Tutorials

Design

The package is centered around one function, report(), which goal is to transform a Julia object into readable text. It also provides useful general and domain-specific functions to efficiently process psychological data.

Simulate some Data

Let's start by simulating some correlated data:

using Psycho  # Import the Psycho package

# Simulate some data wit ha specified correlation coefficient (0.3)
data = simulate_data_correlation(0.3)

# Describe the data
report(data)

The data contains 100 observations of the following variables:
  - y (Mean = 0 ± 1.0 [-2.32, 2.6])
  - Var1 (Mean = 0 ± 1.0 [-3.16, 2.01])

As we can see, we have successfully generated two numeric variables, y and Var1. Moreover, the report() function works on a DataFrame and provide a quick and convenient description of your data.

Fit a Linear Regression (LM)

using GLM  # Import the package for fitting GLMs

model = lm(@formula(y ~ Var1), data)
report(model, std_coefs=false)

We fitted a linear regression to predict y with Var1 (Formula: y ~ 1 + Var1). The model's explanatory power (R²) is
of 0.09 (adj. R² = 0.08). The model's intercept is at -0.0. Within this model:
  - Var1 is significant (Coef = 0.3, t(98) = 3.11, 95% CI [0.11; 0.49], p < .01) and can be considered as small (Std. Coef = 0.3).

Applying the report() function to a linear model returns the model's formula and a general index of the model's predictive performance (here, the normal and adjusted R²). It also reports all the parameters (the "effects" in psychology) and their characteristics: the coefficient (β), the statistic (the t value), degrees of freedom, the confidence interval and the p value. It also returns, by default, the standardized coefficients (which in, in this case, the same as the raw one as our data was generated standardized). It is used as an index of effect size and interpreted with rules of thumb (Cohen's (1988) by default). In our example, the regression coefficient of Var1 is indeed the one that we specified (0.3): everything worked correctly.

Fit a Multiple GLM

Let's fit a more complex model involving more variables and a binomial outcome (made of zeros and ones).

# Simulate some data suited for logistic regression with multiple groups
data = simulate_data_logistic([[0.3, 0.5], [0.1, 0.3]])

# Describe the data
report(data)

The data contains 200 observations of the following variables:
  - y (Mean = 0.72 ± 0.45 [0.0, 1.0])
  - Var1 (Mean = 0 ± 1.01 [-2.37, 2.44])
  - Var2 (Mean = 0.06 ± 0.95 [-2.11, 2.67])
  - Group (1DS, 50.0%; 2QC, 50.0%)

We generated a dataset with one outcome (0 and 1), two numeric variables (Var1 and Var2) and one factor (Group) with two levels. To fit a logistic model (a subtype of GLMs suited for binomial outcomes), we do as previously, but with writing glm instead of lm and adding an additional argument at the end to specify the Binomial nature of the model.

model = glm(@formula(y ~ Var1 + Var2 * Group), data, Binomial())
report(model)

We fitted a logistic regression to predict y with Var1, Var2 and Group (Formula: y ~ 1 + Var1 + Var2 + Group + Var2 & Group).
The model's explanatory power (Tjur's R²) is of 0.07. The model's intercept is at 1.42. Within this model:
  - Var1 is not significant (Coef = 0.25, z(195) = 1.42, 95% CI [-0.1; 0.59], p > .1) and can be considered as very small (Std. Coef = 0.25).
  - Var2 is not significant (Coef = 0.55, z(195) = 1.96, 95% CI [-0.0; 1.1], p = .05) and can be considered as very small (Std. Coef = 0.53).
  - Group: 2HV is not significant (Coef = -0.34, z(195) = -0.96, 95% CI [-1.03; 0.35], p > .1) and can be considered as very small (Std. Coef = -0.34).
  - Var2 & Group: 2HV is not significant (Coef = -0.01, z(195) = -0.03, 95% CI [-0.73; 0.7], p > .1) and can be considered as very small (Std. Coef = -0.01).

Mixed Models

WIP

Bayesian Models

WIP