14. Modeling exercises

Module items¶

R Script file code¶

[[Copy the code]] below ➜ Paste into [[RStudio console]] ➜ Hit Enter

source(url("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/docs/assets/attachments/data/0-packages-data-trashball.R"));
(function(f="14-modeling-exercises.R"){if(!file.exists(f)){download.file("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/docs/assets/attachments/modules/14.-modeling-exercises/14-modeling-exercises.R",f,mode="wb");file.edit(f)}else{download.file("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/docs/assets/attachments/modules/14.-modeling-exercises/14-modeling-exercises.R",gsub(".R","-original.R",f),mode="wb");file.edit(gsub(".R","-original.R",f))}})()

When this R script file opens in a new tab, [[Save R script file|save your previous R script file(s)]], and
- Close the previous tabs (R Script files), which you can find later in the [[Files tab]].

Lab assignment¶

Modeling exercises

Sample lab assignment¶

Sample: Modeling exercises

Learning outcomes¶

Apply logistic regression to a different dataset

The content of the module¶

We will use the dataset created during in-person classes in previous semesters.
189 students tossed a ball into a trash can from various distances.
Those 189 students also filled out a survey with information (both relevant and irrelevant) to predict targeting trash can.

Trashball: Logistic regression classroom activity¶

- The activity involved students attempting to toss a ball into a trash can from various distances.
- Students targeted the wide trash can from 6, 10, 15-feet away and the narrow trash can from 5, 8, 12-feet away.

Recorded data and survey¶

Variable name	Variable label	Variable type	Question wording and response categories	Comparison category
`success`	Hitting the target	Binary-Dummy	Recorded data: (1: Success; 0: No success)
`distance`	Distance from the trash can	Continuous	Recorded data: (Min: 5, Max: 15 feet)
`narrow`	Tossing a ball to a narrow trash can	Binary-Dummy	Recorded data: (1: Tossing a ball to a narrow trash can; 0: Tossing a ball to a wide trash can )	Tossing a ball to a wide trash can
`sleep`	Having at least seven hours sleep	Binary-Dummy	Did you sleep at least 7 hours last night? (1: Yes; 0: No)	Having less than seven hours sleep
`hungry`	Hunger level	Ordinal ✅	How hungry are you right now? (1: Not hungry at all; 2: Slightly hungry, 3: Moderately hungry, 4: Very hungry; 5: Extremely hungry)
`physicallyactive`	The level of physical activity	Ordinal ✅	How physically active are you on a regular basis? (1: Not at all; 2: Slightly active; 3: Moderately active; 4: Very active; 5: Extremely active)
`regularsports`	Playing sports regularly	Binary-Dummy	Do you play any sports regularly? (1: Yes; 0: No)	Not playing sports regularly
`physicallycoordinated`	The level of physical coordination	Ordinal ✅	Do you consider yourself physically coordinated? (1: Not at all; 2: Slightly; 3: Moderately; 4: Very; 5: Extremely)
`competitive`	The level of competitiveness	Ordinal ✅	How competitive do you consider yourself to be? (1: Not at all; 2: Slightly; 3: Moderately; 4: Very; 5: Extremely)
`outgoing`	The level of outgoingness	Ordinal ✅	Would you describe yourself as outgoing? (1: Not at all, 2: Slightly; 3: Moderately; 4: Very; 5: Extremely)
`nervous`	The level of nervousness	Ordinal ✅	How nervous do you generally feel in new situations? (1: Not at all; 2: Slightly; 3: Moderately; 4: Very; 5: Extremely)
`confidence`	The level of confidence	Ordinal ✅	How confident do you feel in general, day-to-day? (1: Not confident at all; 2: Slightly confident; 3: Moderately confident; 4: Very confident; 5: Extremely confident)

Binary variables are already dummy

Binary variables, success, distance, narrow, sleep, and regularsports, are already recorded as dummy variable, 1-0.

In this analysis, we propose a cause-and-effect relationship in which these factor variables may affect (increase or decrease) the odds of hitting the target.

flowchart LR
    subgraph C0[Continuous factor variable]
        direction BT
        C01[Distance from the trash can]
        C02[Physical coordination]
    end

    subgraph D0[Dummy factor variables]
        subgraph I0[Narrow]
            direction TB
            I1[Narrow trash can]
            I2[Wide trash can]
        end

        subgraph M0[Playing sports regularly]
            direction TB
            M1[1: Yes]
            M2[0: No]
        end
    end

    subgraph O0[Dummy outcome variable]
        E[Success<br><br>1: Hitting <br><br> 0: Not hitting]
    end

    C01 -.->|Association?| E
    C02 -.->|Association?| E
    I0 -.->|Association?| E
    M0 -.->|Association?| E

[[Logistic regression]] #code¶

[[Model code]]

model1 <- glm(dummy_outcome_here ~ factor1_here + factor2_here + factor3_here, data = trashball, family = binomial(link="logit"))
tab_model(model1, show.std = T, show.ci = F, collapse.se = T)

[[Working code]]
- 1 2
  model1 <- glm(success ~ distance + narrow + physicallycoordinated + regularsports, data = trashball, family = binomial(link="logit")) tab_model(model1, show.std = T, show.ci = F, collapse.se = T)
  - Line 1: We put success here ➜ outcome_here; distance here ➜ factor1_here; narrow here ➜ factor2_here; physicallycoordinated here ➜ factor3_here; regularsports here ➜ factor4_here.
    - Outcome variable variable first; then, factor variables separated by plus (+).
  - Line 2: Check the first argument: model1. If this is model1, then we should use model1 here
    - This needs to be model1, otherwise this code won't work.
    - Note that the data argument is different since we use a different dataset: data = trashball.
      - [[Find this working code in the R script file]].
        
