Package 'DIMORA'

Title: Diffusion Models R Analysis
Description: The implemented methods are: Standard Bass model, Generalized Bass model (with rectangular shock, exponential shock, and mixed shock. You can choose to add from 1 to 3 shocks), Guseo-Guidolin model and Variable Potential Market model, and UCRCD model. The Bass model consists of a simple differential equation that describes the process of how new products get adopted in a population, the Generalized Bass model is a generalization of the Bass model in which there is a "carrier" function x(t) that allows to change the speed of time sliding. In some real processes the reachable potential of the resource available in a temporal instant may appear to be not constant over time, because of this we use Variable Potential Market model, in which the Guseo-Guidolin has a particular specification for the market function. The UCRCD model (Unbalanced Competition and Regime Change Diachronic) is a diffusion model used to capture the dynamics of the competitive or collaborative transition.
Authors: Zanghi Federico, Savio Andrea, Filippo Ziliotto, Bessi Alessandro
Maintainer: Savio Andrea <[email protected]>
License: GPL (>= 3)
Version: 0.3.6
Built: 2025-02-24 04:33:32 UTC
Source: https://github.com/cran/DIMORA

Help Index

Standard Bass model

Description

Function that estimates the standard Bass model. Fitted values for cumulative and instantaneous data are displayed (if display = T). Out-of-sample prediction is performed based on estimated parameters.

Usage

BM(series, method = "nls", prelimestimates = c(sum(series) + 100, 0.01, 0.1),
   oos = round(length(series)*0.25), alpha = 0.05 ,display = T)

Arguments

series

the instantaneous observed data.
method

the estimation method, 'nlm' or 'optim' (see Details).
prelimestimates

a vector containing the starting values used by the algorithm to estimate the parameters. If no values are specified, the default ones are:

  • market potential: m=∑t(series)+100m = \sum_{t}(series)+100;

  • innovation coefficient: p=0.01p = 0.01;

  • imitation coefficient: q=0.1q = 0.1.

alpha

the significance level for the confidence intervals.
oos

positive integer value: number of predictions after the last observed one. Default setting to 25% of the length of the data.
display

if TRUE returns the fitted values for cumulative and instantaneous observed data. If 'oos' is specified, it also returns the predicted fit values.

Details

The optim method provides only the parameter estimates. It does not provide the standard error and the p-value estimates.

Value

BM returns an object of class "Dimora".

The function summary is used to obtain and print a summary table of the results. The generic accessor functions coefficients, fitted and residuals extract various useful features of the value returned by BM.

An object of class "Dimora" is a list containing at least the following components:

model

the model formula used.
type

the model frame used.
Estimate

a summary table of estimates.
coefficients

a named vector of coefficients.
Rsquared

the statistical measure R-squared.
RSS

the residual sum of squares.
residuals

the residuals (observed cumulative data - fitted cumulative data).
fitted

the cumulative fitted values.
data

the cumulative observed series.
call

the matched call.

Author(s)

References

Guidolin, M. (2023). Innovation Diffusion Models: Theory and Practice, First Edition. John Wiley & Sons Ltd.

Bass, F.M. (1969). A new product growth for model consumer durables. Management science, 15 (5), 215-227.

See Also

The Dimora models: GBM, GGM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
iphone <- DBdimora$iPhone[7:52]

## Example 1
M1 <- BM(iphone)
summary(M1)
plot.Dimora(M1)
plot.Dimora(M1, oos=25)
# 25 predictions


## Example 2
M2 <- BM(iphone, prelimestimates = c(2000, 0.001, 0.1), method = "optim", oos = 100)
summary(M2)

Database DIMORA

Description

New DIMORA dataset which refers to the examples reported on the help files of the functions.

Details

The database contains six time series with the relative time variables: sales units sold for Apple iPhone and iMac, and the annual consumption, in Exajoule, of Denmark gas and renewables and Australian coal and renewables.

