Multiple logistic regression example. p hat n events out of n trials).

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Multiple logistic regression example. com Jan 8, 2024 · As an example of multiple logistic regression, in the 1800s, many people tried to bring their favorite bird species to New Zealand, release them, and hope that they become established in nature. linear_model import LogisticRegression. From this analysis, we can see that the odds ratio for conflict_dich decreases a bit (OR=4. 96-5. Many functions meet this description. The binary value 1 is typically used to indicate that the event (or outcome desired) occured, whereas 0 is typically used to indicate the event did not occur. Logistic regression assumes that the response variable only takes on two possible outcomes. It is the probability pi that we model in relation to the predictor variables. We use logistic regression when the dependent variable is categorical. com, which is a website that hosts data sets and data science competitions. In multiple logistic regression, the coefficients for each independent variable Oct 2, 2020 · Step #2: Explore and Clean the Data. Apr 28, 2020 · Types of Logistic Regression. Logistic regression is used in in almost every industry—marketing, healthcare, social sciences, and others—and is an essential part of any data Examples of ordered logistic regression. We assume that the ϵ i have a normal distribution with mean 0 and constant variance σ 2. Like all regression analyses, logistic regression is a predictive analysis. 658 times higher in persons who are obese as compared to not obese. Dec 31, 2021 · Logistic regression also supports multiple explanatory variables. Other types of regression (multinomial & ordinal logistic regressions, as well as Poisson regressions are left for future posts). It improves model generalizability. Step #4: Split Training and Test Datasets. Logit = log odds = log (π/ (1-π)) When a logistic regression model has been fitted, estimates of π are marked with a hat symbol above the Greek letter pi to denote that the proportion is estimated from the fitted regression model. The goal is to determine a mathematical equation that can be used to predict the probability of event 1. Enter a title (e. For example, To predict whether an email is spam (1) or (0) Whether the tumor is malignant (1) or not (0) Consider a scenario Jun 8, 2020 · Logistic regression work with odds rather than proportions. May 31, 2016 · Logistic regression analysis is a popular and widely used analysis that is similar to linear regression analysis except that the outcome is dichotomous (e. 2 A multiple linear regression model. These questions can in principle be answered by multiple linear regression analysis. Example 1: Suppose that we are interested in the factors. logit(p) = log(p/(1-p))= β 0 + β 1 *x1 + … + β k *xk Applying such a model to our example dataset, each estimated coefficient is the expected change in the log odds of being in an honors class for a unit increase in the corresponding predictor variable Dec 20, 2023 · Binary Logistic Regression: In the binary regression analysis model, we define a category by only two cases. We often estimate the βi β i parameters using a computer. To make things easier for you as a Example: if age was included, the covariate pattern could be as large as n • SAS computes predicted values and residuals for each each individual and you need to aggregate your data by covariate pattern. β 1 β ρ = regression coefficients. An important feature of the multinomial logit model is that it estimates k-1 models, where k is the number of levels of the outcome variable. The model parameters β 0 + β 1 + +β ρ and σ must be estimated from data. This function selects models to minimize AIC, not according to p-values as does the SAS example in the Handbook . 5 Diagnostics for Multiple Logistic Regression. Data transforms of your input variables that better expose this linear relationship can result in a more accurate model. Logistic regression is applicable, for example, if we want to Mar 25, 2024 · Multiple logistic regression is a statistical analysis technique used to model the relationship between multiple independent variables and a binary dependent variable. Ordinal logistic regression. That is, it can take only two values like 1 or 0. 1 Likelihood Function for Logistic Regression Because logistic regression predicts probabilities, rather than just classes, we can fit it using likelihood. Generative and Discriminative Classifiers: The most important difference be-tween naive Bayes and logistic regression is that Apr 27, 2023 · Multiple regression model. y i = β 0 + β 1 x i, 1 + β 2 x i, 2 + … + β p − 1 x i, p − 1 + ϵ i. logistic regression models with multiple predictors. The predictor variables of interest are the amount of money spent on the campaign, the. It is assumed that the observations in the dataset are independent of each other. In general, we can have multiple predictor variables in a logistic regression model. Assume the label of a sample from the dataset takes value from set \ (\ {1,2,\cdots , K Click the Series tab, click in the box for Category (X) axis labels, highlight the numbers from 21 through 90 in the data table, click Next to go to Step 3. Logistic regression can be one of three types based on the output values: Binary Logistic Regression, in which the target variable has only two possible values, e. regressor or predictor variable. 