        [[Highlighting and running]] this code will generate the output below (which will appear in the [[viewer tab]] of RStudio).

[[Logistic regression]] #output¶

Hitting the target

Factors	Odds Ratios	std. OR	p
(Intercept)	278.29 (336.53)	0.64 (0.18)	<0.001***
Distance from the trash can	0.37 (0.06)	0.03 (0.02)	<0.001***
Tossing a ball to a narrow trash can	0.10 (0.06)	0.32 (0.09)	<0.001***
The level of physical coordination	1.48 (0.41)	1.57 (0.50)	0.156
Playing sports regularly	13.70 (11.49)	3.27 (1.24)	0.002**
Observations	189
R² Tjur	0.645

[[Logistic regression]] with dummy variables #interpretation¶

Logistic regression with dummy variables interpretation sample
- First section: The significance levels
  - Distance from the trash can, tossing a ball to a narrow trash can, and playing sports regularly have statistically significant associations with hitting the target since their p-values are less than 0.05.
  - The level of physical coordination is not a statistically significant factor of hitting the target since the p-value is greater than 0.05.
- Second section: The explanation of odds ratios
  - One additional foot of distance from the trash can is associated with 2.70 times lower odds of hitting the target.
  - Tossing a ball to a narrow trash can is associated with 10.00 times lower odds of hitting the target compared with tossing a ball to a wide trash can.
  - Playing sports regularly is associated with 13.70 times higher odds of hitting the target compared with not playing sports regularly.
- Third section: The explanation of standardized odds ratios
  - The largest standardized association with the odds of hitting the target is for distance from the trash can (std. OR=33.33), followed by playing sports regularly (std. OR=3.27), and tossing a ball to a narrow trash can (std. OR=3.13).
- Fourth section: The explanation of Tjur R-squared
  - The Tjur R-squared value indicates that the model, which includes distance from the trash can, tossing a ball to a narrow trash can, the level of physical coordination, and playing sports regularly, distinguishes between the two groups with a 64.5 percentage-point difference in their average predicted probabilities.

Logistic regression with dummy variables interpretation template
- First section: The significance levels
  - [[Variable label]] of significant [[factor variable]] 1, variable label of significant factor variable 2, variable label of significant factor variable 3... have statistically significant associations with variable label of [[outcome variable]] since their p-values are less than 0.05.
  - [If any]: Variable label of nonsignificant factor variable 4 is not a statistically significant factor of variable label of outcome variable since the p-value is greater than 0.05.
- Second section: The explanation of odds ratios
  - One additional [year/point/unit/score of factor variable 1] of variable label of significant factor variable 1 is associated with [odds ratio] times higher/lower odds of variable label of outcome variable.
  - Variable label of included dummy variable 1 is associated with [odds ratio] times higher/lower odds of variable label of outcome variable compared with variable label of omitted - comparison dummy variable 1.
  - Variable label of included dummy variable 2 is associated with [odds ratio] times higher/lower odds of variable label of outcome variable compared with variable label of omitted - comparison dummy variable 2.
- Third section: The explanation of standardized odds ratios
  - The largest standardized association with the odds of variable label of outcome variable is for variable label of the strongest factor variable (std. OR=[value]), followed by variable label of the second strongest factor variable (std. OR=[value])...
    - When a standardized odds ratio is less than 1, divide 1 by the standardized odds ratio before comparing the sizes of associations.
- Fourth section: The explanation of Tjur R-squared
  - The [[Tjur R-squared]] value indicates that the model, which includes variable label of factor variable 1, variable label of factor variable 2, variable label of factor variable 3..., distinguishes between the two groups with a [Tjur R-squared × 100] percentage-point difference in their average predicted probabilities.

Interpretation explanation
- First section: The significance levels
  - We identify the variable labels of factor variables that have statistically significant associations with the odds of the outcome variable.
    - When the p-value is less than 0.05, we say the factor variable has a statistically significant association with the odds of the outcome.
    - When the p-value is greater than 0.05 (p > 0.05), we say the factor variable is not a statistically significant factor of the outcome.
- Second section: The explanation of odds ratios
  - We use the Odds Ratios column to explain the associations of statistically significant factor variables with the odds of the outcome coded 1.
    - For a numerical factor variable, we explain the odds ratio for a one-unit increase (foot, year, point, score, etc.).
    - For a dummy variable, we compare the included group with the omitted comparison group.
    - When the odds ratio is greater than 1, use the odds ratio and write times higher odds.
    - When the odds ratio is less than 1, divide 1 by the odds ratio and write times lower odds.
- Third section: The explanation of standardized odds ratios
  - We use the std. OR column to compare the relative size of the standardized associations with the odds of the outcome.
    - When the standardized odds ratio is less than 1, divide 1 by the standardized odds ratio.
      
      Note: We do not include nonsignificant factor variables in this section.
- Fourth section: The explanation of Tjur R-squared
  - We report Tjur R-squared as a difference in percentage points between the average predicted probabilities of the two groups.
    - We list all factor variables included in the model, including those that are not statistically significant.
    - Note: Tjur R-squared is not the percentage of variation explained by a logistic regression model.