Author(s)

See Also

The Dimora models: BM, GBM, GGM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

DIMORA Package

Description

The main functions of the package are BM, GBM, GGM, and UCRCD. See the full documentation for more details. At the end of this page there are links to the functions.

Note 1: the names of the model functions have been changed! BM refers to the previous BASS.standard, GMB to the BASS.generalized, and GGM to the GG.model.

Note 2: the SARMAX.refinement has been deleted from the previous version. Function Arima() of the forecast library works to implement the SARMAX refinement.

Note 3: there is a new DIMORA dataset (DBdimora) which refers to the examples reported on the help files of the functions.

Author(s)

See Also

The Dimora models: BM, GBM, GGM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Generalized Bass model

Description

Function that estimates the Generalized Bass model with Exponential, Rectangular, or Mixed shock. Fitted values for cumulative and instantaneous data are displayed (if display = T). Out-of-sample prediction is performed based on estimated parameters.

Usage

GBM(series, shock = c("exp", "rett", "mixed"), nshock,
                    prelimestimates, alpha = 0.05,
                    oos = round(length(series)*0.25), display = T)

Arguments

series

the instantaneous observed data.
shock

the parameters which define the shocks. The available options are:

  • "exp" = Exponential;

  • "rett" = Rectangular;

  • "mixed" = Mixed (only when nshock = 2).
nshock

the number of shocks (from 1 to 3).
prelimestimates

a vector containing the preliminary estimates of the parameters (see Details and Examples).
alpha

the significance level for confidence intervals.
oos

positive integer value: number of predictions after the last observed one. Default setting to 25% of the length of the data.
display

if TRUE returns the fitted values for cumulative and instantaneous observed data. If 'oos' is specified, it also returns the predicted fit values.

Details

Each type of shock is characterized by specific parameters.

The analyst has to set both the preliminary estimates of the parameters m, p, q and the ones related to the shock(s) a, b, c. The parameters related to each shock have to be defined as follows:

  • Exponential:

    • a = starting time of the shock

    • b = memory of the effect (typically negative, suggesting an exponentially decaying behavior)

    • c = intensity of the shock (may be either positive or negative)

    In case of more than one shock, preliminary estimates need to be specified as follows: prelimestimates = c(m, p, q, a1, b1, c1, a2, b2, c2, a3, b3, c3)

  • Rectangular:

    • a = starting time of the shock

    • b = ending time of the shock

    • c = intensity of the shock (may be either positive or negative)

    In case of more than one shock, preliminary estimates need to be specified as follows: prelimestimates = c(m, p, q, a1, b1, c1, a2, b2, c2, a3, b3, c3)

  • Mixed: when the series has one exponential and one rectangular shock (you always have to specify the exponential shock before the rectangular one, even if the exponential one occurs later)

    • a1 = starting time of the exponential shock

    • b1 = memory of the effect (typically negative, suggesting an exponentially decaying behavior)

    • c1 = intensity of the exponential shock (may be either positive or negative)

    • a2 = starting time of the rectangular shock

    • b2 = ending time of the rectangular shock

    • c2 = intensity of the rectangular shock (may be either positive or negative)

Value

GBM returns an object of class "Dimora".

The function summary is used to obtain and print a summary table of the results. The generic accessor functions coefficients, fitted and residuals extract various useful features of the value returned by GBM.

An object of class "Dimora" is a list containing at least the following components:

model

the model formula used.
type

the model frame used.
Estimate

a summary table of estimates.
coefficients

a named vector of coefficients.
Rsquared

the statistical measure R-squared.
RSS

the residual sum of squares.
residuals

the residuals (observed cumulative data - fitted cumulative data).
fitted

the cumulative fitted values.
data

the cumulative observed series.
call

the matched call.

Author(s)

References

Guidolin, M. (2023). Innovation Diffusion Models: Theory and Practice, First Edition. John Wiley & Sons Ltd.

