BadLM shiny app

Description

Launches the BadLM shiny app, a tool to explore the consequences of the violation of homoscedasticity and/or normality assumptions in a linear model

Usage

BadLM(dist.custom = NULL, dist.custom.veravar = NULL, dist.custom.param = NULL)

Arguments

Details

Allows to set a data generating mechanism for a response variable Y and an explanatory variable x such that E(Y|X=x)=\beta_1+\beta_2 x, various possible distributions for Y are available, depending on the selected distributional assumptions the variance may also be set as a function of x. The program performs a number of simulations from the fit and visualizes the simulated sampling distributions of the estimators.

The user can also decide the distribution of the explanatory variable x: the shape is chosen by the user, then the variable is standardized to have minimum equal to 0 and maximum equal to x^*<1, also chosen by the user (the purpose of this is to explore the out of sample prediction performance of the estimated model). The observations x_1,\ldots,x_n are simulated only once, and kept fixed as appropriate for a regression model which is conditional on the explanatory variable.

Additional data generating mechanisms may be specified by the user and given as an input to the function calling the shiny app (see examples).

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
BadLM()

# function to generate Y
dist=function(n,my,parvet,par,x) {
  my+parvet*rt(n,df=par[1])
}
# function to give the true value of the variance
varfun=function(my,parvet,par,x){
  if (par[1]>2) {
    veravar=parvet^2*par[1]/(par[1]-2)
  } else {
    veravar=-1
  }
  return(veravar)
}
# dist and varfun must have those argument where
#  my is the vector mean of Y
#  parvet is g() computed at x values
#  par is a vector of two parameters
param=list(nome="Student-t (bis)", #name of dist for drop down menu (optional)
           nomepar1="Gradi di libertà", #name of parameter 1 (optional)
           minpar1=1,maxpar1=30, #min/max of param 1 (needed)
           valuepar1=10, #initial value of param1 (optional)
           steppar1=0.1, #increment of param1 (optional)
           enableVarFunPanel=TRUE #whether the panel to input g should appear
)

BadLM(dist.custom=dist,dist.custom.veravar = varfun,dist.custom.param=param)


dist=function(n,my,parvet,par,x) {
 my+rnorm(n,0,sqrt(par[1]+par[2]*x^2))
}
# function to give the true value of the variance
varfun=function(my,parvet,par,x){
 return(par[1]+par[2]*x^2)
}
# dist and varfun must have those argument where
#  my is the vector mean of Y
#  parvet is g() computed at x values
#  par is a vector of two parameters
param=list(nome="N(.,b1+b2*x^2)", #name of dist for drop down menu (optional)
           nomepar1="b1", #name of parameter 1 (optional)
           minpar1=1,maxpar1=3, #min/max of param 1 (needed)
           valuepar1=1, #initial value of param1 (optional)
           steppar1=0.1, #increment of param1 (optional)
           nomepar2="b2", #name of parameter 1 (optional)
           minpar2=0,maxpar2=3, #min/max of param 1 (needed)
           valuepar2=1, #initial value of param1 (optional)
           steppar2=0.1, #increment of param1 (optional)
           enableVarFunPanel=FALSE, #whether the panel to input g should appear
           showVarFun=TRUE
)

  BadLM(dist.custom=dist,dist.custom.veravar = varfun,dist.custom.param=param)
}
## End(Not run)

Collin shiny app

Description

Launches the Collinearity shiny app, a tool to explore the consequences of collinearity on sampling distributions and inferential procedures in linear models

Usage

Collin()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 Collin()
 }
## End(Not run)

Computer player decision

Description

Decides whether a fitted lm objects residuals are such that a violation of the assumptions of non linearity, heteroscedasticity, non normality occurs

Usage

ComputerDecision.default(fit)

Arguments

Details

The computer answer is determined by a sequence of tests. In particular, a test for non linearity is performed (if the sample size is greater than 30 the program tests for the significance of a non linear regression on the residuals versus x, otherwise Ramsey's RESET test is performed), if the null hypothesis is rejected the computer answer will be non linearity, if not, the Breusch-Pagan test for heteroscedasticity is performed, if the null hypothesis is rejected the computer answer will be heteroscedasticity, otherwise the Shapiro-Wilks test of normality is performed and the answer will be non normality if the null hypothesis is rejected; if no test is significant the answer will be ‘no violation’. (Functions to perform the tests are from the package lmtest.)

