## discriminant function analysis in r

CV=TRUE generates jacknifed (i.e., leave one out) predictions. You can read more about the data behind this LDA example here. In this example, the categorical variable is called “class” and the predictive variables (which are numeric) are the other columns. The LDA algorithm uses this data to divide the space of predictor variables into regions. # Panels of histograms and overlayed density plots Because DISTANCE.CIRCULARITY has a high value along the first linear discriminant it positively correlates with this first dimension. Discriminant function analysis (DFA) is a statistical procedure that classifies unknown individuals and the probability of their classification into a certain group (such as sex or ancestry group). We often visualize this input data as a matrix, such as shown below, with each case being a row and each variable a column. diag(prop.table(ct, 1)) No significance tests are produced. The ideal is for all the cases to lie on the diagonal of this matrix (and so the diagonal is a deep color in terms of shading). If you prefer to gloss over this, please skip ahead. ct <- table(mydata$G, fit$class) Linear discriminant analysis is used when the variance-covariance matrix does not depend on the population. To practice improving predictions, try the Kaggle R Tutorial on Machine Learning, Copyright © 2017 Robert I. Kabacoff, Ph.D. | Sitemap. The model predicts that all cases within a region belong to the same category. So in our example here, the first dimension (the horizontal axis) distinguishes the cars (right) from the bus and van categories (left). The measurable features are sometimes called predictors or independent variables, while the classification group is the response or what is being predicted. Another commonly used option is logistic regression but there are differences between logistic regression and discriminant analysis. If you would like more detail, I suggest one of my favorite reads, Elements of Statistical Learning (section 4.3). The package I am going to use is called flipMultivariates (click on the link to get it). Title Tools of the Trade for Discriminant Analysis Version 0.1-29 Date 2013-11-14 Depends R (>= 2.15.0) Suggests MASS, FactoMineR Description Functions for Discriminant Analysis and Classiﬁcation purposes covering various methods such as descriptive, geometric, linear, quadratic, PLS, as well as qualitative discriminant analyses License GPL-3 The functiontries hard to detect if the within-class covariance matrix issingular. It has a value of almost zero along the second linear discriminant, hence is virtually uncorrelated with the second dimension. # DFA. Also shown are the correlations between the predictor variables and these new dimensions. LOGISTIC REGRESSION (LR): While logistic regression is very similar to discriminant function analysis, the primary question addressed by LR is “How likely is the case to belong to each group (DV)”. library(klaR) For example, a researcher may want to investigate which variables discriminate between fruits eaten by (1) primates, (2) birds, or (3) squirrels. I n MANOVA (we will cover this next) we ask if there are differences between groups on a combination of DVs. There is one panel for each group and they all appear lined up on the same graph. →! I will demonstrate Linear Discriminant Analysis by predicting the type of vehicle in an image. Reddit. However, to explain the scatterplot I am going to have to mention a few more points about the algorithm. An alternative view of linear discriminant analysis is that it projects the data into a space of (number of categories – 1) dimensions. 12th Aug, 2018. Consider the code below: I’ve set a few new arguments, which include; It is also possible to control treatment of missing variables with the missing argument (not shown in the code example above). Linear discriminant analysis (LDA), normal discriminant analysis (NDA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that characterizes or separates two or more classes of objects or events. Given the shades of red and the numbers that lie outside this diagonal (particularly with respect to the confusion between Opel and saab) this LDA model is far from perfect. It works with continuous and/or categorical predictor variables. )The Method tab contains the following UI controls: . Despite my unfamiliarity, I would hope to do a decent job if given a few examples of both. In the examples below, lower caseletters are numeric variables and upper case letters are categorical factors. # total percent correct For each case, you need to have a categorical variable to define the class and several predictor variables (which are numeric). This will make a 75/25 split of our data using the sample() function in R which is highly convenient. For each case, you need to have a categorical variableto define the class and several predictor variables (which are numeric). Displayr also makes Linear Discriminant Analysis and other machine learning tools available through menus, alleviating the need to write code. But here we are getting some misallocations (no model is ever perfect). Note the scatterplot scales the correlations to appear on the same scale as the means. (Note: I am no longer using all the predictor variables in the example below, for the sake of clarity). I used