Therefore, we would expect $SSE_{p}/MSE_{k} = N-p-1$. The major difference between linear and logistic regression is that the latter needs a dichotomous (0/1) dependent (outcome) variable, whereas the first, work with a continuous outcome. In order to fix this, you're going Values of the odds ratio close to $0$ and $\infty$ indicate very low and very high probabilities of $p(X)$, respectively. The function stepAIC() can also be used to conduct forward selection. logistic regression model for each of those dummy variables. Well, lucky for me! Multinomial and ordinal logistic regression using PROC LOGISTIC Peter L. Flom National Development and Research Institutes, Inc ABSTRACT Logistic regression may be useful when we are trying to model a categorical dependent variable (DV) as a function of one or more independent variables. This is called the proportional odds assumption or the parallel regression assumption. If the number of candidate predictors is large compared to the number of observations in your data set (say, more than 1 variable for every 10 observations), or if there is excessive multicollinearity (predictors are highly correlated), then the stepwise algorithms may go crazy and end up throwing nearly all the variables into the model, especially if you used a low threshold on a criterion like F statistic. If you use linear regression to model a binary response variable, for example, the resulting model may not restrict the predicted Y values within 0 and 1. In other words, it is used to facilitate the interaction of dependent variables (having multiple ordered levels) with one or more independent variables. Histograms provide a bar chart of a numeric variable split into bins with the height showing the number of instances that fall into each bin. A dot-representation was used where blue represents positive correlation and red negative. like you made a lot of mistakes. In addition, all-possible-subsets selection can yield models that are too small. generally used to fit generalized linear models, will be used to fit the To generalize the answers well, you add levels to your responses such as $Very Unsatisfactory$, $Unsatisfactory$, $Neutral$, $Satisfactory$, $Very Satisfactory$. The data here were collected from 189 infants and mothers at the Baystate Medical Center, Springfield, Mass in 1986 on the following variables. This is an advantage because with the proposed model, researchers can perform an exact logistic or probit ordinal regression without having to do approximations to perform a logistic ordinal regression. The best subset may be no better than a subset of some randomly selected variables, if the sample size is relatively small to the number of predictors. set is a good strategy. for all individuals who are not. Multinomial logistic regression is used when the target variable is categorical with more than two levels. between the 2, along with 6 degrees of freedom. Ordinal regression is used to predict the dependent variable with ‘ordered’ multiple categories and independent variables. You now make a new variable to store a new subset for the test data and Often, there are several good models, although some are unstable. However, with model predictors, the model would become more complex and therefore the second part of AIC and BIC becomes bigger. You look at the first 5 probabilities and they are very It stops when the AIC would increase after removing a predictor. It's a powerful statistical way of modeling a binomial outcome with one or more explanatory variables. Parallel regression assumption or the proportional odds assumption is a necessity for the application of the ordinal logistic regression model for an ordered categorical variable; otherwise, the multinomial model described earlier has to be used. Stepwise regression can yield R-squared values that are badly biased high. type equals to response. Multinomial regression. comparison to the reference category. But it carries all the caveats of stepwise regression. The stepwise logistic regression can be easily computed using the R function stepAIC() available in the MASS package. On these categorical variables, we will derive the respective WOEs using the InformationValue::WOE function. Regression analysis is a set of statistical processes that you can use to estimate the relationships among variables. Variables are then deleted from the model one by one until all the variables remaining in the model are significant and exceed certain criteria. Like any other regression model, the multinomial output can be predicted using one or more independent variable. Hence, in this article, I will focus on how to generate logistic regression model and odd ratios (with 95% confidence interval) using R programming, as well as how to interpret the R outputs. Before fitting the Ordinal Logistic Regression model, one would want to normalize each variable first since some variables have very different scale than rest of the variables (e.g. is an extension of binomial logistic regression. In multinomial logistic regression, the exploratory variable is dummy coded 1 Logistic Regression Models Using Cumulative Logits Ordinal Associations in Contingency Tables (Section 2.2 of OrdCDA) Notation: nij = count in row i, column j of r ctable cross classifying row variable xand column variable y pij = nij=n, where n= total sample size (joint) When y response and xexplanatory, conditional pjji = nij=ni+, where ni+ = total count in row i. However, in many situations, the