Value

An integer between 1 and 4 where 1=non linearity; 2=heteroscedasticity; 3=non normality; 4=no violation

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

See Also

Simulation.default, checksim

Examples

x=rnorm(10)
y=x+rnorm(10,0,0.4)
fit=lm(y~x)
ComputerDecision.default(fit)

x=rnorm(30)
y=x+rt(30,2)
fit=lm(y~x)
ComputerDecision.default(fit)

ConfInt shiny app

Description

Launches the ConfInt shiny app, a tool to explore confidence intervals and regions for the coefficient of simple linear model

Usage

ConfInt()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 ConfInt()
 }
## End(Not run)

GuessTheLine shiny app

Description

Launches the GuessTheLine shiny app, the user is prompted to guess the least squares fit of a sample of random points

Usage

GuessTheLine()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 GuessTheLine()
 }
## End(Not run)

GuessThePoints shiny app

Description

Launches the GuessThePoints shiny app, the user is prompted to guess a sample of points compatible with a set of parameters.

Usage

GuessThePoints()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 GuessThePoints()
 }
## End(Not run)

LMBoard shiny app

Description

Launches the LMBoard shiny app, user can add remove points and visualize changes in the estimates and residual plots

Usage

LMBoard()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 LMBoard()
 }
## End(Not run)

MultipleLM shiny app

Description

Launches the MultipleLM shiny app, a tool where the user can specify a multiple linearmodel, simulate from it and explore the sampling distribution of estimators under various conditions

Usage

MultipleLM()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 MultipleLM()
 }
## End(Not run)

Prediction shiny app

Description

Launches the Prediction shiny app, a tool to explore confidence and prediction intervals for the conditional mean in a simple linear model

Usage

Prediction()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 Prediction()
 }
## End(Not run)

QuizResidual shiny app

Description

Launches the QuizResidual shiny app

Usage

QuizResidual(
  ComputerDecision = ComputerDecision.default,
  Simulation = Simulation.default,
  dir.images = NULL,
  dir.sounds = NULL
)

Arguments

Details

QuizResidual shiny app is a game in which the player is asked to guess, based on four standard diagnostic plots of a linear model, whether there is a violation of one of the basic assumptions: linearity, homoscedasticity, normality of errors.

The program will simulate a sample (x,Y) from a randomly chosen data generating mechanism possibly violating one of the assumptions (function Simulation.default), fit a linear model and plot the diagnostic.

The computer player makes a guess on whether there is a violation of assumptions (function ComputerDecision.default).

After the answer is given, the true data generating mechanism will be shown in the plot, in particular, the true regression function, the true standard deviation of errors and the true density of errors.

The game can be customized by coding your own Simulation and ComputerDecision functions passing them as arguments.

Sounds will be played depending on whether the correct or wrong answer is given and a final sound is played depending on the outcome, also an appropriate image is shown. (Sounds are taken from the site https://freesound.org/, images from https://wpclipart.com and are public domain, other sounds and images can be used by calling the app with the directories where the images are stored as argument, sounds must be named as follows: suonorr: sound to be played when both the player and the computer give the correct answer; suonowr: sound to be played when the player is correct and the computer is wrong; suonorw and suonoww are analogous; suonofinaleP/V/S: final sound to play in case of tie/win/loss; immagineP/V/S: image to be shown in case of tie/win/loss.)