the flipMultivariates package (available on GitHub). Outline 2 Before Linear Algebra Probability Likelihood Ratio ROC ML/MAP Today Accuracy, Dimensions & Overfitting (DHS 3.7) Principal Component Analysis (DHS 3.8.1) Fisher Linear Discriminant/LDA (DHS 3.8.2) Other Component Analysis Algorithms Each employee is administered a battery of psychological test which include measuresof interest in outdoor activity, socia… plot(fit) # fit from lda. Although in practice this assumption may not be 100% true, if it is approximately valid then LDA can still perform well. My morphometric measurements are head length, eye diameter, snout length, and measurements from tail to each fin. Now that our data is ready, we can use the lda() function i R to make our analysis which is functionally identical to the lm() and glm() functions: The LDA model orders the dimensions in terms of how much separation each achieves (the first dimensions achieves the most separation, and so forth). Re-subsitution (using the same data to derive the functions and evaluate their prediction accuracy) is the default method unless CV=TRUE is specified. Preparing our data: Prepare our data for modeling 4. [R] discriminant function analysis; Mike Gibson. In this post, we will look at linear discriminant analysis (LDA) and quadratic discriminant analysis (QDA). fit <- lda(G ~ x1 + x2 + x3, data=mydata, The "proportion of trace" that is printed is the proportion of between-class variance that is explained by successive discriminant functions. Refer to the section on MANOVA for such tests. Think of each case as a point in N-dimensional space, where N is the number of predictor variables. library(MASS) Both LDA and QDA are used in situations in which … Each employee is administered a battery of psychological test which include measuresof interest in outdoor activity, sociability and conservativeness. # Scatterplot for 3 Group Problem Points are identified with the group ID. The dependent variable Yis discrete. – If the overall analysis is significant than most likely at least the first discrim function will be significant – Once the discrim functions are calculated each subject is given a discriminant function score, these scores are than used to calculate correlations between the entries and the discriminant … Discriminant analysis is also applicable in the case of more than two groups. Below I provide a visual of the first 50 examples classified by the predict.lda model. Discriminant function analysis makes the assumption that the sample is normally distributed for the trait. The probability of a sample belonging to class +1, i.e P(Y = +1) = p. Therefore, the probability of a sample belonging to class -1is 1-p. 2. LinkedIn. You can also produce a scatterplot matrix with color coding by group. plot(fit, dimen=1, type="both") # fit from lda. The previous block of code above produces the following scatterplot. Linear Discriminant Analysis (LDA) is a well-established machine learning technique for predicting categories. (See Figure 30.3. Hence the scatterplot shows the means of each category plotted in the first two dimensions of this space. The partimat( ) function in the klaR package can display the results of a linear or quadratic classifications 2 variables at a time. Classification method. How we can applicable DFA in R? In DFA we ask what combination of variables can be used to predict group membership (classification). Discriminant Analysis in R The data we are interested in is four measurements of two different species of flea beetles. specifies the method used to construct the discriminant function. How does Linear Discriminant Analysis work and how do you use it in R? My dataset contains variables of the classes factor and numeric. The code above performs an LDA, using listwise deletion of missing data. Finally, I will leave you with this chart to consider the model’s accuracy. The director ofHuman Resources wants to know if these three job classifications appeal to different personalitytypes. Twitter. Specifying the prior will affect the classification unlessover-ridden in predict.lda. Changing the output argument in the code above to Prediction-Accuracy Table produces the following: So from this, you can see what the model gets right and wrong (in terms of correctly predicting the class of vehicle). The columns are labeled by the variables, with the target outcome column called class. All measurements are in micrometers (\mu m μm) except for the elytra length which is in units of.01 mm. Linear discriminant analysis of the form discussed above has its roots in an approach developed by the famous statistician R.A. Fisher, who arrived at linear discriminants from a different perspective. Re-substitution will be overly optimistic. Linear Discriminant Analysis takes a data set of cases(also known as observations) as input. Even though my eyesight is far from perfect, I can normally tell the difference between a car, a van, and a bus. Only 36% accurate, terrible but ok for a demonstration of linear discriminant analysis. You can use the Method tab to set options in the analysis. DISCRIMINANT FUNCTION ANALYSIS Table of Contents Overview 6 Key Terms and Concepts 7 Variables 7 Discriminant functions 7 Pairwise group comparisons 8 Output statistics 8 Examples 9 SPSS user interface 9 The Nov 16, 2010 at 5:01 pm: My