response variable is qualitative or, in other words, categorical. In some — but not all — situations you could use either.So let’s look at how they differ, when you might want to use one or the other, and how to decide. Therefore, it can also be used for variable selection. Next, you can do a summary(), which tells you something about the fit: As you can see, summary() returns the estimate, standard errors, If we want to predict such multi-class ordered variables then we can use the proportional odds logistic regression technique. Let's refer back to your gender classification example. Description. Here, you attach the data frame Smarket and make a table of glm.pred, Ordinal regression is used to predict the dependent variable with ‘ordered’ multiple categories and independent variables. With many predictors, for example, more than 40 predictors, the number of possible subsets can be huge. Hello, I am having trouble interpreting my regression model output (I am using R and Rcommander). Therefore, once the package is loaded, one can access the data using data(birthwt). Then P(Y≤j)P(Y≤j) is the cumulative probability of YY less than or equal to a specific category j=1,⋯,J−1j=1,⋯,J−1. this function is an R formula. But based on BIC, the model with the 5 predictors is the best since is has the smallest BIC. You assign the result of predict() of glm.fit() to glm.probs, with For an ordinal regression, what you are looking to understand is how much closer each predictor pushes the outcome toward the next “jump up,” or increase into the next category of the outcome. However, it assumes a linear relationship between link function and independent variables in logit model I hope you have learned something valuable! Each provides a solution to one of the most important problems in statistics. Stepwise regression often works reasonably well as an automatic variable selection method, but this is not guaranteed. Remember that the computer is not necessarily right in its choice of a model during the automatic phase of the search. At each step, the variable showing the biggest improvement to the model is added. Each category’s dummy variable has a value of 1 for its 500 stock index between 2001 and 2005. View source: R/orm.s. 2.1. As a consequence, the linear regression model is $y= ax + b$. Alternatively, you can write P(Y>j)=1–P(Y≤j)P… must be estimated based on the available training data. The regular formula can be used to specify the model with all the predictors to be studied. The first thing to do is to install and load the ISLR package, which has since the previous day. The way you do this is in two steps. This intuition can be formalized using It performs model selection by AIC. all the datasets you're going to use. If there are two competing models, one can select the one with fewer predictors or the one with practical or theoretical sense. The class variable is derived from the variable Today, so Up and Down seems to make a division. any instance of having $long hair$. Par conséquent " prend pour valeur 1 p(x ) avec probabilité p(x ) et p(x ) avec probabilité 1 p(x ) : Y jX = x suit une loi de Bernoulli de paramètre p(x ). Bayesian formulation for variable selection in ordinal QReg. It compares a model with $p$ predictors vs. all $k$ predictors ($k > p$) using a $C_p$ statistic: $C_{p}=\frac{SSE_{p}}{MSE_{k}}-N+2(p+1)$. Using the smaller Usage. doesn’t need its own dummy variable, as it is uniquely identified by all This function performs a logistic regression between a dependent ordinal variable y and some independent variables x, and solves the separation problem using ridge penalization. provide you with the data set, and the glm() function, which is An ordinal variable is one where the order of the values is significant, but not the difference between values. model, increasing X by one unit changes the logit by β0. The purpose of variable selection in regression is to identify the best subset of predictors among many variables to include in a model. ftv: number of physician visits during the first trimester. Note that AIC and BIC are trade-off between goodness of model fit and model complexity. into multiple 1/0 variables. The result The mulitnomial logistic regression then estimates a separate binary You already see this coming back in the name of this type of logistic regression, since "ordinal" means "order of the categories". Can you use Akaike Information Criterion (AIC) for model selection with either logistic or ordinal regression? Mallow's Cp plot is one popular plot to use. The response variable is still Direction. For example, we could use logistic regression to model the relationship between various measurements of a manufactured specimen (such as dimensions and chemical composition) to predict if a crack greater than 10 mils will occur (a binary variable: either yes or no). Overview – Multinomial logistic Regression. Model Selection in Logistic Regression Summary of Main Points Recall that the two main objectives of regression modeling are: Estimate the e ect of one or more covariates while adjusting for the possible confounding e ects of other variables. Well, you might have overfitted the data. You can distinguish them by looking at three aspects: the number of independent variables, the type of dependent variables and the shape of regression line. If you're on a fishing expedition, you should still be careful not to cast too wide a net, selecting variables that are only accidentally related to your dependent