88). LogisticRegression. Apr 23, 2022 · 8. y^ = β0 +β1x1 +β2x2 + ⋯ +βkxk (14. 75. generalizability). A population model for a multiple linear regression model that relates a y -variable to p -1 x -variables is written as. Yes/No or Positive/Negative. The statistical model for logistic regression is. It is used to describe data and to explain the relationship between one dependent binary variable and one or more nominal, ordinal, interval or Jan 17, 2013 · Regression Analysis. 2. Logistic Regression (aka logit, MaxEnt) classifier. p(X) = eβ0+β1X 1 + eβ0+β1X (1) (1) p ( X) = e β 0 + β 1 X 1 + e In this tutorial, we will be using the Titanic data set combined with a Python logistic regression model to predict whether or not a passenger survived the Titanic crash. Goodness of Fit and Model Diagnostics • Matching (group and individual) • Conditional vs Unconditional analysis • Methods III: Advanced Regression Methods Logistic Regression – A Complete Tutorial With Examples in R. 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 The next section of the multiple logistic regression results provides a number of useful model diagnostics for determining how well the data fit the selected model. Before fitting a model to a dataset, logistic regression makes the following assumptions: Assumption #1: The Response Variable is Binary. Most computer programs for polytomous logistic regression can handle grouped or ungrouped data. 4. Interested readers should see Kleinbaum, Kupper and Muller for more May 11, 2023 · The three types of logistic regression are: Binary logistic regression is the statistical technique used to predict the relationship between the dependent variable (Y) and the independent variable (X), where the dependent variable is binary in nature. Multiple logistic regression analyses, one for each pair of outcomes: One problem with this approach is that each analysis is potentially run on a different sample. In this section we introduce logistic regression as a tool for building models when there is a categorical response variable with two levels. Oct 28, 2019 · Logistic regression is a model for binary classification predictive modeling. These are the same assumptions that we used in simple Aug 25, 2016 · Yes you can run a multinomial logistic regression with three outcomes in stata . In Chapter 8, we explore multiple regression, …. 1. 12. Whether the data are grouped or ungrouped, we will imagine the response to be multinomial. ols() linear regression function, we can add multiple explanatory variables to the smf. p hat n events out of n trials). The occupational choices will be the outcome variable which consists Aug 6, 2021 · This tutorial provides a brief explanation of each type of logistic regression model along with examples of each. That is, the "response" for row i, y i = ( y i 1, y i 2, …, y i r) T, is assumed to have a multinomial distribution with index n i = ∑ j = 1 r y i j and 2. The observations are independent. survived versus died or poor outcome versus good outcome), logistic regression also requires less assumptions as compared to multiple linear regression or Analysis of Covariance Jan 17, 2013 · The logistic regression analysis reveals the following: The simple logistic regression model relates obesity to the log odds of incident CVD: Obesity is an indicator variable in the model, coded as follows: 1=obese and 0=not obese. For Binary logistic regression the number of dependent variables is two, whereas the number of dependent variables for multinomial logistic regression is more than two. Logitic regression is a nonlinear regression model used when the dependent variable (outcome) is binary (0 or 1). These techniques are often referred to as stepwise model selection strategies, because they add or delete one variable at a time as they "step" through the candidate predictors. In addition, it assumes that the mean of Yi, μi, is a linear function of all predictors. Here, L(1) is the probability that an individual with values x1, x2 ,…, xm is in group g. . 4: Introduction to Logistic Regression. Hence, Logistic Regression is a special case of GliM with Binomial distribution on the Y’s and the link function: E(Yi) = 1 exp() exp( ) 0 1 0 1 i i i x x P Which is non-linear in the X’s. # instantiate the model (using the default parameters) logreg = LogisticRegression ( random_state =16) # fit the model with data. Apr 22, 2021 · Logistic regression is a statistical model used to estimate the effect of factors when we have categorical response. B – These are the estimated multinomial logistic regression coefficients for the models. Estimation and Interpretation of Parameters 3. Multiple logistic regression often involves model selection and checking for multicollinearity. Step #8: Interpret the Results. A regression model fitted using a sample size not much larger than the number of predictors will perform poorly in terms of out-of-sample accuracy. the effect that increasing the value of the independent variable has on the