GGM {DIMORA}

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)

• Zanghi Federico: [e-mail]

  • https://www.linkedin.com/in/federico-zanghi-75512b165/

  • https://github.com/federicozanghi

• Savio Andrea: [e-mail]

  • https://www.linkedin.com/in/andrea-savio-51861b191/

• Ziliotto Filippo: [e-mail]

  • https://www.linkedin.com/in/FilippoZiliottoDev/

• Bessi Alessandro: [e-mail]

  • https://www.linkedin.com/in/alessandro-bessi-419812194/

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)