Boda-boda riders
MAB7203 Conditional Logistics Assignment: (Instructor: Nazarius Mbona Tumwesigye)
Robert Serunjogi (2024/HD07/22352U)
2025-04-07
Table of contents
1 Conditional Logistics
2
1.1
Boxplot by Age . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.2
Characteristics table . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.3
Conditional Logit Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4
Model diagnostics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4.1
Wald’s test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
1.4.2
Areas under the curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.4.3
Residuals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.5
Conditional logistic table
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.6
McNemar’s Chi-squared Test . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1
1
Conditional Logistics
1.1
Boxplot by Age
The Controls (median age = 30) were significantly older compared to the cases (median age =
28).
1.2
Characteristics table
1.3
Conditional Logit Model
boda_clr <- clogit(casecont ~ takealcohol
+ agegrp
+ strata(matchedcase)
,data = bodaboda)
1.4
Model diagnostics
1.4.1
Wald’s test
Table 1: Wald Test Results
takealcoholYes
agegrp18-24
agegrp30-34
Characteristic
p-value
takealcoholYes
agegrp18-24
agegrp30-34
0.000
0.000
0.055
2
agegrp35-39
agegrp40+
1.4.2
Characteristic
p-value
agegrp35-39
agegrp40+
0.375
0.053
Areas under the curve
# Get actual outcome variable (0/1) and predicted values
actual_outcome <- bodaboda$casecont #assuming this is the 0/1 outcome
predicted_scores <- predict(boda_clr, type = "lp")# linear predictor(log odds)
# ROC curve
roc_curve_boda_clr <- roc(actual_outcome
, predicted_scores)
Setting levels: control = 0, case = 1
Setting direction: controls < cases
# Plot
plot(roc_curve_boda_clr, main = "ROC Curve for Clogit Model")
text(0.6, 0.2, labels = paste("AUC ="
, round(auc(roc_curve_boda_clr), 3)))
# Print AUC
auc_value <- auc(roc_curve_boda_clr)
print(auc_value)
Area under the curve: 0.7092
3
Characteristic
Marital Status
DIVORCED/SEPARATED
MARRIED/COHABITING
SINGLE/WIDOWED
Age Group
25-29
18-24
30-34
35-39
40+
Takes Alcohol
drugs
(Missing)
cargo
(Missing)
Passengers
1 Passenger
2+ Passengers
(Missing)
1
2
Control N = 2891
Case N = 2891
Overall N = 5781
4 (1.4%)
235 (81.3%)
50 (17.3%)
20 (6.9%)
191 (66.1%)
78 (27.0%)
24 (4.2%)
426 (73.7%)
128 (22.1%)
99 (34.3%)
39 (13.5%)
64 (22.1%)
48 (16.6%)
39 (13.5%)
52 (18.0%)
2 (0.9%)
75
12 (5.7%)
77
86 (29.8%)
79 (27.3%)
77 (26.6%)
29 (10.0%)
18 (6.2%)
86 (29.8%)
5 (1.7%)
0
10 (3.5%)
3
185 (32.0%)
118 (20.4%)
141 (24.4%)
77 (13.3%)
57 (9.9%)
138 (23.9%)
7 (1.4%)
75
22 (4.4%)
80
135 (63.4%)
78 (36.6%)
76
145 (50.3%)
143 (49.7%)
1
280 (55.9%)
221 (44.1%)
77
p-value2
<0.001
<0.001
<0.001
0.7
0.2
0.004
n (%)
Pearson’s Chi-squared test; Fisher’s exact test
AUC = 0.71 suggests that your model has good discrimination ability.
It means there is a 71% chance that the model will correctly assign a higher predicted score to
a true case than to a control chosen at random.