predicted y value sklearn. Mar 31, 2021 · Logistic Function (Image by author) Hence the name logistic regression. It can also be used to assess the presence of effect modification. regplot(x='target', y='variable', data=data, logistic=True) But that takes a single variable input. By default, the two values reported here include the degrees of freedom and corrected Akaike's Information Criterion (AICc) for both an "Intercept-only model" and the "Selected model". Logistic regression is a simple but powerful model to predict binary outcomes. Irrespective of the type of logistic regression that we choose, training the logistic regression model follows a similar process in all cases. For logistic regression, this usually includes looking at descriptive statistics, for example The fitted multiple logistic regression model predicts the data very well. 1 Global F-Test. Here are a couple examples: Example 1: NBA Draft 14. There are multiple ways to train a Logistic Regression model (fit the S shaped line to our data). The earlier discussion in this module provided a demonstration of how regression analysis can provide control of confounding for multiple Oct 9, 2020 · Multiple logistic regression is a classification algorithm that outputs the probability that an example falls into a certain category. Step #3: Transform the Categorical Variables: Creating Dummy Variables. Since you are trying to find correlations with a large number of inputs, I would look for feature importance first, running this. In the multiclass case, the training algorithm uses the one-vs-rest (OvR) scheme if the ‘multi_class’ option is set to ‘ovr’, and uses the cross-entropy loss if the ‘multi_class’ option is set to ‘multinomial’. Step #5: Transform the Numerical Variables: Scaling. Model diagnostics and residual plots indicate adequate fit of the multiple logistic regression model. Mathematically, Odds = p/1-p. 6 Logistic Regression Has Similar Features to Linear Regression. • Multiple logistic regression 1. This basic introduction was limited to the essentials of logistic regression. import seaborn as sns. We’ll introduce the mathematics of logistic regression in the next few sections. Usually x1 = 1 (that is, an intercept is included), but this is not necessary. linear_model. 1 and illustrated in the right figure above. Logistic regression is a supervised learning algorithm used to predict a dependent categorical target variable. If necessary, refer back to Exercise 8. For example, if you were given a dog and an orange and you wanted to find out whether each of these items was an animal Rule of thumb: select all the variables whose p-value < 0. Please see the code below: mlogit if the function in Stata for the multinomial logistic regression model. Apr 27, 2023 · Two common strategies for adding or removing variables in a multiple regression model are called backward-selection and forward-selection. May 31, 2016 · Logistic Regression Analysis. Dec 13, 2023 · SAS Code for Multiple Linear Regression. 9545. The Y-axis is P, which indicates the proportion of 1s (yes) at any given value of age (in bins of 10) Again, it pays to know how your variables are coded! The regression line is nonlinear. Jan 20, 2017 · The traditional logistic regression model is always used binary classification tasks, such as a person’s gender (male or female). The other problem is that without constraining the logistic models, we can end up with the probability of choosing all possible outcome categories greater than 1. As an example, suppose that the effective life of a cutting tool depends on the cutting speed and the tool angle. In logistic regression, we use the logistic function, which is defined in Eq. ¶. Beside the fact that most clinical outcomes are defined as binary form (e. a. In this study, let Y 1i, Y 2i, and Y 3i are binary response of stunting, underweight and wasting of the i th under-five children, respectively. If we have more than two classified sections to categorize our data, then we can use this regression We would like to show you a description here but the site won’t allow us. 5) y ^ = β 0 + β 1 x 1 + β 2 x 2 + ⋯ + β k x k. A regression model that contains more than one regressor vari-able is called a multiple regression model. Gaussian Distribution: Logistic regression is a linear algorithm (with a non-linear transform on output). In this section, we will look at the case of two numeric explanatory variables, and for visualization, we will use color to denote the response. Jan 30, 2024 · Binary logistic regression being the most common and the easiest one to interpret among the different types of logistic regression, this post will focus only on the binary logistic regression. Other than that, it's a fairly straightforward extension of simple logistic regression. Model Fitting Strategies 6. Oct 28, 2020 · Logistic regression is a method we can use to fit a regression model when the response variable is binary. In this case, reducing the number of predictors in the model by using stepwise regression will improve out-of-sample accuracy (i. model selection/building using cross-validation and grid search. It is widely used in the medical field, in sociology, in epidemiology, in quantitative Oct 13, 