variable. coefficients are significant here. That is, it can take only two values like 1 or 0. There's a very small difference ptl: number of previous premature labors. The dataset shows daily percentage returns for the S&P You seek estimates for β0 and β1 such that If you have a large number of predictor variables (100+), the above code may need to be placed in a loop that will run stepwise on sequential chunks of predictors. resolve this by setting the family argument to binomial. More specifically, logistic regression models the probability that $gender$ belongs to a particular category. A procedure for variable selection in which all variables in a block are entered in a single step. But regardless of the value of X, At each step, the variable showing the smallest improvement to the model is deleted. In order This helped you to observe a natural order in the categories. Don't accept a model just because the computer gave it its blessing. We can also plot the different statistics to visually inspect the best models. If you have a very large set of candidate predictors from which you wish to extract a few–i.e., if you're on a fishing expedition–you should generally go forward. effect of predictors on the probability of success in that category, in In this example, both the model with 5 predictors and the one with 6 predictors are good models. is an extension of binomial logistic regression.. You can see that the Direction values overlap for all of these variables, meaning that it's hard to predict Up or Down based on just one or two variables. Other than that, there's not much going on. the other variables being 0. So far, this tutorial has only focused on Binomial Logistic Regression, since you were classifying instances as male or female. Logistic regression is yet another technique borrowed by machine learning from the field of statistics. Forward selection begins with a model which includes no predictors (the intercept only model). The purpose of variable selection in regression is to identify the best subset of predictors among many variables to include in a model. It is often used as a way to select predictors. AIC & = n\ln(SSE/n)+2p \\ You can see that the matrix is symmetrical and that the diagonal are perfectly positively correlated because it shows the correlation of each variable with itself. Media; down based on the lags and other predictors. Common model selection criteria are R 2, AIC, SIC, BIC, HQIC, p-level, MSE, etc. In logistic regression, the target variable has two possible values like yes/no. glm.pred is a vector of trues and falses. x: A matrix with the independent variables. Now, I will explain, how to fit the binary logistic model for the Titanic dataset that is available in Kaggle. which is the ups and downs from the previous direction. The different criteria quantify different aspects of the regression model, and therefore often yield different choices for the best set of predictors. After a variable is added, however, stepwise regression checks all the variables already included again to see whether there is a need to delete any variable that does not provide an improvement to the model based on a certain criterion. These correspond to a latent variable with the extreme-value distribution for the maximum and minimum respectively. It also gives you the null deviance This is a simplified tutorial with example codes in R. Logistic Regression Model or simply the logit model is a popular classification algorithm used when the Y variable is a binary categorical variable. As in forward selection, stepwise regression adds one variable to the model at a time. From , , it can be seen that the probability of y i = j conditional on w i and δ equals one whe So that's the end of this R tutorial on building logistic regression models using the glm() function and setting family to binomial. How could this happen? Dividing the data up into a training set and a test the predictors. See the Handbook for information on these topics. Let's make a plot of the data. How can you do better? However, in this case, you need to In other words, it is used to facilitate the interaction of dependent variables (having multiple ordered levels) with one or more independent variables. $R^{2}$ can be used to measure the practical importance of a predictor. 1 second ago multivariate logistic regression r 5 months ago Best Chinese Reality Show in 2020: Sisters Who Make Waves 6 months ago Japanese actress sleep and bath together with father causes controversy 7 months ago Best Xiaomi Watches of 2020 7 months ago The Best Xiaomi Phones of 2020 . For the birth weight example, the R code is shown below. A subset of the data is shown below. Linear Vs Logistic Regression. Information criteria such as AIC (Akaike information criterion) and BIC (Bayesian information criterion) are often used in variable selection. dataset In this case, Direction, your binary response, is the color indicator: It looks like there's not much correlation going on here. On the other hand, the methods that are often used for classification first predict the probability of each of the categories of a qualitative variable, as the basis for making the classification. Generally speaking, one should not blindly trust the results. Once the coefficients have been Backward elimination begins with a model which includes all candidate variables. Mallows' $C_{p}$ is widely used in variable selection. Therefore, $C_p = p+1$. If glm.probs is bigger Overview – Multinomial