x, ...)

Arguments

Value

Invisibly returns a list of summary tables for each variable.

Examples

sumry(penguins)
sumry(data.frame(a = rnorm(100),
          b = c(NA, 1:98, NA),
          c = sample(letters[4:6], 100, TRUE)),
          transpose = TRUE, pad = 1)
sumry(lm(Sepal.Length ~ ., data = iris))
sumry(leaps::regsubsets(mpg ~ ., data = mtcars, nbest = 2))

Summary Descriptive Statistics for List or Data Frame

Description

Computes and prints summary descriptive statistics for each variable in a data frame, list, or vector including counts, numeric summaries (min, quartiles, mean, max, standard deviation), and factor summaries (levels and frequencies).

Usage

## Default S3 method:
sumry(
  x,
  ...,
  transpose = FALSE,
  pad = 2,
  maxsum = 10,
  opts = list(digits = 4, scipen = 2)
)

Arguments

Details

For each variable in x, the function computes the count of non-missing and missing values. Numeric variables are summarized by minimum, first quartile, median, mean, third quartile, maximum, and standard deviation. Factor, logical, and character variables are summarized by level frequencies, where level names may be abbreviated for readability. Results are formatted in a table and printed. The function returns a list containing numeric or factor summaries for each variable.

Value

Invisibly returns a list containing a summary data frame for each variable with no rounding. For example, smry <- sumry.df(df[c("A", "B", "C")]); smry$A$std.dev gives the standard deviation of variable A in data frame df

Examples

sumry(penguins)
sumry(data.frame(a = rnorm(100),
                 b = c(NA, 1:98, NA),
                 c = sample(letters[4:6], 100, TRUE)),
                 transpose = TRUE, pad = 1)

Method sumry to Summarize Linear Model (lm) Objects

Description

Computes a comprehensive summary for an object of class lm, including performance statistics, ANOVA, coefficients with VIFs, and correlation/covariance tables. Handles factor variable recoding and collinearity/singularity warnings.

Usage

## S3 method for class 'lm'
sumry(x, ...)

Arguments

Details

The returned sumry object includes:

• stats: Performance statistics (F-statistic, R-squared, RMSE, etc.)

• anova: Simplified ANOVA table (Sum of squares, mean squares, F-statistic, p-value)

• coefficients: Table of regression coefficients with standard errors, t-stats, p-values, and VIFs

• cov.unscaled, correlation: Covariance and correlation matrices for coefficients

• v.correlation: Variable correlation matrix (for models with interaction terms)

• fits: Observed, fitted, and residual values

• aliased: Logical vector indicating aliased coefficients

• df: Degrees of freedom

• sigma: Estimated standard deviation of residuals

• r.squared, adj.r.squared: R-squared and adjusted R-squared

• fstatistic, f.pval: F-statistic and p-value for overall regression

• notes: Warnings, singularity, and collinearity notes (attached as attribute)

Factor variable names are recoded for clarity, and coefficients for aliased or singular variables are omitted with notes produced as attributes.

Value

An object of class sumry.lm containing tables and statistics described above.

See Also

print.sumry.lm, lm

Examples

mdl <- lm(Sepal.Length ~ Sepal.Width + Petal.Length, data = iris)
sumry(mdl)

Summary for Subset Selection (regsubsets) Objects

Description

Generates a BAQM summary for objects of class regsubsets (from the leaps package), showing model selection statistics for best subsets, including R-squared, adjusted R-squared, standard error of estimate, Mallows' Cp, and AIC.

Usage

## S3 method for class 'regsubsets'
sumry(x, ...)

Arguments

Details

The function formats a table summarizing the best models selected, including the number of predictors, R-squared, adjusted R-squared, standard error of estimate (SEE), Mallows' Cp, and included variables. It is first converted to a summary.regsubsets with summary(). If not, the object is returned unmodified.

Value

Returns a matrix containing a summary table for the best subsets analysis. Each row summarizes a model showing: the number of predictors, k, used; "which best" that model is for that k; performance statistics (see above); and a series of columns with asterisks indicating the specific predictors included in the model.

See Also

regsubsets, print.sumry.regsubsets

Examples

fit <- leaps::regsubsets(Fertility ~ ., data = swiss, nbest = 3)
sumry(fit)