2020 · Logistic regression is a method that we can use to fit a regression model when the response variable is binary. log (p/1-p) = β0 + β1x Apr 27, 2023 · Logistic regression is a generalized linear model where the outcome is a two-level categorical variable. Step 2: Fit a multiple logistic regression model using the variables selected in step 1. Logistic regression is a technique used when the dependent variable is categorical (or nominal). Regression analysis is a widely used technique which is useful for evaluating multiple independent variables. outcome (response) variable is binary (0/1); win or lose. 11. The occupational choices will be the outcome variable which consists To avoid this problem, we must model p (X) using a function that gives outputs between 0 and 1 for all values of X. 1. 9507 (95. Exercise 8. where: X j: The j th predictor variable Logistic regression analysis is a statistical technique to evaluate the relationship between various predictor variables (either categorical or continuous) and an outcome which is binary (dichotomous). The odds are defined mathematically as P (Y=1) / P (Y=0). First, we assess the overall model with the F test; if the F-value is large and the p-value is <0. Jan 8, 2024 · Simple logistic regression finds the equation that best predicts the value of the \(Y\) variable for each value of the \(X\) variable. In essence, if you have a large set of data that you want to categorize, logistic regression may be able to help. Effects of omitted variables 5. Use the regression table below to answer the following questions. , pass/fail or win/lose. Example 1: A marketing research firm wants to investigate what factors influence the size of soda (small, medium, large or extra large) that people order at a fast-food chain. Logistic Regression is used when the dependent variable (target) is categorical. Area under the model ROC curve is 0. Verify the importance of each variable in this multiple model using Wald statistic. 05, we can say there is a significant relationship between the dependent and independent variables. (We now realize that this is very bad for the native species, so if you were thinking about trying this, please don't. 000; CI= 3. Binary variables can be generalized to categorical variables when there are more than two possible values (e. The log odds are then just the natural log (Ln) of the odds. To explain this a bit in more detail: 1-First you have to transform you outcome variable in a numeric one in which all categorise are ranked as 1, 2, 3. Selva Prabhakaran. 3 Training logistic regression the use of multinomial logistic regression for more than two classes in Section5. For example, the output can be Success/Failure, 0/1 , True/False, or Yes/No. Feb 15, 2014 · Logistic regression is a powerful tool, especially in epidemiologic studies, allowing multiple explanatory variables being analyzed simultaneously, meanwhile reducing the effect of confounding factors. that influence whether a political candidate wins an election. ) Example. That is, whether something will happen or not. Binary logistic regression models are a type of logistic regression in which the response variable can only belong to two categories. In this instance, SPSS is treating the vanilla as the referent group and therefore estimated a model for Feb 8, 2020 · That is a good question. model selection using/building Akaike Information Criterion (if there is time) In data science, typically we have a sample of observational units, and we are interested in the Examples of multinomial logistic regression. The outcome, Yi, takes the value 1 (in our application, this represents a spam message) with probability pi and the value 0 with probability 1 − pi. It's a type of classification model for supervised machine learning. The occupational choices will be the outcome variable which consists Logistic regression estimates the probability of an event occurring, such as voted or didn’t vote, based on a given data set of independent variables. Now let’s split the loaded glass dataset into four different datasets. Fitted proportional responses are often referred to as event probabilities (i. If the multiple categories are ordered, one can use the ordinal logistic regression (for example the The multiple logistic regression model is given by the g equations . , success/failure, or yes/no, or died/lived). That is, L(1) = Pr ( y = g | x ). We can use an iterative optimisation algorithm like Gradient Descent to calculate the parameters of the model (the weights) or we can use probabilistic methods like Maximum likelihood. Oct 27, 2020 · Logistic regression uses the following assumptions: 1. This is similar to multiple logistic regression, except the target categorical variables are ordered (for example, “medal on the Olympics”). e. The regression line is a rolling average, just as in linear regression. The parameters of a logistic regression model can be estimated by the probabilistic framework called maximum likelihood estimation. σ = σ res = residual standard deviation Apr 23, 2022 · David Diez, Christopher Barr, & Mine Çetinkaya-Rundel. logit (π) = log (π/ (1-π)) = α + β 1 * x1 + + … + β k * xk = α + x β. 6. If we define p as the probability that the outcome is 1, the multiple logistic regression model can be written as follows: 11. Note, also, that in this example the step function found a different model than did the procedure in the Handbook. For binary response Y ji and a vector of explanatory variables X, the logistic Feb 20, 2020 · The formula for a multiple linear regression is: = the predicted value of the dependent variable. The original Titanic data set is publicly available on Kaggle. 