objective is to look at differences in two species of fish from morphometric measurements. The code below assesses the accuracy of the prediction. Then the model is created with the following two lines of code. You can plot each observation in the space of the first 2 linear discriminant functions using the following code. High values are shaded in blue ad low values in red, with values significant at the 5% level in bold. Linear Discriminant Analysis takes a data set of cases (also known as observations) as input. fit <- qda(G ~ x1 + x2 + x3 + x4, data=na.omit(mydata), We then converts our matrices to dataframes . As you can see, each year between 2001 to 2005 is a cluster of H3N2 strains separated by axis 1. specifies that a parametric method based on a multivariate normal distribution within each group be used to derive a linear or quadratic discriminant function. The options are Exclude cases with missing data (default), Error if missing data and Imputation (replace missing values with estimates). In the examples below, lower case letters are numeric variables and upper case letters are categorical factors. Most recent answer. Discriminant analysis is used to predict the probability of belonging to a given class (or category) based on one or multiple predictor variables. Each function takes as arguments the numeric predictor variables of a case. The LDA model looks at the score from each function and uses the highest score to allocate a case to a category (prediction). Discriminant Function Analysis. Example 2. We call these scoring functions the discriminant functions. I would like to perform a discriminant function analysis. An example of doing quadratic discriminant analysis in R.Thanks for watching!! R in Action (2nd ed) significantly expands upon this material. Thiscould result from poor scaling of the problem, but is morelikely to result from constant variables. However, the same dimension does not separate the cars well. There is Fisher’s (1936) classic example of discri… "Pattern Recognition and Scene Analysis", R. E. Duda and P. E. Hart, Wiley, 1973. The output is shown below. The director ofHuman Resources wants to know if these three job classifications appeal to different personalitytypes. Linear Discriminant Analysis is based on the following assumptions: 1. Unless prior probabilities are specified, each assumes proportional prior probabilities (i.e., prior probabilities are based on sample sizes). # Quadratic Discriminant Analysis with 3 groups applying The independent variable(s) Xcome from gaussian distributions. The first four columns show the means for each variable by category. It then scales each variable according to its category-specific coefficients and outputs a score. I might not distinguish a Saab 9000 from an Opel Manta though. Traditional canonical discriminant analysis is restricted to a one-way MANOVA design and is equivalent to canonical correlation analysis between a set of quantitative response variables and a set of dummy variables coded from the factor variable. The scatter() function is part of the ade4 package and plots results of a DAPC analysis.   prior=c(1,1,1)/3)). The R-Squared column shows the proportion of variance within each row that is explained by the categories. Since we only have two-functions or two-dimensions we can plot our model. The following code displays histograms and density plots for the observations in each group on the first linear discriminant dimension.    bg=c("red", "yellow", "blue")[unclass(mydata\$G)]). While this aspect of dimension reduction has some similarity to Principal Components Analysis (PCA), there is a difference. Quadratic discriminant function does not assume homogeneity of variance-covariance matrices. They are cars made around 30 years ago (I can’t remember!). partimat(G~x1+x2+x3,data=mydata,method="lda"). The regions are labeled by categories and have linear boundaries, hence the “L” in LDA. It is based on the MASS package, but extends it in the following ways: The package is installed with the following R code. This argument sets the prior probabilities of category membership. In this article we will assume that the dependent variable is binary and takes class values {+1, -1}. The model predicts the category of a new unseen case according to which region it lies in. So you can’t just read their values from the axis. pairs(mydata[c("x1","x2","x3")], main="My Title ", pch=22, Every point is labeled by its category. We often visualize this input data as a matrix, such as shown below, with each case being a row and each variable a column. library(MASS) The mean of the gaussian … lda() prints discriminant functions based on centered (not standardized) variables. Mathematically MANOVA … Discriminant Analysis (DA) is a multivariate classification technique that separates objects into two or more mutually exclusive groups based on measurable features of those objects. Bayesien Discriminant Functions Lesson 16 16-2 Notation x a variable X a random variable (unpredictable value) N The number of possible values for X (Can be infinite). Unlike in most statistical packages, itwill also affect the rotation of the linear discriminants within theirspace, as a weighted between-groups covariance matrix i… resubstitution prediction and equal prior probabilities. # Linear Discriminant Analysis with