Factors influencing SMEs CloudERP adoption: A test with generalized linear model and artificial neural network

This article present data concerning the factors influencing small and medium-sized enterprises (SMEs) intention to use/adopt CloudERP system in Jordan. Generalized Linear Modeling (GLM) and Artificial Neural Network (ANN) modeling techniques in R version 1.0.136 were used to analyze data obtained from 394 SMEs. Computer self-efficacy, organizational support, perceived usefulness, perceived ease of use, facilitating conditions, security and relative advantage have significant influence on the intention to use/adoption CloudERP systems. The survey data-set is made publicly available to amplify further inquiry.

Training of neural networks using the backpropagation, resilient backpropagation with (Riedmiller, 1994) or without weight backtracking (Riedmiller, 1993) or the modified globally convergent version by Anastasiadis et al. (2005). The package allows flexible settings through custom-choice of error and activation function. Furthermore, the calculation of generalized weights (Intrator O & Intrator N, 1993) is implemented.

Note
This work has been supported by the German Research Foundation (DFG: http://www.dfg.de) under grant scheme PI 345/3-1.

See Also
plot.nn for plotting of the neural network.
gwplot for plotting of the generalized weights.
compute for computation of the calculated network.
confidence.interval for calculation of a confidence interval for the weights.
prediction for calculation of a prediction.

Arguments
x an object of class nn. covariate a dataframe or matrix containing the variables that had been used to train the neural network. rep an integer indicating the neural network's repetition which should be used.
Value compute returns a list containing the following components: neurons a list of the neurons' output for each layer of the neural network. net.result a matrix containing the overall result of the neural network.

confidence.interval
Calculates confidence intervals of the weights Description confidence.interval, a method for objects of class nn, typically produced by neuralnet. Calculates confidence intervals of the weights (White, 1989) and the network information criteria NIC (Murata et al. 1994). All confidence intervals are calculated under the assumption of a local identification of the given neural network. If this assumption is violated, the results will not be reasonable. Please make also sure that the chosen error function equals the negative log-likelihood function, otherwise the results are not meaningfull, too. Value confidence.interval returns a list containing the following components: lower.ci a list containing the lower confidence bounds of all weights of the neural network differentiated by the repetitions.
upper.ci a list containing the upper confidence bounds of all weights of the neural network differentiated by the repetitions.
nic a vector containg the information criteria NIC for every repetition.

Arguments
x an object of class nn rep an integer indicating the repetition to plot. If rep="best", the repetition with the smallest error will be plotted. If not stated all repetitions will be plotted. max maximum of the y axis. In default, max is set to the highest y-value. min minimum of the y axis. In default, min is set to the smallest y-value. file a character string naming the plot to write to. If not stated, the plot will not be saved. selected.covariate either a string of the covariate's name or an integer of the ordered covariates, indicating the reference covariate in the generalized weights plot. Defaulting to the first covariate. selected.response either a string of the response variable's name or an integer of the ordered response variables, indicating the reference response in the generalized weights plot. Defaulting to the first response variable. highlight a logical value, indicating whether to highlight (red color) the best repetition (smallest error). Only reasonable if rep=NULL. Default is FALSE type a character indicating the type of plotting; actually any of the types as in plot.default. col a color of the generalized weights. ...
Arguments to be passed to methods, such as graphical parameters (see par).