07%). A multiple regression model that might describe this relationship is (12-1) May 15, 2017 · test_y. As a result, it is particularly useful for assess and adjusting for confounding. In the next two lessons, we study binomial logistic regression, a special case of a generalized linear model. Type #1: Binary Logistic Regression. 3. The response variable is binary. In this section, we introduce how to adapt the traditional logistic regression model to multiple classification task. = the y-intercept (value of y when all other parameters are set to 0) = the regression coefficient () of the first independent variable () (a. The outcome in logistic regression analysis is often coded as 0 or 1, where 1 indicates that the outcome of interest is present, and 0 indicates that the outcome of interest is absent. But let’s begin with some high-level issues. The likelihood Examples of logistic regression. This generalizes the General Linear Model into a GENERALIZED LINEAR MODEL (GliM). Similar to a simple linear regression model, a multiple linear regression model assumes a observation specific mean μi for the i -th response variable Yi . People’s occupational choices might be influenced by their parents’ occupations and their own education level. The difference between logistic regression and multiple logistic regression is that more than one feature is being used to make the prediction when using multiple logistic regression. Introduction to Multinomial Logistic Regression. 1 - Logistic Regression. proc reg; model crpl=bwkg1 race sex age bmi cursmk; run;. However, researchers must pay attention to model building, avoiding just feeding software with raw data and going forward to results. For each training data-point, we have a vector of features, x i, and an observed class, y i. We can either interpret the model using the logit scale, or we can convert the log of odds back to the probability such that. This type of statistical model (also known as logit model) is often used for classification and predictive analytics. , Modeled proportion of single drivers who drink alcohol), enter Age for the Category (X) axis, click Next to go to Step 4, and Click Finish. Logistic regression is one of the most utilised statistical analyses in multivariable models especially in medical research. g. This article will focus on the implementation of logistic regression for multiclass classification problems. 4 considers a model that predicts the number of days absent using three predictors: ethnic background (eth), gender (sex), and learner status (lrn). k. The principles of simple linear regression lay the foundation for more sophisticated regression methods used in a wide range of challenging settings. This logistic function is a simple strategy to map the linear combination “z”, lying in the (-inf,inf) range to the probability interval of [0,1] (in the context of logistic regression, this z will be called the log(odd) or logit or log(p/1-p)) (see the above plot). 5) (14. We are going to use the train_x and train_y for modeling the multinomial logistic regression model and use the test_x and test_y for calculating the accuracy of our trained multinomial logistic regression model. We can study the relationship of one’s occupation choice with education level and father’s occupation. Yi ∣ μi, σind ∼ Normal(μi, σ), i = 1, ⋯, n. Logistic regression uses a method known as maximum likelihood estimation to find an equation of the following form: log[p(X) / (1-p(X))] = β 0 + β 1 X 1 + β 2 X 2 + … + β p X p. 4 Model Fitness Evaluation 1. Multinomial Logistic Regression: Multinominal logistic analysis works with three or more classifications. In this article, we discuss logistic regression analysis and the limitations of this technique. The model 2. For example, 3 to 1 odds is another way of saying that the P (Y=1) is 0. The. 83) when including stress in the model. Is this coefficient significantly different from 0? Solution: Note that cond_new is a two-level categorical variable that takes value 1 when the game is new and value 0 when the game is used. The log odds of incident CVD is 0. It is an extension of simple logistic regression, which only considers one independent variable. We will discuss these Apr 4, 2024 · Logistic regression is the appropriate regression analysis to conduct when the dependent variable is dichotomous (binary). 