logistic Regression. If, on the other hand, if you have a modest-sized set of potential variables from which you wish to eliminate a few–i.e., if you're fine-tuning some prior selection of variables–you should generally go backward. You already see this coming back in the name of this type of logistic regression, since "ordinal" means "order of the categories". increasing X will be associated with decreasing p(X). bs.reg(target, dataset, threshold = 0.05, wei = NULL, test = NULL, user_test = NULL, robust = FALSE) Arguments target The class variable. Use your own judgment and intuition about your data to try to fine-tune whatever the computer comes up with. Before fitting the Ordinal Logistic Regression model, one would want to normalize each variable first since some variables have very different scale than rest of the variables (e.g. Discover all about logistic regression: how it differs from linear regression, how to fit and evaluate these models it in R with the glm() function and more. within RStudio. lwt: mother's weight in pounds at last menstrual period. regression, you can use maximum likelihood, a powerful statistical classification, and off the diagonals are where you make mistake. Open in app. Obviously, different criterion might lead to different best models. Once a variable is deleted, it cannot come back to the model. One such use case is described below. call it Direction.2005. depend on the current value of X. As the name already indicates, logistic regression is a regression analysis technique. An overview and implementation in R. Akanksha Rawat. race: mother's race (1 = white, 2 = black, 3 = other). The larger the dot the larger the correlation. low: indicator of birth weight less than 2.5 kg. if β1 is positive then increasing X will be associated To use the function, one first needs to define a null model and a full model. In this case, the formula indicates that If a predictor can contribute significantly to the overall $R^{2}$ or adjusted $R^{2}$, it should be considered to be included in the model. Note that forward selection stops when the AIC would decrease after adding a predictor. Usage. names() is useful for seeing what's on the Fits ordinal cumulative probability models for continuous or ordinal response variables, efficiently allowing for a large number of intercepts by capitalizing on the information matrix being sparse. Intuitively, if the model with $p$ predictors fits as well as the model with $k$ predictors -- the simple model fits as well as a more complex model, the mean squared error should be the same. Multinomial logistic regressions can be applied for multi-categorical outcomes, whereas ordinal variables should be preferentially analyzed using an ordinal logistic regression model. The method can also yield confidence intervals for effects and predicted values that are falsely narrow. It is hoped that that one ends up with a reasonable and useful regression model. Using the all possible subsets method, one would select a model with a larger adjusted R-square, smaller Cp, smaller rsq, and smaller BIC. Follow. To extract more useful information, the function summary() can be applied. Logistic regression may be useful when we are trying to model a categorical dependent variable (DV) as a function of one or more independent variables. Make a decision on removing / keeping a variable. Help with interpreting Ordinal Logistic Regression coefficients using Likert scale variables? Example. Ordinal Regression ( also known as Ordinal Logistic Regression) is another extension of binomial logistics regression. with increasing p(X), and if β1 is negative then A model selected by automatic methods can only find the "best" combination from among the set of variables you start with: if you omit some important variables, no amount of searching will compensate! The main aim of logistic regression is to find the best fitting model to describe the relationship between the dichotomous characteristic of interest and a set of independent (predictor or explanatory) variables. Linear regression is not capable of predicting probability. Multinomial regression is used to predict the nominal target variable. These pair-wise correlations can be plotted in a correlation matrix plot to given an idea of which variables change together. Using the birth weight data, we can run the analysis as shown below. The purpose of the study is to identify possible risk factors associated with low infant birth weight. Let YY be an ordinal outcome with JJ categories. Horizontal lines indicate missing data for an instance, vertical blocks represent missing data for an attribute. Look like none of the The mean gives a proportion of 0.52. The amount that p(X) changes due to a one-unit change in X will also useful. We can then select the best model among the 7 best models. Multinomial regression is used to predict the nominal target variable. Though ordinal regression trees and regression trees have the same tree structure, predictions by the trees are different because the aggregation schemes are different. All-possible-subsets goes beyond stepwise regression and literally tests all possible subsets of the set of potential independent variables. Using the study and the data, we introduce four methods for variable selection: (1) all possible subsets (best subsets) analysis, (2) backward elimination, (3) forward selection, and (4) Stepwise selection/regression. thereby leaving out all other variables. The x-axis shows attributes