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

See Also

ComputerDecision.default, Simulation.default

Examples

## Not run:
if (interactive()){
  QuizResidual()
  # if custom sounds and images are in the directory www in the working directory
  QuizResidual(dir.images=paste0(getwd(),"/www"),dir.sounds=paste0(getwd(),"/www"))
}
## End(Not run)

SampleDist shiny app

Description

Launches the SampleDist shiny app, a tool to explore sampling variability of the linear model and the sampling distributions of the least squares estimators

Usage

SampleDist()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 SampleDist()
 }
## End(Not run)

SimpleLM shiny app

Description

Launches the SimpleLM shiny app, which allows to input the parameters of a linear model and simulate from it, exploring the various diagnostics and sampling distributions

Usage

SimpleLM()

Details

Full help is available from within the shiny app.

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 SimpleLM()
 }
## End(Not run)

Simulates a sample

Description

Simulates an (x,y) sample (suitable for estimating a lm) which can be either non linear/heteroscedastic/non normal or in line with standard lm assumptions

Usage

Simulation.default(model.to.sim)

Arguments

Details

The sample size is simulated between 10 and 1000 according to a uniform distribution. The explanatory variable is simulated as uniform, Gaussian, chi.square, t or a mixture of normal distributions. If non linearity or heteroscedasticity is chosen a random regression function or variance function is defined, if non normality is chosen the (always additive) error is simulated from a chi.square, t, Beta or truncated normal.#'

Value

A list of objects (of which the first two are essential, the following are needed to display the correct solution in the shiny app)

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

See Also

ComputerDecision.default, checksim

Examples

Simulation.default(1)

Simulation.default(sample(1:4,1))

SlopeTest shiny app

Description

Launches the SlopeTest shiny app, a tool to illustrate hypotheses testing on the slope in a simple regression model

Usage

SlopeTest()

Details

Full help is available from within the shiny app.

Value

None

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

Examples

## Not run:
if (interactive()){
 SlopeTest()
 }
## End(Not run)

Test the computer player performance

Description

Assesses (by simulation) the performance of an algorithm for detecting non linearity/heteroscedasticity/non normality (ComputerDecision.default) on data generated by the function Simulation (Simulation.default).

Usage

checksim(
  m,
  ComputerDecision = ComputerDecision.default,
  Simulation = Simulation.default
)

Arguments

Value

Author(s)

Francesco Pauli, francesco.pauli@deams.units.it

See Also

ComputerDecision.default,Simulation.default

Examples

checksim(10)

lmviz: A package to visualize linear models features and play with them.

Description

The lmviz package contains a suite of shyny apps

SimpleLM

allows to input the parameters of a simple linear model and simulate from it, exploring the various diagnostics and sampling distributions

SampleDist

allows to input the parameters of a linear model and simulate from it, exploring the sampling distributions of the estimators of the coefficients

ConfInt

allows to input the parameters of a simple linear model and simulate from it, illustrating confidence intervals and regions for the coefficients

SlopeTest

allows to input the parameters of a simple linear model, simulate from it and repeatedly perform hypotheses testing on the slope, exploring repeated sampling properties

Prediction

allows to input the parameters of a simple linear model and simulate from it illustrating confidence and prediction intervals for E(Y|X=x)

MultipleLM

allows to input the parameters of a multiple linear model with two covariates and simulate from it, exploring the sampling distributions of the estimators of the coefficients

Collin

allows to input the parameters of a multiple linear model with two covariates and simulate from it, exploring the consequences of collinearity on sampling distributions and inferential procedures

LMBoard

the user can draw (the points of) a scatter diagram, the corresponding linear regression model is estimated

BadLM

allows to set a data generating mechanism violating the homoscedasticity and/or normality assumptions of the linear model and explore by simulation its consequences on inference

QuizResidual

a game in which the user is prompted to guess whether the diagnostic plots of a linear model suggest some hypotheses is violated

GuessTheLine

a game in which the user is shown a (random) scatter diagram and must guess the least squares line

GuessThePoints

a game in which the user must draw a scatter diagram compatible with a series of statistics