Bass, F.M., Krishnan, T.V., & Jain, D.C. (1994). Why the Bass model fits without decision variables. Marketing science, 13 (3), 203-223.

See Also

The Dimora models: BM, GGM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
iphone<- DBdimora$iPhone[7:52]
imac<- DBdimora$iMac[1:52]

## Example 1: exponential shock
M3 <- GBM(iphone, shock = "exp", nshock = 1,
          prelimestimates = c(BM(iphone, display=FALSE)$Estimate[1,1],
                              BM(iphone, display=FALSE)$Estimate[2,1],
                              BM(iphone, display=FALSE)$Estimate[3,1],
                              17,-0.1,0.1))
summary(M3)
plot.Dimora(M3, oos=25)
# 25 predictions

## Example 2: rectangular shock
M4 <- GBM(imac,shock = "rett",nshock = 1,
           prelimestimates = c(BM(imac, display=FALSE)$Estimate[1,1],
                               BM(imac, display=FALSE)$Estimate[2,1],
                               BM(imac, display=FALSE)$Estimate[3,1],
                               20,30,0.1), oos=20)
summary(M4)

## Example 3: mixed shock
## The prelimestimates of m, p, q are their relative values estimated through M4.

M5 <- GBM(imac,shock = "mixed",nshock = 2,
           prelimestimates = c(M4$Estimate[1,1],
                               M4$Estimate[2,1],
                               M4$Estimate[3,1],
                               6,-0.1,0.1, 20,30,0.1), oos=0)
summary(M5)

Guseo-Guidolin model

Description

Function that estimates the dynamic market potential model. Fitted values for cumulative and instantaneous data are displayed (if display = T). Out-of-sample prediction is performed based on estimated parameters. Function m(t) is defined, as default, as the standard Guseo-Guidolin model, but it can also be defined as a general function with some constraints (see Details and exmaples).

Usage

GGM(series, prelimestimates = NULL, mt = 'base', alpha = 0.05,
       oos = round(length(series)*0.25), display = T)

Arguments

series

the instantaneous observed data.
prelimestimates

a vector containing the preliminary estimates of the parameters (see Details and Examples).
mt

function that define the dynamic market potential.
alpha

the significance level for the confidence intervals.
oos

positive integer value: number of predictions after the last observed one. Default setting to 25% of the length of the data.
display

if TRUE returns the fitted values for cumulative and instantaneous observed data. If 'oos' is specified, it also returns the predicted fit values.

Details

The GGM function allows to define the parameter m(t) in two ways:

  • use the standard GGM model. Note: define the prelimestimates = c(K, qc, pc, qs, ps) (see Example 1 below).

  • define function m(t) according to modeling needs. Note: function m(t) must be positive and is essential a c.d.f.; default values for prelimestimates are based on the BM function (see Example 2 below).

Value

GGM returns an object of class "Dimora". The function summary is used to obtain and print a summary table of the results. The generic accessor functions coefficients, fitted and residuals extract various useful features of the value returned by GGM.

An object of class "Dimora" is a list containing at least the following components:

model

the model formula used.
type

the model frame used.
Estimate

a summary table of estimates.
coefficients

a named vector of coefficients.
Rsquared

the statistical measure R-squared.
RSS

the residual sum of squares.
residuals

the residuals (observed cumulative data - fitted cumulative data).
fitted

the cumulative fitted values.
data

the cumulative observed series.
call

the matched call.

Author(s)

References

Guidolin, M. (2023). Innovation Diffusion Models: Theory and Practice, First Edition. John Wiley & Sons Ltd.

Guseo, R., & Guidolin, M. (2009). Modelling a dynamic market potential: A class of automata networks for diffusion of innovations. Technological Forecasting and Social Change, 76(6), 806-820.

