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<h1 class="title toc-ignore">Regression for Suicide</h1>
</div>
<p>Based on the visualization of suicide analysis, the US national
suicide rates have changed a lot through time. And the differences in
suicide rates by sex, age can be observed. We will detect the group
difference by year, sex, and age by doing regression analysis. Since the
suicide trend for males by various age groups is different from the
suicide trend for females by various age groups, there might a
interaction happening between sex and age. So, interaction term between
sex and age group will be considered in the regression analysis.</p>
The model we have:
<div align="center">
<span class="math inline">\(Suicide~per~100k = \beta_0 + \beta_1
(Year_{i}) + \beta_2 (Sex_{i})+ \beta_3 (Age_{i}) + \beta_4
(Sex_{i}*Age_{i})\)</span>
</div>
<p><br />
</p>
<pre class="r"><code>suicide_df =
read_excel(
"./data/suicide_data.xlsx",
sheet = 1,
col_names = TRUE) %>%
janitor::clean_names() %>%
mutate(
population = (suicide_no / suicide_100k) * 100000,
sex = as.factor(sex),
age = as.factor(age)
)</code></pre>
<div id="diagnostics" class="section level2">
<h2>Diagnostics</h2>
<pre class="r"><code>sui_reg = lm (suicide_100k ~ year + sex + age + sex*age, data = suicide_df)</code></pre>
<p>After we build our linear model, we will check the several
assumptions by using to produce some diagnostic plots visualizing the
residual errors.</p>
<ul>
<li>Linearity of data: Ideally, the residual plot would not display any
fitting patterns. Consequently, the red line should be roughly
horizontal at zero. Based on our plot in the top-left chart, the
residual plot lacks a pattern. This shows that a linear relationship
between predictors and outcome variables can be assumed.</li>
<li>Homogeneity of variance:In the plot on the bottom-left, it can be
seen that the variability (variances) of the residual points is roughly
same with the value of the fitted outcome variable, suggesting constant
variances in the residuals errors (or heteroscedasticity) in
overall.</li>
<li>Normality of residuals:The normality assumption may be visually
verified using the QQ plot of residuals. The residuals’ normal
probability plot should roughly resemble a straight line. We may infer
normalcy since in our plot in the top-right chart, outside of three
outliers, most of the points roughly lie along this reference line.</li>
<li>Outliers and high levarage points: The plot on the bottom-right
highlights the top 3 potential outliers (#10, #12 and #36).And none of
them exceed the contour of cook’s distance to be considered as
influential observations.</li>
</ul>
<pre class="r"><code>par(mfrow = c(2, 2))
plot(sui_reg) </code></pre>
<p><img src="suicide_model_files/figure-html/unnamed-chunk-3-1.png" width="90%" /></p>
</div>
<div id="results" class="section level2">
<h2>Results</h2>
<pre class="r"><code>sui_reg %>%
summary() %>%
broom::glance() %>% kbl(
caption = "Key Statistics for Model Performance"
, col.names = c(
"R-squared", "Adj. R-squared"
, "Sigma", "F-statistic", "p-value", "df", "Residual df", "N")
, digits = c( 2, 2, 0, 2, 5, 0, 0, 0)
) %>%
kable_paper("striped", full_width = F) %>%
column_spec(1, bold = T)</code></pre>
<table class=" lightable-paper lightable-striped" style="font-family: "Arial Narrow", arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>
Key Statistics for Model Performance
</caption>
<thead>
<tr>
<th style="text-align:right;">
R-squared
</th>
<th style="text-align:right;">
Adj. R-squared
</th>
<th style="text-align:right;">
Sigma
</th>
<th style="text-align:right;">
F-statistic
</th>
<th style="text-align:right;">
p-value
</th>
<th style="text-align:right;">
df
</th>
<th style="text-align:right;">
Residual df
</th>
<th style="text-align:right;">
N
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:right;font-weight: bold;">
0.99
</td>
<td style="text-align:right;">
0.99
</td>
<td style="text-align:right;">
1
</td>
<td style="text-align:right;">
1994.27
</td>
<td style="text-align:right;">
0
</td>
<td style="text-align:right;">
12
</td>
<td style="text-align:right;">
239
</td>
<td style="text-align:right;">
252
</td>
</tr>
</tbody>
</table>
<p>As F-statistic is 1994.27, df=12, and the p-value is much less than
0.05, so we reject the null hypothesis at the significance level of
0.05. Hence there is a significant relationship between the outcome
<code>suicide rate</code> and the variables (<code>Year</code>,
<code>Sex</code>, <code>Age</code>, and the interaction term
<code>Sex*Age</code>)in the linear regression model of the suicide
dataset.</p>
<pre class="r"><code>sui_reg %>%
summary() %>%
broom::tidy() %>%
kbl(
caption = "Effect of Selected Predictors on the US National Suicide Rate, 2000-2020"
, col.names = c("Predictor", "Estimate", "SE", "t-statistic", "p-value"),
digits= 6) %>%
# further map to a more professional-looking table
kable_paper("striped", full_width = F) %>%