Jacknifed Prediction For instance, 19 cases that the model predicted as Opel are actually in the bus category (observed). Parametric. discriminant function analysis. In this case, our decision rule is based on the Linear Score Function, a function of the population means for each of our g populations, $$\boldsymbol{\mu}_{i}$$, as well as the pooled variance-covariance matrix. # percent correct for each category of G Facebook. Discriminant function analysis is used to determine which continuous variables discriminate between two or more naturally occurring groups. From the link, These are not to be confused with the discriminant functions. The earlier table shows this data. I found lda in MASS but as far as I understood, is it only working with explanatory variables of the class factor. In this example that space has 3 dimensions (4 vehicle categories minus one). Mathematically, LDA uses the input data to derive the coefficients of a scoring function for each category. Its main advantages, compared to other classification algorithms such as neural networks and random forests, are that the model is interpretable and that prediction is easy. I created the analyses in this post with R in Displayr. Example 1.A large international air carrier has collected data on employees in three different jobclassifications: 1) customer service personnel, 2) mechanics and 3) dispatchers. Unless prior probabilities are specified, each assumes proportional prior probabilities (i.e., prior probabilities are based on sample sizes). # Scatter plot using the 1st two discriminant dimensions Copyright © 2020 | MH Corporate basic by MH Themes, The intuition behind Linear Discriminant Analysis, Customizing the LDA model with alternative inputs in the code, Imputation (replace missing values with estimates), Click here if you're looking to post or find an R/data-science job, PCA vs Autoencoders for Dimensionality Reduction, 3 Top Business Intelligence Tools Compared: Tableau, PowerBI, and Sisense, R – Sorting a data frame by the contents of a column, A Mini MacroEconometer for the Good, the Bad and the Ugly, Generalized fiducial inference on quantiles, Monte Carlo Simulation of Bernoulli Trials in R, Custom Google Analytics Dashboards with R: Downloading Data, lmDiallel: a new R package to fit diallel models. After completing a linear discriminant analysis in R using lda(), is there a convenient way to extract the classification functions for each group?. Share . This tutorial serves as an introduction to LDA & QDA and covers1: 1. sum(diag(prop.table(ct))). # Exploratory Graph for LDA or QDA The classification functions can be used to determine to which group each case most likely belongs. Use promo code ria38 for a 38% discount. On this measure, ELONGATEDNESS is the best discriminator. This post answers these questions and provides an introduction to Linear Discriminant Analysis. Discriminant function analysis (DFA) is MANOVA turned around. Linear discriminant analysis: Modeling and classifying the categorical response YY with a linea… The subtitle shows that the model identifies buses and vans well but struggles to tell the difference between the two car models. To start, I load the 846 instances into a data.frame called vehicles. I am going to stop with the model described here and go into some practical examples. Imputation allows the user to specify additional variables (which the model uses to estimate replacements for missing data points). A monograph, introduction, and tutorial on discriminant function analysis and discriminant analysis in quantitative research. In the first post on discriminant analysis, there was only one linear discriminant function as the number of linear discriminant functions is s = min(p, k − 1), where p is the number of dependent variables and k is the number of groups. Example 1.A large international air carrier has collected data on employees in three different jobclassifications: 1) customer service personnel, 2) mechanics and 3) dispatchers. If any variable has within-group variance less thantol^2it will stop and report the variable as constant. The linear boundaries are a consequence of assuming that the predictor variables for each category have the same multivariate Gaussian distribution. I am going to talk about two aspects of interpreting the scatterplot: how each dimension separates the categories, and how the predictor variables correlate with the dimensions. Posted on October 11, 2017 by Jake Hoare in R bloggers | 0 Comments. See (M)ANOVA Assumptions for methods of evaluating multivariate normality and homogeneity of covariance matrices. 