See Also

The Dimora models: BM, GBM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
iphone <- DBdimora$iPhone[7:52]

## Example 1
M6 <- GGM(iphone, prelimestimates=c(1823, 0.001, 0.1, 0.001, 0.1), oos=100)
# 1823 refers to the estimated parameter m of the standard Bass model on iphone
summary(M6)
plot.Dimora(M6, oos=25)
# 25 predictions

## Example 2
M7 <- GGM(iphone, mt = function(x) pchisq(x,10))
summary(M7)

Function that transforms your data

Description

Function that transforms cumulative data into instantaneous; this function can be useful because all the model functions in this package require the istantaneous data as input.

Usage

make.instantaneous(cumulate.data)

Arguments

cumulate.data

the cumulative data.

Author(s)

See Also

The Dimora models: BM, GBM, GGM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

Examples

cumulate.data = c(1,2,3,6,12)
data.inst = make.instantaneous(cumulate.data)

Plot method for Dimora models

Description

Plot method for the DIMORA package models.

Usage

## S3 method for class 'Dimora'
plot(x,..., type = c('all','res','fit'), oos = 0)

Arguments

x

an object of class Dimora.
type

specifies the type of plot. Default setting is 'all':

  • 'fit' returns the cumulative and instantaneous fit of the model;

  • 'res' returns the 'Residuals VS Time' graphic and the ACF of the residuals of the model;

  • 'all' returns the two types before combined in an unique graphical window.
oos

positive integer value: number of predictions after the last observed one. If specified, it also determines the xlim for the plots. It only works for univariate models.
...

other graphics parameters.

Author(s)

See Also

The Dimora models: BM, GBM, GGM, UCRCD.

summary.Dimora for summaries.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
iphone <- DBdimora$iPhone[7:52]
Gd <- DBdimora$Gdenmark[1:36]
Rd <- DBdimora$Rdenmark[13:36]

## Plot with univariate model
M1 <- BM(iphone,display = FALSE)
plot.Dimora(M1,type='all',oos = 20)

## Plot with multivariate model
M8 <- UCRCD(Gd,Rd)
plot.Dimora(M8,type='fit')

Predict method for Dimora objects

Description

Prediction of test data using any model of the package.

Usage

## S3 method for class 'Dimora'
predict(object, ..., newx)

Arguments

object

an object of class Dimora, as that created by BM, GBM or GGM.
newx

a number or a vector of numeric values rapresenting the time window (see Example below).
...

additional arguments affecting the predictions produced.

Details

It works only for univariate models; specifically, for the models BM, GBM, GGM, it returns a vector of the cumulative predicted values.

Value

The method returns a vector of predicted values.

Author(s)

See Also

The Dimora models: BM, GBM, GGM, UCRCD.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
iphone <- DBdimora$iPhone[7:52]
M1 <- BM(iphone)

# Predict the values of the observed series (lenght(iphone)=46)
predict.Dimora(M1, newx = c(1:46))


# Predict the values of the observed series and other 34 future values
predict.Dimora(M1, newx = c(1:80))

Summary method for Dimora objects

Description

Summary method for the Dimora objects.

Usage

## S3 method for class 'Dimora'
summary(object,...)

Arguments

object

an object of class Dimora, as that created by BM, GBM, GGM or UCRCD.
...

additional arguments affecting the summary produced.

Value

summary is a generic function used to produce summaries of the results of various model fitting functions. The function invokes particular methods which depend on the class of the first argument; in this case, the class is Dimora.

Author(s)

See Also

The Dimora models: BM, GBM, GGM, UCRCD.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
iphone <- DBdimora$iPhone[7:52]

M1 <- BM(iphone)
summary(M1)

UCRCD model

Description

Function that estimates the Unbalanced Competition Regime Change Diachronic model. Fitted values for cumulative and instantaneous data are displayed (if display = T).