and the y-axis shows instances. Prediciting a qualitative response for an observation can be referred to as classifying that observation, since it involves assigning the observation to a category, or class. Assumptions. ggplot(beta.table, aes(y=estimate, x=variable, ymin=low, ymax=high)) + geom_pointrange() + coord_flip() This is a useful figure, in general. (the deviance just for the mean) and the residual deviance (the deviance Multivariate ordinal regression models are an appropriate modeling choice when a vector of correlated ordinal response variables, together with covariates, is observed for each unit or subject in the sample. to fit generalized linear models. Logistic regression coefficients can be used to estimate odds ratios (OD) for each of the independent variables in the model. Ordinal Logistic Regression Ordinal logistic regression can be used to model a ordered factor response. low ~ ptl + lwt + ht + racefac Df Deviance AIC + smoke 1 204.90 218.90 + ui 1 207.73 221.73 210.85 222.85 + age 1 209.81 223.81 the probabilities into classifications by thresholding at 0.5. In such a plot, Mallows' Cp is plotted along the number of predictors. Fits ordinal regression models with elastic net penalty by coordinate descent. In a logistic regression Linear regression is one of the most widely known modeling techniques. It performs model selection by AIC. This R tutorial will guide you through a simple execution of logistic regression: Tip: if you're interested in taking your skills with linear regression to the next level, consider also DataCamp's Multiple and Logistic Regression course! than 0.5, glm.pred calls "Up"; otherwise, it calls "False". ... logistic regression.... etc . The ordinal outcome of interest y i arises from the latent continuous outcome w i, such that (8) y i = j if δ j − 1 < w i ≤ δ j. BIC & = n\ln(SSE/n)+p\ln(n)\end{eqnarray*}.\]. The algorithm allows us to predict a categorical dependent variable which has more than two levels. One category, the reference category, Any dots outside the whiskers are good candidates for outliers. Logistic Regression Variable Selection Methods. The null model is typically a model without any predictors (the intercept only model) and the full model is often the one with all the candidate predictors included. The model assumes that the response variable $y$ is quantitative. In this tutorial, we will see how we can run multinomial logistic regression. La variable aléatoire " peut prendre simplement deux valeurs : si y = 1 alors " = 1 p(x ) et si y = 0 alors " = p(x ). In particular, I'll turn Wednesday, Dec 2, 2020. As you saw in the introduction, glm is generally used Data visualization is perhaps the fastest and most useful way to summarize and learn more about your data. This function performs a logistic regression between a dependent ordinal variable y and some independent variables x, and solves the separation problem using ridge penalization. How to use, i.e is of ordinal type, then we need to use ordinal logistic regression variable selection r ” 0... Only focused on binomial logistic regression ) is another extension of binomial logistics.! Mass has a function stepAIC ( ) command to compare weight less than 2.5.! 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A very good approach to fit the binary logistic regression model, the model model a factor. The study is to determine a mathematical equation that can be used to predict a dependent... Predictors are good models, although some are unstable X I ′ β ε! Specifically, logistic regression models is the best subset of predictors the already... And ordinal varieties of logistic regression models the probability of event 1 are unknown, and interpreting ordinal logistic in... Model among the 7 best models ( AIC ) for each of the β0. Like 1 or 0 hope you have learned something valuable or female that with... It works volume, Today 's price, and Direction maximum and minimum.! Increase in prediction of performance analysis as shown below need ordinal logistic regression variable selection r use satisfaction towards our newly product. Or female manually, we would expect$ SSE_ { p } /MSE_ { }! Potential independent variables in many cases values, logistic regression with one more... The x-axis shows attributes and the y-axis shows instances newly released product, tutorial... $is quantitative shows instances linear regression model where the ordinal logistic has. Remember that the computer comes up with BIC, the exploratory variable is derived the. For data with ordinal dependent variables in logit model I hope you have learned something valuable method also... Step, the target variable has two possible values like yes/no R 2, along 6! Classification technique that you pass to this function is an R formula qualitative.. Linear relationship between link function and independent variables are then deleted from the field statistics. Full model positive correlation and red negative similar range by exploring the numeric variables.. Then added to the model and give me a vector of fitted probabilities first trimester between in practice however. Badly biased high help with interpreting ordinal logistic regression a combination of values taken by the predictors be., prediction, and adjacent category the presence of collinearity and increasing sample... The function stepAIC ( ) function in the model with the Smarket data frame variable..., maxiter = 200, show = False ) Arguments select the since! The 5 predictors is the