Resilience Index Measurement and Analysis using Structural Equation Modeling
Mar, 2022
Resilience has been defined as the capacity of socioeconomic systems (e.g., households) to withstand shocks through absorption, adaptation and transformation.
One way to estimate resilience is through RIMA II method used by FAO that utilizes structural equation modeling (SEM): SEM combines Confirmatory Factor Analysis and Path Analysis: Generally, there are two steps followed:
- First, the resilience pillars are estimated from observed variables through Factor Analysis (FA).
- Second, the resilience index is estimated from the pillars, using path analysis (e.g. ordinary least square) with the outcome variable being a food security indicator(s) such as dietary diversity score.
FAO uses SEMs to measure Resilience Capacity Index (RCI) based on four pillars:
1. Access to basic services (ABS)
2. Assets (AST)
3. Social safety nets (SSN)
4. Adaptive capacity (AC)
For this data the food security indicator will be the proportion of income spent on food and will perform the role of an endogenous variable
The data that will be used will have pillars already identified through factor analysis.
library(lavaan)
library(knitr)
library(broom)
library(readxl)
library(haven)
library(knitr)
library(png)
library(dplyr)
library(kableExtra)
library(tidyverse)
library(ggthemes)We now load the dataset whose labels are shown in the table below:
setwd("E:/Structural Equation Model")
resilience.d <- read_sav("data.sav")
head(resilience.d,10) %>%
kable("html") %>%
kable_styling(font_size=12) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))| animal_asset | sources | income_sources | coping_strategies | no_groups | food.e |
|---|---|---|---|---|---|
| 16 | 2 | 1 | 1 | 1 | 0.20 |
| 16 | 3 | 1 | 1 | 0 | 0.67 |
| 8 | 1 | 1 | 1 | 1 | 1.00 |
| 3 | 1 | 1 | 2 | 1 | 1.00 |
| 42 | 1 | 1 | 0 | 1 | 0.50 |
| 32 | 1 | 1 | 0 | 1 | 0.70 |
| 6 | 1 | 1 | 0 | 1 | 0.50 |
| 55 | 1 | 1 | 1 | 1 | 0.42 |
| 10 | 1 | 1 | 1 | 2 | 0.14 |
| 6 | 2 | 1 | 1 | 1 | 0.10 |
Structural equation model
First, we will need to establish a measurement model for each pillar. Notably, each pillar is most oftenly a latent factor established from more than one indicator. The table below shows each pillar and variables (indicators) used in the analysis; in our case only one pillar (AC- Adaptive Capacity) is a latent variable.
rcimodel='
AST=~animal_asset
ABS=~sources
AC=~income_sources+coping_strategies
SSN=~no_groups
RCI_score=~food.e
# regression
RCI_score~AST+ABS+AC+SSN'
fit <- sem(rcimodel,data=resilience.d)
summary(fit, standardized=TRUE, fit.measures=TRUE)## lavaan 0.6-9 ended normally after 75 iterations
##
## Estimator ML
## Optimization method NLMINB
## Number of model parameters 18
##
## Number of observations 959
##
## Model Test User Model:
##
## Test statistic 93.383
## Degrees of freedom 3
## P-value (Chi-square) 0.000
##
## Model Test Baseline Model:
##
## Test statistic 235.482
## Degrees of freedom 15
## P-value 0.000
##
## User Model versus Baseline Model:
##
## Comparative Fit Index (CFI) 0.590
## Tucker-Lewis Index (TLI) -1.050
##
## Loglikelihood and Information Criteria:
##
## Loglikelihood user model (H0) -10043.745
## Loglikelihood unrestricted model (H1) -9997.053
##
## Akaike (AIC) 20123.489
## Bayesian (BIC) 20211.075
## Sample-size adjusted Bayesian (BIC) 20153.908
##
## Root Mean Square Error of Approximation:
##
## RMSEA 0.177
## 90 Percent confidence interval - lower 0.147
## 90 Percent confidence interval - upper 0.209
## P-value RMSEA <= 0.05 0.000
##
## Standardized Root Mean Square Residual:
##
## SRMR 0.070
##
## Parameter Estimates:
##
## Standard errors Standard
## Information Expected
## Information saturated (h1) model Structured
##
## Latent Variables:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AST =~
## animal_asset 1.000 102.782 1.000
## ABS =~
## sources 1.000 0.861 1.000
## AC =~
## income_sources 1.000 3.633 5.860
## coping_stratgs 0.002 0.134 0.015 0.988 0.007 0.011
## SSN =~
## no_groups 1.000 0.796 1.000
## RCI_score =~
## food.e 1.000 0.261 1.000
##
## Regressions:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## RCI_score ~
## AST -0.000 0.000 -4.817 0.000 -0.168 -0.168
## ABS -0.028 0.017 -1.649 0.099 -0.094 -0.094
## AC -0.001 0.096 -0.015 0.988 -0.021 -0.021
## SSN 0.035 0.011 3.249 0.001 0.108 0.108
##
## Covariances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## AST ~~
## ABS 12.280 2.884 4.257 0.000 0.139 0.139
## AC 5.952 2.063 2.884 0.004 0.016 0.016
## SSN 4.602 2.646 1.739 0.082 0.056 0.056
## ABS ~~
## AC 0.115 0.018 6.536 0.000 0.037 0.037
## SSN 0.018 0.022 0.827 0.408 0.027 0.027
## AC ~~
## SSN 0.028 0.016 1.728 0.084 0.010 0.010
##
## Variances:
## Estimate Std.Err z-value P(>|z|) Std.lv Std.all
## .animal_asset 0.000 0.000 0.000
## .sources 0.000 0.000 0.000
## .income_sources -12.817 855.807 -0.015 0.988 -12.817 -33.338
## .coping_stratgs 0.451 0.021 21.565 0.000 0.451 1.000
## .no_groups 0.000 0.000 0.000
## .food.e 0.000 0.000 0.000
## AST 10564.237 482.441 21.897 0.000 1.000 1.000
## ABS 0.741 0.034 21.897 0.000 1.000 1.000
## AC 13.202 855.807 0.015 0.988 1.000 1.000
## SSN 0.634 0.029 21.897 0.000 1.000 1.000
## .RCI_score 0.065 0.003 18.442 0.000 0.949 0.949Save the scores: we now save factor scores and the most important score is the resilience capacity index (RCI) factor score in the last column
fit2<- cfa(rcimodel, data=resilience.d)
fscores <- lavPredict(fit2)
newdata<-cbind(resilience.d,fscores)
head(newdata,10) %>%
kable("html") %>%
kable_styling(font_size=12) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))| animal_asset | sources | income_sources | coping_strategies | no_groups | food.e | AST | ABS | AC | SSN | RCI_score |
|---|---|---|---|---|---|---|---|---|---|---|
| 16 | 2 | 1 | 1 | 1 | 0.20 | -57.2586 | 0.1386861 | -32.37460 | -0.5078206 | -0.2531491 |
| 16 | 3 | 1 | 1 | 0 | 0.67 | -57.2586 | 1.1386861 | -30.57509 | -1.5078206 | 0.2168509 |
| 8 | 1 | 1 | 1 | 1 | 1.00 | -65.2586 | -0.8613139 | -18.56528 | -0.5078206 | 0.5468509 |
| 3 | 1 | 1 | 2 | 1 | 1.00 | -70.2586 | -0.8613139 | -20.68413 | -0.5078206 | 0.5468509 |
| 42 | 1 | 1 | 0 | 1 | 0.50 | -31.2586 | -0.8613139 | -22.15270 | -0.5078206 | 0.0468509 |
| 32 | 1 | 1 | 0 | 1 | 0.70 | -41.2586 | -0.8613139 | -19.88432 | -0.5078206 | 0.2468509 |
| 6 | 1 | 1 | 0 | 1 | 0.50 | -67.2586 | -0.8613139 | -21.83474 | -0.5078206 | 0.0468509 |
