Creating Data<\/strong><\/span><\/p>\n We will create two fake data sets:<\/p>\n <\/p>\n Exponentially Weighted Moving Average (EWMA)<\/strong><\/span><\/p>\n We will apply an exponentially weighted moving average to the data as this type of equation requires within column aggregation.<\/p>\n EWMA is calculated as:<\/p>\n EWMA_t = lamda*x_t + (1 – lamda) * Z_t-1<\/strong><\/em><\/p>\n Where:<\/p>\n accumulate()<\/strong><\/span><\/p>\n Within {tidyverse<\/strong>} we will use the accumulate()<\/strong> function, which allows us to create this type of within column aggregation. The function takes a few key arguments:<\/p>\n Here is what it looks like in our smaller data set, df_2<\/strong><\/em><\/p>\n <\/p>\n Here, we are using mutate()<\/strong> to create a new column called ewma. <\/strong>We used accumulate()<\/strong> and passed it the value<\/strong> column, which is the column of our data that has our observations and our function for calculating ewma, which follows the tilde.<\/p>\n Within this function we see .y, <\/strong>the most recent observation and .x<\/strong>, the lag ewma value. By default, the first row of the new ewma<\/strong> column will be the first observation in the value<\/strong> row. Here is what the first few rows of the data look like:<\/p>\n Now that new column has been created we can visualize the observed values and the EWMA values:<\/p>\n Applying the approach to all of the subjects<\/strong><\/span><\/p>\n To apply this approach to all of the subjects in our data we simply need to use the group_by()<\/strong> function to tell R that we want to have the algorithm start over whenever it encounters a new subject ID.<\/p>\n And then we can plot the outcome:<\/p>\n Pretty easy!<\/p>\n What if we want the start value to be 0 (or something else) instead of the first observation?<\/strong><\/span><\/p>\n This is a quick fix within the accumulate() <\/strong>function by using the .init<\/strong> argument and simply passing it whatever value you want the new column to begin with. What you need to be aware of when you do this, however, is that this argument will add an additional observation to the vector of data and thus we need to remove the last row of the data set to ensure that {tidyverse<\/strong>} can perform the operation without giving you an error. To accomplish this, when I pass the value <\/strong>column to the function I add a bracket and then minus 1 of the total count, n()<\/strong>, of observations in that column.<\/p>\n![\"\"](\"https:\/\/optimumsportsperformance.com\/blog\/wp-content\/uploads\/2021\/10\/Screen-Shot-2021-10-24-at-8.18.47-PM.png\")
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\nThis type of function is pretty common in excel but it can be a little tricky in R. I’ve been meaning to do a blog about this after a few questions that I’ve gotten and Aaron Pearson<\/a><\/strong><\/span> reminded me about it last night, so let’s try and tackle it.<\/p>\n\n
\r\n\r\nlibrary(tidyverse)\r\n\r\n## simulate data\r\nset.seed(1)\r\nsubject <- rep(LETTERS[1:3], each = 50)\r\nday <- rep(1:50, times = 3)\r\nvalue <- c(\r\n round(rnorm(n = 20, mean = 120, sd = 40), 2),\r\n round(rnorm(n = 10, mean = 150, sd = 20), 2),\r\n round(rnorm(n = 20, mean = 110, sd = 30), 2),\r\n round(rnorm(n = 20, mean = 120, sd = 40), 2),\r\n round(rnorm(n = 10, mean = 150, sd = 20), 2),\r\n round(rnorm(n = 20, mean = 110, sd = 30), 2),\r\n round(rnorm(n = 20, mean = 120, sd = 40), 2),\r\n round(rnorm(n = 10, mean = 150, sd = 20), 2),\r\n round(rnorm(n = 20, mean = 110, sd = 30), 2))\r\n\r\ndf_1 <- data.frame(subject, day, value) df_1 %>% head()\r\n\r\n### Create a data frame of one subject for a simple example\r\ndf_2 <- df_1 %>%\r\n filter(subject == "A")\r\n\r\n<\/pre>\n
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\r\ndf_2 <- df_2 %>%\r\n mutate(ewma = accumulate(value, ~ lamda * .y + (1 - lamda) * .x))\r\n\r\n<\/pre>\n
<\/a><\/p>\n<\/a><\/p>\n\r\n\r\ndf_1 <- df_1 %>%\r\n group_by(subject) %>%\r\n mutate(ewma = accumulate(value, ~ lamda * .y + (1 - lamda) * .x))\r\n\r\n<\/pre>\n
<\/a><\/p>\n\r\ndf_2 %>%\r\n mutate(ewma = accumulate(value[-n()], ~ lamda * .y + (1 - lamda) * .x, .init = 0)) %>%\r\n head()\r\n<\/pre>\n