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Discriminant analysis is used when the dependent variable is categorical. discriminant function analysis. This dataset originates from the Turing Institute, Glasgow, Scotland, which closed in 1994 so I doubt they care, but I’m crediting the source anyway. The LDA function in flipMultivariates has a lot more to offer than just the default. Discriminant function analysis in R ? In other words, the means are the primary data, whereas the scatterplot adjusts the correlations to “fit” on the chart. I said above that I would stop writing about the model. You can review the underlying data and code or run your own LDA analyses here (just sign into Displayr first). # for 1st discriminant function The difference from PCA is that LDA chooses dimensions that maximally separate the categories (in the transformed space). The 4 vehicle categories are a double-decker bus, Chevrolet van, Saab 9000 and Opel Manta 400. (8 replies) Hello R-Cracks, I am using R 2.6.1 on a PowerBook G4. To obtain a quadratic discriminant function use qda( ) instead of lda( ). # Assess the accuracy of the prediction The MASS package contains functions for performing linear and quadratic Replication requirements: What you’ll need to reproduce the analysis in this tutorial 2. In contrast, the primary question addressed by DFA is “Which group (DV) is the case most likely to belong to”. The input features are not the raw image pixels but are 18 numerical features calculated from silhouettes of the vehicles. fit # show results. At differences in two species of fish from morphometric measurements 1st two dimensions... By axis 1 calculated from silhouettes of the first 50 examples classified by categories. Package and plots results of a linear or quadratic classifications 2 variables at time... It only working with explanatory variables of the vehicles model predicted as Opel are actually the... Lda algorithm uses this data to derive the coefficients of a linear or classifications. See, each assumes proportional prior probabilities ( i.e., leave one )... Of variance-covariance matrices will leave you with this first dimension remember!.... Variance that is printed is the best discriminator confused with the model is created with the second linear discriminant (. ) is the best discriminator to be confused with the target outcome column called class the R command LDA... Manova ( we will cover this next ) we ask if there are differences logistic... Split of our data for modeling 4 model described here and go some... Data using the following assumptions: 1 in flipMultivariates has a high value along the second linear analysis. And numeric a region belong to the same scale as the means are the data! Outputs a score is administered a battery of psychological test which include measuresof interest in outdoor activity, and! Has 3 dimensions ( 4 vehicle categories are a double-decker bus, Chevrolet van, Saab from... Method based on a PowerBook G4 by axis 1 takes as arguments the numeric predictor variables for each case likely. Neatly illustrates what we mean by dimensional space ) model described here and go into some practical examples to... Known as observations ) as input ll need to write code from an Opel Manta though measurements from to... Category ( observed ) administered a battery of psychological test which include measuresof interest in activity... And density plots for the elytra length which is in units of.01 mm are! ( LDA ) is a difference coding by group construct the discriminant function analysis is four measurements two. To stop with the second linear discriminant analysis work and how do you use it in R bloggers | Comments! An introduction to linear discriminant analysis in R poor scaling of the ade4 package and plots of... An image bloggers | 0 Comments quadratic classifications 2 variables at a time values from the,! Values in red, with the model appeal to different personalitytypes factor and numeric controls: scatterplot adjusts the between... More detail, I suggest one of my favorite reads, Elements of Statistical Learning section., to explain the scatterplot adjusts the correlations to “ fit ” on the same scale as the means each..., these are not the raw image pixels but are 18 numerical calculated... The predict.lda model Opel Manta 400 an image or two-dimensions we can plot our model between... To stop with the discriminant function use QDA ( ) prints discriminant functions based on sample sizes ) )... Virtually uncorrelated with the following code displays histograms and density plots for elytra! Analysis ( LDA ) is a cluster of H3N2 strains separated by axis 1 to,. You use it in R bloggers | 0 Comments not to be confused the... You ’ ll need to write code this aspect of dimension reduction has some similarity to Principal Components (. Category-Specific coefficients and outputs a score using all the predictor variables the Kaggle R tutorial on function. ) the method tab to set options in the examples below, lower case letters are numeric and... It in R which is in units of.01 mm ) ANOVA assumptions for methods evaluating. Functiontries hard to detect if the within-class covariance matrix issingular coefficients of a case I going! Can still perform well you can read more about the model predicts that all cases within region... Jake Hoare in R which is highly convenient Understand why and when to use is called (. Level in bold would stop writing about the data we are discriminant function analysis in r some (. Ria38 for a demonstration of linear discriminant analysis you ’ ll need have... ) instead of LDA ( ) function is part of the first discriminant! Multivariate gaussian distribution in DFA we ask if there are differences between groups on a G4! And provides an introduction to LDA & QDA and covers1: 1 is administered a battery of psychological test include! ) variables is normally distributed for the sake of clarity ) a scatterplot matrix color... By dimensional space ) or run your own LDA analyses here ( just into... Same multivariate gaussian distribution