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Artificial Intelligence Basics
Published in Subasish Das, Artificial Intelligence in Highway Safety, 2023
Note that a better model is linked to a larger log-likelihood. Subsequently, a lower AIC value is typically associated with a better model. If one assumes the noise to be a zero-mean normal random variable, then for regression models estimating the AIC is direct. The noise variance, and thus the model’s log-likelihood, is given by estimation of the mean-squared error. Two points are important to watch; first, k, the total number of parameters that are predicted to fit the model (e.g., in a linear regression model, wherein one models y as xTβ + ξ to estimate β̂ and the variance of ξ (in order to get the log-likelihood), d parameters need to be estimated; k = d + 1 in this situation). Second, typically log-likelihood is known only up to a constant, thus, various constants are frequently used by different software, which can be tremendously confusing. Bayes’ information criterion (BIC) is an alternate measure, which can be written as: 2klogN−2L
Model Selection
Published in Prabhanjan Narayanachar Tattar, H. J. Vaman, Survival Analysis, 2022
Prabhanjan Narayanachar Tattar, H. J. Vaman
The genesis of AIC is in information theory and it was invented by Hirotugu Akaike, Akaike (1973)[5]. A statistical model is used to represent the process that is believed to generate the data. There will be loss of information in the representation and the AIC tries to capture the relative loss of information. Thus, the lesser the value of AIC of a model, the more parsimonious it is for applications. By adding the number of parameters, 2k in Equation 7.1, we are penalizing the model where more parameters are used. Thus, if the number of parameters increases and the new variables are useful in explaining the variance of the lifetimes, it is vital that it results in significant decrease in the loss of information as captured by −2logL(θ^,data).
Generalized Regression Penalty against Complexity
Published in Chong Ho Alex Yu, Data Mining and Exploration, 2022
The original Akaike’s information criterion (MC), developed by Hirotsugu Akaike (1973), is in alignment with the philosophy of Ockham’s razor: Given all things being equal, the simplest model tends to be the best one; and simplicity is a function of the number of adjustable parameters. Thus, a smaller AIC suggests a better model. Specifically, AIC is a fitness index for trading off the complexity of a model against how well the model fits the data. The general form of AIC is: AIC =2k – 2lnL where k is the number of parameters and L is the likelihood function of the estimated parameters. Increasing the number of free parameters to be estimated improves the model fitness; however, the model might be unnecessarily complex. To reach a balance between fitness and parsimony, AIC not only rewards goodness of fit, but also includes a penalty that is an increasing function of the number of estimated parameters. This penalty discourages over-fitting and complexity. Hence, the best model is the one with the lowest AIC value. Since MC attempts to find the model that best explains the data with a minimum of free parameters, it is considered an approach favoring simplicity In this sense, AIC is better than R and adjusted R, which always go up as additional variables enter in the model. Needless to say, the traditional approach favors complexity However, AIC does not necessarily change by adding variables. Rather, it varies based upon the composition of the predictors, and thus it is a better indicator of the model quality (Faraway 2005).
Crossing conflict models for urban un-signalized T-intersections in India
Published in Transportation Letters, 2023
Jaydip Goyani, Ninad Gore, Shriniwas Arkatkar
Scaled deviance, scaled Pearson chi-square, Akaike’s Information Criteria (AIC), and Bayesian Information Criteria (BIC), frequently used goodness-of-fit metrics. The maximum likelihood estimation technique determined all models’ scale or dispersion parameters. The scaled deviance and Pearson chi-square values for the developed models are close to the total degree of freedom (df), and as a result, the developed models can be regarded as having a good fit. The AIC and BIC criteria also determine the model’s fit quality. The AIC can be considered a measure of how well an estimated statistical model fits the data. BIC is one way to choose a model from a group of parametric models with various numbers of parameters. Generally, for the acceptance of any model, the BIC value should be higher than the AIC criteria. In light of this, the present study developed models using 75% of the data. The model summary and corresponding goodness-of-fit measures are presented in Table 4. It is observed that both CV and OV significantly influence the number of crossing conflicts (CC and NCC). The number of CC and NCC increases with the OV. Further, the number of CC increases with the CV. This can be attributed to the average gap in the traffic stream decreasing at higher volumes. As a result, drivers maneuver the intersection while accepting smaller gaps. CC increase due to smaller accepted gap values. The PET value is very low for the smaller accepted gap.
Exploring the spatial differences in travel mode choice of rail transit in Chongqing
Published in Transportation Planning and Technology, 2023
Lixun Liu, Adam Dennett, Robin Hickman
In order to reduce problems when data in regions are distributed unevenly, this study adopts a spatially varying weighting method to calibrate the weighting matrix. It involves a bi-square weighting function which is related to the Nth nearest neighbours of point . The weighting function determines the weight of each data point up to the Nth, and all data points beyond the Nth are set to zero. Therefore, the bandwidth is adaptive to include the same number of data points (N) at each regression point. The Akaike information criterion (AIC) is a measure of the relative quality of a statistical model for a given set of data. AIC provides a means for model selection. A corrected AIC (referred to as ) takes into account the different number of degrees of freedom in different models, so that their relative performances can be compared more accurately. A model with a lower than another is held to be a better fit of the data.
Parametric modelling of a wire electrical discharge machining process using path analysis approach
Published in International Journal of Modelling and Simulation, 2022
Baneswar Sarker, Shankar Chakraborty
As mentioned earlier, the metric chosen to compare the model performance is AIC. It favours models with lower bias and larger log-likelihood values. In other words, AIC chooses a model, which is the best-fit with the data and has the least number of path parameters, thus examining both overfitting and underfitting of the model [25]. A lower value of AIC for a model indicates a better model fit. In this case, model IV is identified to be the best model with the lowest AIC value. Model II is the second best model to appropriately represent the WEDM process, followed by models III and I, according to their appropriateness. While comparing the two models that consider GC as an intermediate parameter influencing the other two responses (i.e. models III and IV), it can be observed that the TLI value for model IV is less than that of model III. As mentioned earlier, the ideal value of TLI is equal to 1. Thus, the lower AIC value of model IV compared to model III implies that model III suffers from overfitting more than model IV. Thus, the AIC value suggests that model IV has the most balanced trade-off between bias and log-likelihood. Hence, the model, which does not include WF as a process parameter and discards the causal relationship between GC and SR in its analysis, can be considered as the most appropriate path analysis-based model to illustrate the relationships between the process parameters and responses of the considered WEDM process.