Usage

UCRCD(series1, series2, display=T, alpha=0.05,
      delta=0.01, gamma=0.01, par="double",
      m1  = BM(series1,display = F)$Estimate[1,1],
      m2  = BM(series2,display = F)$Estimate[1,1],
      p1c = BM(series1,display = F)$Estimate[2,1],
      q1c = BM(series1,display = F)$Estimate[3,1],
      p2  = BM(series2,display = F)$Estimate[2,1],
      q2  = BM(series2,display = F)$Estimate[3,1])

Arguments

series1

the istantaneous observed data of the first product.
series2

the istantaneous observed data of the second product.
alpha

the significance level for confidence intervals.
par

default is 'double'. Instead 'unique', meaning the costraint delta equal to gamma has been selected.
display

if TRUE returns the predicted values for cumulative and instantaneous observed data.
delta

preliminary estimate of delta.
gamma

preliminary estimate of gamma.
m1

preliminary estimate of the first product's market potential under competition
m2

preliminary estimate of the second product's market potential

p1c

preliminary estimate of the first product's innovation coefficient under competition
p2

preliminary estimate of the second product's innovation coefficient
q1c

preliminary estimate of the first product's imitation coefficient under competition
q2

preliminary estimate of the second product's imitation coefficient

Details

The model estimates several parameters that refer both to the stand-alone phase and the competition phase. The description of the parameters is reported below: (wom = "Word Of Mouth")

  • ma : Market Potential 1 (stand-alone phase)

  • p1a : Innovation coefficient 1 (stand-alone phase)

  • q1a : Imitation coefficient 1 (stand-alone phase)

  • mc : Market Potential 1 (competition phase)

  • p1c : Innovation coefficient 1 (competition phase)

  • q1c+delta : Within-product wom 1 (competition phase)

  • q1c : Cross-product wom 1 (competition phase)

  • p2 : Innovation coefficient 2

  • q2 : Within-product wom 2

  • q2-gamma : Cross-product wom 2

Value

UCRCD returns an object of class "Dimora".

The function summary is used to obtain and print a summary table of the results. The generic accessor functions coefficients, fitted and residuals extract various useful features of the value returned by UCRCD.

An object of class "Dimora" is a list containing at least the following components:

model

the model formula used.
type

the model frame used.
Estimate

a summary table of estimates.
coefficients

a named vector of coefficients.
Rsquared

the statistical measure R-squared (on the istantaneous data).
RSS

the residual sum of squares (on the istantaneous data).
residuals

the residuals (observed cumulative data - fitted cumulative data).
fitted

the cumulative fitted values.
data

the cumlative observed data.
call

the matched call.

The UCRCD model is estimated on the instantaneous data. For this reason, the UCRCD function also returns the following elements:

data.i

the instantaneous observed data.
fitted.i

the instantaneous fitted values.
residuals.i

the residuals (observed instantaneous data - fitted instantaneous data).

Author(s)

References

Guidolin, M. (2023). Innovation Diffusion Models: Theory and Practice, First Edition. John Wiley & Sons Ltd.

Guseo, R., & Mortarino, C. (2014). Within-brand and cross-brand word-of-mouth for sequential multi-innovation diffusions. IMA Journal of Management Mathematics, 25(3), 287-311.

See Also

The Dimora models: BM, GBM, GGM.

summary.Dimora for summaries.

plot.Dimora for graphics and residuals analysis.

predict.Dimora for prediction.

make.instantaneous to create instantaneous series from the cumulative one.

Examples

data(DBdimora)
Gd <- DBdimora$Gdenmark[1:36]
Rd <- DBdimora$Rdenmark[13:36]
Ca <- DBdimora$Caustralia
Ra <- DBdimora$Raustralia[26:56]

## Example 1
M8 <- UCRCD(Gd,Rd)
summary(M8)
plot.Dimora(M8,type="fit")

## Example 2
M9 <- UCRCD(Ca,Ra,par = "unique",display=FALSE)
summary(M9)
plot.Dimora(M9)