4 for additional details about each variable. Let p be the proportion of one outcome, then 1-p will be the proportion of the second outcome. Lecture 19: Multiple Logistic Regression – p. It was then used in many social science applications. A multiple regression model is a linear model with many predictors. β 0 = intercept. Look at various descriptive statistics to get a feel for the data. Compare the coefficients of the each variable with the Mar 22, 2013 · Summary This chapter contains sections titled: Introduction The Multiple Logistic Regression Model Fitting the Multiple Logistic Regression Model Testing for the Significance of the Model Confidenc a bit more on the logistic regression cost function. I am assuming that you already know how to implement a binary classification with Logistic Regression. P-value of Hosmer and Lemeshow goodness of fit test is 0. Step #7: Evaluate the Model. Logistic regression is a predictive modelling algorithm that is used when the Y variable is binary categorical. For logistic regression, there are only two possible values of response (zero and one), and the predicted responses’ values should Like with the smf. Confounding and Interaction 4. Aug 30, 2018 · Introduction. Logistic regression models a relationship between predictor variables and a categorical response variable. The probability of that class was either p, if y i =1, or 1− p, if y i =0. Mar 15, 2018 · Logistic Regression was used in the biological sciences in early twentieth century. whether an image is of a cat, dog, lion, etc. logit() logistic regression function by adding the respective column names on the right hand side of the formula string. Logistic regression assumes: 1) The outcome is dichotomous; 2) There is a linear relationship between the logit of the outcome and each continuous predictor variable; 3) There are no influential cases/outliers; 4) There is no multicollinearity among the predictors. Examples of multinomial logistic regression. See full list on statstest. Keywords: Biostatistics, logistic models A logistic regression model describes a linear relationship between the logit, which is the log of odds, and a set of predictors. 13/44 Sep 5, 2020 · Logistic regression is a very popular machine learning technique. Logistic regression fits a linear regression model to the log odds. Step #6: Fit the Logistic Regression Model. What makes logistic regression different from linear regression is that you do not measure the \(Y\) variable directly; it is instead the probability of obtaining a particular value of a nominal variable. It is assumed that the response variable can only take on two possible outcomes. ), and the binary logistic regression generalized to multinomial logistic regression. The odds are simply calculated as a ratio of proportions of two possible outcomes. Under this framework, a probability distribution for the target variable (class label) must be assumed and then a likelihood function defined that calculates the probability of observing For example, you could use multinomial logistic regression to understand which type of drink consumers prefer based on location in the UK and age (i. Logistic regression is a type of generalized linear model (GLM) for response variables where regular multiple regression does not work very well. People have often seen odds used in reference to betting. In general, we write the model as. Multiple logistic regression can be determined by a stepwise procedure using the step function. Interpret the coefficient for the game’s condition in the model. sns. Now we perform a multiple logistic regression analysis with conflict_dich, sex, year, age_cat, qual, stress, and health_dich . Then, fit your model on the train set using fit () and perform prediction on the test set using predict (). # import the class from sklearn. Since the outcome is a probability, the dependent variable is bounded Dec 26, 2021 · I could suggest plotting the logistic regression using. The interpretation of the coeffiecients are not straightforward as they Models can handle more complicated situations and analyze the simultaneous effects of multiple variables, including combinations of categorical and continuous variables. Logistic Regression - Next Steps. In the multiple linear regression model, Y has normal distribution with mean. when there are k predictors. 2. You can do this by using scale=none and aggregate=(smoke ui ptd) in the model options. Example 1. These factors may include what type of sandwich is ordered (burger or chicken), whether or not fries are also ordered, and age of Logistic regression is a frequently used method because it allows to model binomial (typically binary) variables, multinomial variables (qualitative variables with more than two categories) or ordinal (qualitative variables whose categories can be ordered). 25 along with the variables of known clinical importance. However, the association is still significant (P=0. OpenIntro Statistics. It does assume a linear relationship between the input variables with the output. , the dependent variable would be "type of drink", with four categories – Coffee, Soft Drink, Tea and Water – and your independent variables would be the nominal variable, "location in UK May 21, 2023 · The comparison between the multiple regression model and the logistic regression model showed that the logistic regression model is the most appropriate for determining the relationship between Logistic regression with many variables Logistic regression with interaction terms In all cases, we will follow a similar procedure to that followed for multiple linear regression: 1. oh ll vy yo pa cg nq vg lf uv