Training of neural networks
Description neuralnet is used to train neural networks using backpropagation, resilient backpropagation (RPROP) with (Riedmiller, 1994) or without weight backtracking (Riedmiller and Braun, 1993) or the modified globally convergent version (GRPROP) by Anastasiadis et al. (2005). The function allows flexible settings through custom-choice of error and activation function. Furthermore the calculation of generalized weights (Intrator O. and Intrator N., 1993) is implemented.
Usage neuralnet(formula, data, hidden = 1, threshold = 0.01, stepmax = 1e+05, rep = 1, startweights = NULL, learningrate.limit = NULL, learningrate.factor = list(minus = 0.5, plus = 1.2), learningrate=NULL, lifesign = "none", lifesign.step = 1000, algorithm = "rprop+", err.fct = "sse", act.fct = "logistic", linear.output = TRUE, exclude = NULL, constant.weights = NULL, likelihood = FALSE) Arguments formula a symbolic description of the model to be fitted. data a data frame containing the variables specified in formula. hidden a vector of integers specifying the number of hidden neurons (vertices) in each layer. threshold a numeric value specifying the threshold for the partial derivatives of the error function as stopping criteria. stepmax the maximum steps for the training of the neural network. Reaching this maximum leads to a stop of the neural network's training process. rep the number of repetitions for the neural network's training.
startweights a vector containing starting values for the weights. The weights will not be randomly initialized. learningrate.limit a vector or a list containing the lowest and highest limit for the learning rate. Used only for RPROP and GRPROP. learningrate.factor a vector or a list containing the multiplication factors for the upper and lower learning rate. Used only for RPROP and GRPROP. learningrate a numeric value specifying the learning rate used by traditional backpropagation. Used only for traditional backpropagation. lifesign a string specifying how much the function will print during the calculation of the neural network. 'none', 'minimal' or 'full'. lifesign.step an integer specifying the stepsize to print the minimal threshold in full lifesign mode. algorithm a string containing the algorithm type to calculate the neural network. The following types are possible: 'backprop', 'rprop+', 'rprop-', 'sag', or 'slr'. 'backprop' refers to backpropagation, 'rprop+' and 'rprop-' refer to the resilient backpropagation with and without weight backtracking, while 'sag' and 'slr' induce the usage of the modified globally convergent algorithm (grprop). See Details for more information. err.fct a differentiable function that is used for the calculation of the error. Alternatively, the strings 'sse' and 'ce' which stand for the sum of squared errors and the cross-entropy can be used. act.fct a differentiable function that is used for smoothing the result of the cross product of the covariate or neurons and the weights. Additionally the strings, 'logistic' and 'tanh' are possible for the logistic function and tangent hyperbolicus. linear.output logical. If act.fct should not be applied to the output neurons set linear output to TRUE, otherwise to FALSE. exclude a vector or a matrix specifying the weights, that are excluded from the calculation. If given as a vector, the exact positions of the weights must be known. A matrix with n-rows and 3 columns will exclude n weights, where the first column stands for the layer, the second column for the input neuron and the third column for the output neuron of the weight. constant.weights a vector specifying the values of the weights that are excluded from the training process and treated as fix. likelihood logical. If the error function is equal to the negative log-likelihood function, the information criteria AIC and BIC will be calculated. Furthermore the usage of confidence.interval is meaningfull.

Details
The globally convergent algorithm is based on the resilient backpropagation without weight backtracking and additionally modifies one learning rate, either the learningrate associated with the smallest absolute gradient (sag) or the smallest learningrate (slr) itself. The learning rates in the grprop algorithm are limited to the boundaries defined in learningrate.limit.

Value
neuralnet returns an object of class nn. An object of class nn is a list containing at most the following components: call the matched call.
response extracted from the data argument.
covariate the variables extracted from the data argument.
model.list a list containing the covariates and the response variables extracted from the formula argument.
err.fct the error function.
act.fct the activation function.
data the data argument.
net.result a list containing the overall result of the neural network for every repetition.
weights a list containing the fitted weights of the neural network for every repetition.
generalized.weights a list containing the generalized weights of the neural network for every repetition. result.matrix a matrix containing the reached threshold, needed steps, error, AIC and BIC (if computed) and weights for every repetition. Each column represents one repetition.
startweights a list containing the startweights of the neural network for every repetition.

See Also
plot.nn for plotting the neural network.
gwplot for plotting the generalized weights.
compute for computation of a given neural network for given covariate vectors.
confidence.interval for calculation of confidence intervals of the weights.
prediction for a summary of the output of the neural network.

Arguments
x an object of class nn rep repetition of the neural network. If rep="best", the repetition with the smallest error will be plotted. If not stated all repetitions will be plotted, each in a separate window.
x.entry x-coordinate of the entry layer. Depends on the arrow.length in default. x.out x-coordinate of the output layer. radius radius of the neurons. arrow.length length of the entry and out arrows. intercept a logical value indicating whether to plot the intercept. intercept.factor x-position factor of the intercept. The closer the factor is to 0, the closer the intercept is to its left neuron. information a logical value indicating whether to add the error and steps to the plot. information.pos y-position of the information. col.entry.synapse color of the synapses leading to the input neurons. col.entry color of the input neurons. col.hidden color of the neurons in the hidden layer. col.hidden.synapse color of the weighted synapses. col.out color of the output neurons. col.out.synapse color of the synapses leading away from the output neurons. col.intercept color of the intercept.

fontsize
fontsize of the text. dimension size of the plot in inches. show.weights a logical value indicating whether to print the calculated weights above the synapses. file a character string naming the plot to write to. If not stated, the plot will not be saved. ...
arguments to be passed to methods, such as graphical parameters (see par).

See Also
neuralnet Examples XOR <-c(0,1,1,0) xor.data <-data.frame(expand.grid(c(0,1), c(0,1)), XOR) print(net.xor <-neuralnet( XOR~Var1+Var2, xor.data, hidden=2, rep=5)) plot(net.xor, rep="best") prediction prediction Summarizes the output of the neural network, the data and the fitted values of glm objects (if available) Description prediction, a method for objects of class nn, typically produced by neuralnet. In a first step, the dataframe will be amended by a mean response, the mean of all responses corresponding to the same covariate-vector. The calculated data.error is the error function between the original response and the new mean response. In a second step, all duplicate rows will be erased to get a quick overview of the data. To obtain an overview of the results of the neural network and the glm objects, the covariate matrix will be bound to the output of the neural network and the fitted values of the glm object(if available) and will be reduced by all duplicate rows.