# make variable names bold
column_spec(1, bold = T)</code></pre>
<table class=" lightable-paper lightable-striped" style="font-family: "Arial Narrow", arial, helvetica, sans-serif; width: auto !important; margin-left: auto; margin-right: auto;">
<caption>
Effect of Selected Predictors on the US National Suicide Rate, 2000-2020
</caption>
<thead>
<tr>
<th style="text-align:left;">
Predictor
</th>
<th style="text-align:right;">
Estimate
</th>
<th style="text-align:right;">
SE
</th>
<th style="text-align:right;">
t-statistic
</th>
<th style="text-align:right;">
p-value
</th>
</tr>
</thead>
<tbody>
<tr>
<td style="text-align:left;font-weight: bold;">
(Intercept)
</td>
<td style="text-align:right;">
-345.151190
</td>
<td style="text-align:right;">
25.419955
</td>
<td style="text-align:right;">
-13.577962
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
year
</td>
<td style="text-align:right;">
0.172262
</td>
<td style="text-align:right;">
0.012646
</td>
<td style="text-align:right;">
13.621790
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
sexmale
</td>
<td style="text-align:right;">
1.100000
</td>
<td style="text-align:right;">
0.375143
</td>
<td style="text-align:right;">
2.932218
</td>
<td style="text-align:right;">
0.003692
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
age15-24
</td>
<td style="text-align:right;">
3.061905
</td>
<td style="text-align:right;">
0.375143
</td>
<td style="text-align:right;">
8.161975
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
age25-44
</td>
<td style="text-align:right;">
5.490476
</td>
<td style="text-align:right;">
0.375143
</td>
<td style="text-align:right;">
14.635704
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
age45-64
</td>
<td style="text-align:right;">
7.304762
</td>
<td style="text-align:right;">
0.375143
</td>
<td style="text-align:right;">
19.471960
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
age65-74
</td>
<td style="text-align:right;">
3.809524
</td>
<td style="text-align:right;">
0.375143
</td>
<td style="text-align:right;">
10.154868
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
age75+
</td>
<td style="text-align:right;">
2.819048
</td>
<td style="text-align:right;">
0.375143
</td>
<td style="text-align:right;">
7.514602
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
sexmale:age15-24
</td>
<td style="text-align:right;">
12.819048
</td>
<td style="text-align:right;">
0.530532
</td>
<td style="text-align:right;">
24.162638
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
sexmale:age25-44
</td>
<td style="text-align:right;">
16.452381
</td>
<td style="text-align:right;">
0.530532
</td>
<td style="text-align:right;">
31.011113
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
sexmale:age45-64
</td>
<td style="text-align:right;">
17.504762
</td>
<td style="text-align:right;">
0.530532
</td>
<td style="text-align:right;">
32.994747
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
sexmale:age65-74
</td>
<td style="text-align:right;">
18.485714
</td>
<td style="text-align:right;">
0.530532
</td>
<td style="text-align:right;">
34.843745
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
<tr>
<td style="text-align:left;font-weight: bold;">
sexmale:age75+
</td>
<td style="text-align:right;">
33.490476
</td>
<td style="text-align:right;">
0.530532
</td>
<td style="text-align:right;">
63.126239
</td>
<td style="text-align:right;">
0.000000
</td>
</tr>
</tbody>
</table>
<p>According to the table, all the p-values are quite close to 0, so our
regression indicates that each predictor(<code>Year</code>,
<code>Sex</code>, <code>Age</code>) and the interaction term
(<code>Sex*Age</code>) have the statistically significant relationship
with the suicide rates.</p>
<p>The estimate for predictor <code>Year</code> is 0.17, which means
that when one year increases, the suicide rate will also increase 0.17,
assuming all other variables stay constant. This finding is not totally
consistent with the summary described in our previous visualization
process, probably because the suicide rate trend ripple is not enough
obvious or the variable <code>Year</code> is affected by other unknown
variables.</p>
<p>The estimate for predictor <code>Sexmale</code> is 1.10, which means
that when sex changes from male to female, the value of the suicide rate
will increase 1.10, assuming all other variables stay constant. Among
all the females, the predictor <code>Age45-64</code> has the largest
value of the estimate, showing that the age group 45-64 has the higher
suicide rates than all other age groups. Among all the males, we need to
combine the estimates with age groups and the interaction terms, and
obtain that the age group 75+ has the higher suicide rates than all
other age groups. And these findings match with our summary from the
foregoing descriptive analyses.</p>
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