Explore Everyday Empathy Data
Below are histograms of the extent to which specific components of empathy were reported in the face of specific discrete emotions. Data is from a sample of 7,343 surveys, which includes 1,389 opportunities to empathize in everyday life. Choose the component of empathy and the specific emotion you wish to plot from the menus below.
Psychometric Analysis
In Psychology and other social sciences, we often study concepts or constructs that cannot be measured directly 🏃♂️📏 (e.g., depression) using a ‘scale’ or a set of theoretically related questions (e.g., the Center for Epidemiological Studies Depression Scale). From a Classical Test Theory perspective, we assume the scale measures only one thing (unidimensional) and all questions (or items) predict this underlying, or latent, thing equally well (tau-equivalence). When these assumptions are met, we can use Cronbach’s alpha to get at the reliability or internal consistency of our scale.
When they are not met, Mcdonald’s omega is an alternative measure of reliability. With omega, we estimate our underlying construct with a ‘general factor’ and calculate how well the items predict this thing, rather than assuming they load equally. Omega can also be extended to ‘multi-dimensional’ scales such as the Big Five5️⃣Inventory which has five dimensions of personality. With multi-dimensional scales, omega total gives us a sense of how reliable the measure is overall, and omega hierarchical gives us a sense of how much this reliability is due to the general factor. Combining these two can be informative. If omega total is high, and omega hierarchical is low, this suggests our scale may be multi-dimensional. If omega hierarchical is very close to omega total, this suggests the general factor explains much of the reliability and could be unidimensional.
Item Response Theory makes the item the unit of analysis rather than the test. Item Response Theory (IRT) assumes that items tap an underlying latent construct, but it seeks to estimate the probability of individuals answering specific items in particular ways based on their underlying level of the trait (theta). Furthermore, IRT also considers features of the item itself, such as the relative difficulty and discrimination of the item. Developed in the context of assessing ability, IRT models can track the probability of getting an item right as theta increases, but this can also be extended to items with more than two options (polytmous). There, IRT models can show the probability of selecting a particular option (e.g., 1, 2, 3, 4, or 5), as well as the relative information provided by the item, at different levels of the underlying trait.
Another approach leaves ‘latent’ dimensions behind to look at direct relationships between items. This can be done using Network Analysis. In this approach, we might look at how the questions relate to one another controlling for all other relationships in the data using a ‘partial correlation network’. To avoid having too many false positive relationships in the network, we can shrink the relationships using ‘regularization’, for example, using graphical lasso (🤠). We can then plot this network of correlations in an undirected network graph, with individual questions represented as circles (nodes) which are connected by lines (edges) whose strength is illustrated by the thickness of the line, and whose direction is illustrated with color (e.g., green = positive, red = negative). The structure of this network can be informative as nodes placement in space is reflective of their relationships. We can also look at properties of specific items such as influence in the network based on the number and strength of connections.
With the app below you can upload your data, indicate your items and how they should be coded, and input how many dimensions your scale has (1 or more). Using this info., the app will do a few things, including obtain and plot average scale scores, and calculate alpha and omega (hierarchical, total, and asymptotic), as well as perform an Exploratory Factor Analysis, and plot the items in a glasso network graph. I’m very open to correcting or improving the app, so let me know if you have suggestions or critiques. My next step will be to add some analysis and plots from an Item Response Theory perspective, so stay tuned for that. In the meantime, feel free to check it out.
Link to Psychometrics shiny: https://gregdepow.shinyapps.io/shiny2
Response Surface Analysis
NOTE: Full model always plotted by default, model selection only working for the summary. Working on a fix. First plot shows which model performed best based on model weight. Choose the best performing model from the list (or another if you wish) and it will output that model summary.
Response surface analysis using the RSA package. In the shinyapp below, you can upload your own data and perform response surface analysis (RSA). Imagine two predictor variables and their range of values as a two-dimensional space. A given individual might land anywhere in that space. RSA allows us to estimate the value of an outcome variable of interest for all points in that space. The RSA package (https://cran.r-project.org/web/packages/RSA/RSA.pdf) by Felix Schönbrodt is doing the heavy-lifting here. What the shinyapp does is allow you to upload your data, choose two predictor variables and an outcome variable, and access aspects of the RSA package. When you click the Run RSA button, the app will use the RSA function to fit the default list of models (see model options for list), then use the aictab function to compare the models and display the winning model based on which is most probable given the data. It will also provide summary output for any model you select from the list. It currently plots the full model rather than the selected model, so you might look at the plot as the most complex model of the relationship between your variables given the data. However, if the aictab plot shows a model other than the full model, the relationship is likely better explained by the simpler model.
Some reading is needed to apply and interpret these models correctly, I am on this journey myself. I will supply some starting points below. The shiny app will input the median in place of missing values in your data, so you should ensure you have no missing values, your data is correctly structured, and your variables are appropriately-centred. Edwards & Parry advise centering such that 0 is the midpoint of the scale. *The shiny app will not display errors, so if you want to use RSA for research purposes, I recommend using and citing the RSA package directly in R–it is very user friendly. I will try to make the app more robust and possibly add features in the future. In the meantime, feel free to have some fun mapping out your variables in a 3D space.
#This code should let you implement the analysis from the shiny app in R. This will also afford you more flexibility in specifying different kinds of models and in customizing the plot.
install.packages("RSA")
library(RSA)
setwd("path of folder you are working in") # set working directory
data <- read.csv(file = "YourDataFile.csv") # Read in data
model <- RSA(formula = DV ~ IV1 * IV2, data = data) # Run RSA, fitting a number of models. Swap out variable names for your variables of interest.
aictab(model, plot = TRUE) # compare fitted models to see which is most probable given the data (model weight)
plot(model, model = "model name") # use plot to get a 3d plot of your desired model (e.g. the winning model)
summary(model, model = "model name") # use summary to get the stats outputRSA Reading Starters:
https://osf.io/9vk3h/wiki/home/ (Collection of readings with supp. material from Schönbrodt)
https://pubmed.ncbi.nlm.nih.gov/33074694/ (Humberg et al., 2021 Cubic RSA and congruence)
https://onlinelibrary.wiley.com/doi/full/10.1002/per.2169 (Schönbrodt et al., 2021 dyadic RSA)
https://www.skiplab.org/response-surface-analysis (Two papers from Karlson SKIP lab about RSA)
https://doi.org/10.1080/00273171.2021.1884522 (Humberg and Grund, 2021 RSA with missing data)
http://public.kenan-flagler.unc.edu/faculty/edwardsj/EdwardsParry1993.pdf (Poly reg as alt to diff scores)
https://link.springer.com/chapter/10.1007/978-1-4612-4380-9_22 (Draper, 1992 intro to Box and Wilson)
https://www.jstor.org/stable/2983966 (seminal Box and Wilson, 1951)
Link to RSA shiny on it’s own: https://gregdepow.shinyapps.io/shiny6/
Note: All apps created using R shinyapps. Data presented here for descriptive purposes. This data is exploratory and correlational, meaning causation cannot be established and findings should be replicated with future research. We should be particularly cautious drawing conclusions about emotions with smaller samples. Data is at the observation level, meaning a single participant may have multiple reports in the figure, depending on how often they reported observing a specific emotion. See here for a description of data collection and further analysis: paper and here for the data.