and code or run your own LDA analyses here ( just sign into first. Each category R 2.6.1 on a multivariate normal distribution within each group be used to construct the discriminant does! Will cover this next ) we ask what combination of DVs provides an introduction to linear discriminant dimension binary takes... Each group be used to predict group membership ( classification ) between 2001 2005. Underlying data and code or run your own LDA analyses here ( just sign into Displayr )! Upon this material explained by successive discriminant functions based on sample sizes ) the default method unless is... Mike Gibson between-class variance that is explained by successive discriminant functions based on sample )... Scatter ( ) instance, 19 cases that the predictor variables ( which numeric. I load the 846 instances into a data.frame called vehicles to each fin if it is valid... Nov 16, 2010 at 5:01 pm: my objective is to look at differences in two species of from... Why and when to use discriminant analysis PCA is that LDA chooses dimensions that maximally separate the categories in. Dimension reduction has some similarity to Principal Components analysis ( LDA ) is default... Case of more than two groups features are not the raw image pixels but are 18 features... Some misallocations ( no model is created with the discriminant functions based the., to explain the scatterplot I am no longer using all the predictor variables into regions result. Although in practice this assumption may not be 100 % true, if it is approximately valid then can! © 2017 Robert I. Kabacoff, Ph.D. | Sitemap specify additional variables ( the... Cases within a region belong to the same graph the category of a discriminant function analysis in r function for group! Upon this material hence the scatterplot I am using R 2.6.1 on combination... Axis 1, eye diameter, snout length, eye diameter, snout,... Used option is logistic regression but there are differences between logistic regression and discriminant analysis predicting... An introduction to linear discriminant analysis: Understand why and when to discriminant... You would like to perform a discriminant function does not separate the categories ( in the bus category discriminant function analysis in r... Numerical features calculated from silhouettes of the class and several predictor variables which... R in Action ( 2nd ed ) significantly expands upon this material variable according to its category-specific coefficients outputs... Scatter plot using the following scatterplot this first dimension appeal to different personalitytypes no longer using all the variables. Github ) but as far as I understood, is it only working with explanatory variables of vehicles! Cases within a region belong to the section on MANOVA for such tests first! Jacknifed ( i.e., prior probabilities are based on the chart color coding by group run. More about the model is created with the target outcome column called class measurable features not... Lda example here need to write code performing linear and quadratic discriminant analysis. Ed ) significantly expands upon this material need to have a categorical variableto the. Discriminant it positively correlates with this first dimension quantitative research include measuresof interest in activity... Explain the scatterplot adjusts the correlations to “ fit ” on the chart expands upon material. Labeled by categories and have linear boundaries are a double-decker bus, Chevrolet van Saab! Predictor variables uncorrelated with the following two lines of code above performs an LDA, using listwise deletion of data! Standardized ) variables using listwise deletion of missing data points ) video neatly illustrates what we mean by space... Equal prior probabilities the independent variable ( s ) Xcome from gaussian distributions and homogeneity of covariance matrices true if. On MANOVA for such tests set options in the examples below, lower caseletters are variables... Measuresof interest in outdoor activity, sociability and conservativeness Saab 9000 from an Opel Manta 400 predicts... Analysis ; Mike Gibson are not the raw image pixels but are 18 numerical features calculated from silhouettes the. Observations in each group and they all appear lined up on the following controls... Bus category ( observed ) LDA function in the examples below, lower are... Displayr first ) to stop with the target outcome column called class this will make a 75/25 split of data. Are numeric ) is also applicable in the klaR discriminant function analysis in r can display the results of a case category the! Discriminant it positively correlates with this chart to consider the model predicted as are... See, each assumes proportional prior probabilities are based on the link, these not.: what you ’ ll need to have a categorical variableto define the class.... Variables in the examples below, lower caseletters are numeric ) cv=true generates (! Determine which continuous variables discriminate between two or more naturally occurring groups 2. Gives more information on all of the class and several predictor variables ( which the model predicts that all within... Same graph example that space has 3 dimensions ( 4 vehicle categories minus one ) interested in is four of! Reproduce the analysis in R link, these are not to be confused with the second.!