| 55 | 1 | 1 | 1 | 1 | 0.42 | -18.2586 | -0.8613139 | -25.30255 | -0.5078206 | -0.0331491 |
| 10 | 1 | 1 | 1 | 2 | 0.14 | -63.2586 | -0.8613139 | -29.65201 | 0.4921794 | -0.3131491 |
| 6 | 2 | 1 | 1 | 1 | 0.10 | -67.2586 | 0.1386861 | -33.37631 | -0.5078206 | -0.3531491 |
To get the Resilience Index, a min-max scaling is used to transform the RCI scores into a standardized index ranging between 0 and 100. The linear scaling is based on on formula below: The - Mean is the RCI
\[\begin{equation} RCI=\frac{RCI-RCI_{min}}{RCI_{max}-RCI_{min}} \end{equation}\]
rcidata<-newdata %>%
mutate(RCI=(RCI_score-min(RCI_score))/(max(RCI_score)-min(RCI_score)))
head(rcidata,10) %>%
kable("html") %>%
kable_styling(font_size=12) %>%
kable_styling(bootstrap_options = c("striped", "hover", "condensed", "responsive"))| animal_asset | sources | income_sources | coping_strategies | no_groups | food.e | AST | ABS | AC | SSN | RCI_score | RCI |
|---|---|---|---|---|---|---|---|---|---|---|---|
| 16 | 2 | 1 | 1 | 1 | 0.20 | -57.2586 | 0.1386861 | -32.37460 | -0.5078206 | -0.2531491 | 0.1919192 |
| 16 | 3 | 1 | 1 | 0 | 0.67 | -57.2586 | 1.1386861 | -30.57509 | -1.5078206 | 0.2168509 | 0.6666667 |
| 8 | 1 | 1 | 1 | 1 | 1.00 | -65.2586 | -0.8613139 | -18.56528 | -0.5078206 | 0.5468509 | 1.0000000 |
| 3 | 1 | 1 | 2 | 1 | 1.00 | -70.2586 | -0.8613139 | -20.68413 | -0.5078206 | 0.5468509 | 1.0000000 |
| 42 | 1 | 1 | 0 | 1 | 0.50 | -31.2586 | -0.8613139 | -22.15270 | -0.5078206 | 0.0468509 | 0.4949495 |
| 32 | 1 | 1 | 0 | 1 | 0.70 | -41.2586 | -0.8613139 | -19.88432 | -0.5078206 | 0.2468509 | 0.6969697 |
| 6 | 1 | 1 | 0 | 1 | 0.50 | -67.2586 | -0.8613139 | -21.83474 | -0.5078206 | 0.0468509 | 0.4949495 |
| 55 | 1 | 1 | 1 | 1 | 0.42 | -18.2586 | -0.8613139 | -25.30255 | -0.5078206 | -0.0331491 | 0.4141414 |
| 10 | 1 | 1 | 1 | 2 | 0.14 | -63.2586 | -0.8613139 | -29.65201 | 0.4921794 | -0.3131491 | 0.1313131 |
| 6 | 2 | 1 | 1 | 1 | 0.10 | -67.2586 | 0.1386861 | -33.37631 | -0.5078206 | -0.3531491 | 0.0909091 |
In this the RCI=0.45
We now look at the strength of each pillar in explaining RCI. We will use sum of squares of regression from anova to determine the proportion of variance each pillar explains when regressed against resilience capacity of each household.
attach(rcidata)
fit1<-lm(RCI~ABS+AST+AC+SSN)
var.amt<-anova(fit1)
afss<-var.amt$"Sum Sq"[1:4]
Pct.var=round(afss/sum(afss)*100,0)
Pillars=c("ABS","AST","AC","SSN")
Proportion=Pct.var
pillar.data<-data.frame(Pillars,Proportion)
pillar.data<- pillar.data %>%
mutate(pillar.label = "Pillars")Pillar contribution to resilience
From the chart below, assets (AST) are linked to high resilience capacity of a household followed by access to basic services (ABS) and social security network (SSN)
ggplot(pillar.data, aes(x =pillar.label, y = Proportion, fill = Pillars)) +
geom_col(width = 0.3) +
geom_text(aes(label = paste0(Proportion, "%")),
position = position_stack(vjust = 0.5)) +
theme_economist(base_size = 5) +
scale_fill_economist() +
theme(legend.position = "right",
legend.title = element_blank()) +
theme(axis.title.y = element_text(margin = margin(r = 20))) +
ylab("Percentage") +
xlab(NULL)