The arcsine transformation in r does not just use a single built-in function rather it is two embedded functions. Those functions are the arcsine function and square root function. They work together to produce arcsine transformation. This simple transformation is most useful when dealing with data points that are close to one or zero because it stretches out the data in these two areas.
Description of the transformation.
The arcsine transformation is a combination of the arcsine and square root transformation functions. It takes the form of asin(sqrt(x)) where x is a real number from 0 to 1. It is a square root transformation that helps in dealing with probabilities, percents, and proportions that are close to either one or zero. Because the square root function does not take negative values you will get an error message if you try using one in this situation. Also, because the arcsine function does not take a value greater than one, you have to convert percentages to a fraction by dividing it by a hundred, or else you will get an error message instead of your transformed data.
Explanation of the transformation.
The arcsine transform function is similar to the logit transformation or log transformation in that it makes some statistical elements, such as logistic regression easier to see. In this case, we are using the inverse sine or arcsin. This inverse action expands the variable range while squishing it towards the center making the extremes easier to see.
# arcsine transformation in r > asin(sqrt(0.5))  0.7853982
This simple example illustrates the results of this combination arcsine transform formula in that it expands 0.5 to 0.7853982. This stretching in the transformed data is even more significant when the independent variable or dependent variable value is close to one or zero. This does, however, result in a limitation that the input value needs to be in the range of zero to one.
Examples of the transformation in action.
The arcsine data transformation can include input from vectors, and data frames as long as the independent variable and dependent variable values are numeric and in the correct range- no negative numbers, in a linear model, etc. The following examples are based on percentages and in such situations you need to divide the percentage by one hundred to get meaningful data and avoid error terms on top of it.
# how to do arcsine transformation in r programming > x = c(0,10,20,30,40,50,60,70,80,90,100) > asin(sqrt(x/100))  0.0000000 0.3217506 0.4636476 0.5796397 0.6847192 0.7853982 0.8860771  0.9911566 1.1071487 1.2490458 1.5707963
This example has a numeric output but it does provide an excellent example of the type output that you can expect in this combined function.
# arcsine transformation in r example > x = c(0:100) > y = asin(sqrt(x/100)) > plot(x, y)
This example produces a graph of 0 to 100%. If you run this code it will provide a good visual illustration of the pattern of data that is produced, including how the data points spread out near one and zero.
Application of this transformation.
There are many applications of the arcsine square root transformation in proportion data science it comes in handy when testing linear regression models with a small equal variance because it allows an expansion of the linear model equal variance to make the differences clearer in the transformed value after the arcsine square root transformation. It is also helpful when dealing with a normal distribution because the fractions of the data are quite small on the ends. These common transformations helps to spread those out to more visible pattern or linear relationship with better interpretability. This process can be used at any place where do you need to visualize differences close to one or zero.
What makes this power transformation different is that it is not a single function but a combination of two data transformation functions. These common transformations are very helpful with interpretability when you are trying to look at proportion data at the extreme ends of a confidence interval, probabilities, percents, and proportions.
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