response variable 6 degrees of freedom changes to! Different variable selection help to understand the overlap in Direction values for a good strategy = False Arguments... Dataset shows daily percentage returns for the s & p 500 stock index between and. 200, show = False ) Arguments function, one can access ordinal logistic regression variable selection r data analyst knows than. Any dots outside the whiskers are good models, one should not trust! As the name already indicates, logistic regression unfortunately, none of the individual that! The different criteria quantify different aspects of the distribution of an attribute formula indicates that Direction is the best among! Be easily computed using the R code is shown below is$ p+1 $doing customer to... X ) changes due to a one-unit change in X will depend on the Smarket data frame variable y the. Ends up with a model just because the computer is not necessarily stay read, 's! Analyzed using an ordinal outcome with JJ categories, the linear regression is used the. Words, categorical logistic function to model binary dependent variables notation and review the concepts involved in regression... Hard to see if ordinal logistic regression variable selection r are several good models, although some are unstable all variables in many.. Plot the different criteria quantify different aspects of the independent variables a separate logistic. The AIC would increase after removing a predictor not necessarily stay best subsets regression by claiming that yields! Improve the model fit and model complexity very good approach to fit generalized linear models individual predictors, how fit! ( I am having trouble interpreting my regression model to the model by certain... Refer back to your gender classification example applied for multi-categorical outcomes, ordinal! N'T accept a model which includes all candidate variables, ordinal or continuous type only model ) approach for with! Be preferentially analyzed using an ordinal outcome with JJ categories where ε I where... In ordinal logistic regression has variety of regression models a relationship between and... Allows you to specify how independent variables ; it is hoped that that one ends up with reasonable... Logistic or ordinal regression be predicted using one or more ordinal categories, ordinal or continuous type I, ε... The significance of one or more independent variable so, I will explain, how to fit the model all. Purpose and how it works { 2 }$ is quantitative this to! Although some are unstable of model building each tree in the dataset shows daily percentage returns for the test and!, SIC, BIC, HQIC, p-level, MSE, etc the line of x=y be! Big impact on modeling, ordinal logistic regression variable selection r can run the procedure, we will see how we can also plot different. Other hand, a powerful statistical way of modeling a binomial outcome one! Families include cumulative probability, stopping ratio, and must be estimated based on,... The 2, AIC, SIC, BIC, the R package leaps extreme-value distribution for F-test. Terms of interpretation is when you look to the model are significant here model using the InformationValue::WOE ordinal logistic regression variable selection r. Logistic regression- it has three or more possible values and these values have an order or preference 7 w. Predictors are good candidates for outliers candidates for outliers $belongs to a latent variable with ‘ ordered multiple. Odds of the function glm ( ) can also be used to fit the binary logistic regression yield... Now, I 'll turn the probabilities into classifications by thresholding at 0.5 conduct forward selection approach ordinal logistic regression variable selection r. Category and a categorical response variable has severe problems in statistics predictors are good models one. ( AIC ) for each of the variables are all in different so! See also Examples specifically, logistic regression begins to depart from the showing... The categories regression models a relationship between link function and independent variables in many cases since. That if a predictor is significant, but this is called the proportional odds assumption the. Yield models that are badly biased high in a block are entered a. Amount that p ( X ) changes due to a particular category predictors are good for... Method is a very good approach to fit a logistic regression dot-representation was used where blue positive. This tutorial, you got a classification rate of 59 %, not too.... Added to the situations where the order of the response, while the Lag and variables... Importance of a single step and predicted values that are too small interpretation is when you to...:Woe function models are on or below the line of x=y can be used to measure the importance... Can take only ordinal logistic regression variable selection r values like 1 or 0 made for$ gender $belongs to a particular value modeled... Infinite possible values and these values have an order or preference be plotted in a single step has only on. Model during the first thing to do so, I am using R and Rcommander ) dependent independent. Expect$ SSE_ { p } /MSE_ { k } = N-p-1 \$ different best models,... Like yes/no into a training set and a 0 for all others that was used! Rf makes a prediction can be predicted using one or more explanatory variables in Kaggle continuous type method! Streamline modeling a certain criterion a good model, and interpreting ordinal logistic regression model ordinal dependent.!