1.4.3
Residuals
# Ensure residuals are correctly computed
boda_clr_residuals <- residuals(boda_clr, type = "deviance")
# Ensure fitted values are computed correctly
boda_clr_values <- fitted(boda_clr)
# Create residual plot
ggplot(data = data.frame(boda_clr_values, boda_clr_residuals)
, aes(x = boda_clr_values, y = boda_clr_residuals)) +
geom_point() +
geom_hline(yintercept = 0, color = "red") +
labs(x = "Fitted Values"
, y = "Residuals"
, title = "Residual Plot for the Model") +
theme_tq()
4
Characteristic
OR
Takes Alcohol
No
—
Yes
2.29
Age Group
25-29
—
18-24
2.79
30-34
1.59
35-39
0.78
40+
0.53
Abbreviations: CI = Confidence Interval, OR = Odds Ratio
95% CI
p-value
—
1.47, 3.55
<0.001
—
1.63, 4.78
0.99, 2.55
0.44, 1.36
0.28, 1.01
<0.001
0.055
0.4
0.053
The model appears to fit the data reasonably well, as residuals are mostly randomly scattered
around zero with no strong systematic patterns.
1.5
Conditional logistic table
tbl_boda_clr <- tbl_regression(boda_clr
,exponentiate = T
,label = takealcohol ~ "Takes Alcohol")
tbl_boda_clr
Reference groups for age was 18-24
The odds of men who consumed alcohol having an accident were 2.29 times (OR = 2.29, 95%
CI: 1.47, 3.55, p < 0.001) those who do not drink alcohol.
This showed a statistical significance and a strong positive association between alcohol consumption and the likelihood of accidents.
5
bb_cc <- bodaboda %>%
select(casecont, alcohol, matchedcase)
1.6
McNemar’s Chi-squared Test
# Reshape the dataset from long to wide format
bb_wide_data <- bb_cc %>%
pivot_wider(names_from = casecont
, values_from = alcohol
, names_prefix = "alcohol")
# Create a 2x2 contingency table
contingency_table <- table(bb_wide_data$alcohol1
, bb_wide_data$alcohol0)
# Perform McNemar's test
result1 <- mcnemar.test(contingency_table,correct=T)
result2 <- mcnemar.test(contingency_table,correct=F)
result3 <- mcnemar.exact(contingency_table)
exact_mcnemar_result <- exact2x2(contingency_table)
mcc(table = table(bb_wide_data$alcohol0
, bb_wide_data$alcohol1))
$data
Controls
Cases
Unexposed Exposed Total
Unexposed
168
69
237
Exposed
35
17
52
Total
203
86
289
$mcnemar_chi2
McNemar's Chi-squared test
data: mcc_table
McNemar's chi-squared = 11.115, df = 1, p-value = 0.0008561
$mcnemar_exact_p
Exact McNemar significance probability
0.001108621
$proportions
Proportion with factor
Cases Controls
0.8200692 0.7024221
$statistics
6
estimate [95% CI]
statistic
estimate
lower
upper
difference 0.1176471 0.04636803 0.1889261
1.1674877 1.06580258 1.2788743
ratio
rel. diff. 0.3953488 0.21462362 0.5760741
odds ratio 1.9714286 1.29443899 3.0515292
McNemar’s Chi-squared Test: McNemar’s test is used to compare paired proportions. In this
context, it tests whether the proportion of exposed is different between cases and controls.
The small p-value (0.0008561) indicates that there is a statistically significant difference in
exposure status between cases and controls, meaning cases were significantly more likely to
have been exposed to accidents compared to controls.
McNemar’s test, which is more accurate for small sample sizes. The p-value is also statistically
significant, confirming the finding from the chi-squared test.
A higher proportion of cases was exposed (82.01%) compared to controls (70.24%). The proportion of exposed is higher in cases by 11.76%. The confidence interval shows the range where
the true difference likely lies.
Ratio of proportions: 1.1675 (95% CI: 1.0658, 1.2789). The proportion of exposed in cases is
1.1675 times the proportion of exposed in controls.
The odds of exposure among cases was 1.9714 times (95% CI: 1.2944, 3.0515) the odds of
exposure among controls. This is a key measure of association in case-control studies.
7