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14. Modeling exercises⚓︎

Module items⚓︎

R Script file⚓︎

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

source(url("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/regression/docs/assets/r-scripts/0_packages_data.R")); 
download.file("https://raw.githubusercontent.com/ttezcann/ssric-reg/refs/heads/main/regression/docs/assets/r-scripts/14-modeling-exercises.R", "14-modeling-exercises.R"); 
file.edit("14-modeling-exercises.R")

Lab assignment⚓︎

Modeling exercises

Sample lab assignment⚓︎

Sample: Modeling exercises

Learning outcomes⚓︎

  1. Practice logistic regression analysis

Suggested reading⚓︎

  • 📖
    Sperandei, Sandro. 2014. “Understanding Logistic Regression Analysis.” Biochemia Medica 24(1):12–18. doi:10.11613/BM.2014.003

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⚓︎

Diagram of a ball-toss activity with one toss line leading to a wide trash can and another to a narrow trash can. Students throw toward the wide trash can from 6, 10, and 15 feet away, and toward the narrow trash can from 5, 8, and 12 feet away.

  • 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 -.->|May affect| E
    C02 -.->|May affect| E
    I0 -.->|May affect| E
    M0 -.->|May affect| E

[[Logistic regression]] #code⚓︎

  • Model code 
    1
2
    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
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    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)

    Code explanation

    • 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.

[[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 template. Click to expand

First section: The significance levels
Mention which variables [variable labels] are statistically significant, and which variables are statistically nonsignificant (if any). Variables with at least one asterisk (*) are statistically significant.

[Variable label of significant factor variable 1], [Variable label of significant factor variable 2], [Variable label of significant factor variable 3]... are statistically significant factors of [Variable label of outcome variable] since the p values are less than 0.05. [If any]: [Variable label of significant factor variable 4], [Variable label of significant factor variable 5]... is(are) not statistically significant factor(s) of [Variable label of outcome variable] since the p value(s) is(are) greater than 0.05.

Second section: The explanation of odd ratios
Mention how significant factor variables increase or decrease the odds of the outcome variable happening, using the “Odd ratios” column. When reporting the odd ratios of continuos variables, ensure that the sentence includes the unit of analysis (one unit, a day, a score, a year, a dollar, etc.) of both the factor variables and the outcome variable. When reporting the odd ratios of dummy variables, ensure that the sentence includes omitted - comparison category. When reporting the negative odd ratios of the dummy factor variables, make sure to divide 1 by the odd ratios.

A [unit/day/score,year,dollar (unit of analysis of continuous factor variable1)] increase in [Variable label of significant continuous factor variable1] increases/decreases the odds of [Variable label of outcome variable] by [odd ratio + times.

[Variable label of included dummy variable1] increases/decreases the odds of [Variable label of outcome variable] by [odd ratio + times

[Variable label of included dummy variable2] increases/decreases the odds of [Variable label of outcome variable] by [odd ratio + times

Note: Do not mention nonsignificant variables here.

Third section: The explanation of standardized odd ratios
Mention the strongest factor variables of the outcome variable using the "Standardized odd ratios" (Std. OR column) in order. Only mention the statistically significant ones. "Standardized odd ratio" is an absolute number, which means -.56 is stronger than .45.

The strongest factor of [Variable label of outcome variable] is the [Variable label of first strongest factor variable] (std. OR=0.xx), followed by [Variable label of second strongest factor variable] (std. OR=0.xx), and [Variable label of third strongest factor variable] (std. OR=0.xx).

Note: Do not mention nonsignificant variables here.

Fourth section: The explanation of Tjur R-squared
Report the Tjur R-squared value as a percentage with the statistically significant variables.

The Tjur R-squared value indicates that [Tjur R-squared value] of the variation in [Variable label of outcome variable] can be explained by [Variable label of significant factor variable1], [Variable label of significant factor variable2], [Variable label of significant factor variable3]...

Note: Do not mention nonsignificant variables here.

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 are statistically significant factors of hitting the target since the 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 odd ratios

A foot increase in distance from the trash can decreases the odds of hitting the target by 2.70 times.

Tossing a ball to a narrow trash can decreases the odds of hitting the target by 9.82 times compared to tossing a ball to a wide trash can.

Playing sports regularly increases the odds of hitting the target by 13.70 times compared to not playing sports regularly.

Third section: The explanation of standardized odd ratios

The strongest factor of hitting the target is 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=3.12).

Fourth section: The explanation of Tjur R-squared

The Tjur R-squared value indicates that 64.5% of the variation in hitting the target can be explained by distance from the trash can, tossing a ball to a narrow trash can, and playing sports regularly.