# Evaluating Formative Measurement Model - Step 3: Indicator Weights

### SEMinR Lecture Series

This session is focused on step 3 of the formative measurement model assessment. The tutorial will guide on how to assess the indicator weights using SEMinR.

## Evaluating Formative Measurement Model

- PLS-SEM is the preferred approach when formatively specified constructs are included in the PLS path model (Hair, Risher, Sarstedt, & Ringle, 2019).
- In this part of the series, I discuss the key steps for evaluating
**formative measurement models**(Fig.). Relevant criteria include the assessment of Convergent validity,indicator collinearity, and Statistical significance and relevance of the indicator weights. - Next, I will introduce key criteria and their thresholds and illustrate their use with an example.

## The Example

- The proposed model has three constructs (Vision, Development, and Reward) measured formatively that impact a reflectively measured construct (Collaborative Culture).
- The three constructs are formative constructs, estimated with
**mode_B**, while*Collaborative Culture*is reflective construct, estimated with**mode_A**. - The
parameter of the*weights***composite()**function is set by default to**mode_A**. Thus, when no weights are specified, the construct is estimated as being reflective. - Alternatively, we can explicitly specify the
**mode_A**setting for reflectively measured constructs or the**mode_B**setting for formatively measured constructs. - Once the model is set up, we use the
**estimate_pls****()**function to estimate the model, this time specifying theand*measurement_model*.*structural_model* - Finally, we apply the
**summary()**function to the estimated SEMinR model object**simple_model**and store the output in the**summary_simple**object.

## Step 3: Indicator Weights

- Next, analyze the indicator weights for their significance and relevance.
- First, consider the significance of the indicator weights by means of bootstrapping. To run the bootstrapping procedure using the
**bootstrap_model****()**function. - The first parameter (i.e.,
) allows specifying the model on which we apply bootstrapping. The second parameter*seminr_model*allows us to select the number of bootstrap samples to use. Per default, we should use 10,000 bootstrap samples (Streukens & Leroi-Werelds, 2016).*nboot* - Since using such a great number of samples requires much computational time, you may choose a smaller number of samples (e.g., 1,000) for the initial model estimation.
- For the final result reporting, however, we should use the recommended number of 10,000 bootstrap samples.
- The
parameter enables us to use multiple cores of your computer’s central processing unit (CPU). Recommended is using this option since it makes bootstrapping much faster.*cores* - As you might not know the number of cores in your device, recommended is using the
**parallel::****detectCores****()**function to automatically detect the number of cores and use the maximum cores available. - By default,
**cores**will be set to the maximum value and as such, if you do not specify this parameter, your bootstrap will default to using the maximum computing power of your CPU. - Finally,
**seed**allows reproducing the results of a specific bootstrap run while maintaining the random nature of the process. - Assign the output of the
**bootstrap_model()**function to the**summary_boot**object. - Finally, we need to run the
**summary()**function on the**summary_boot**object and set theparameter. The*alpha*parameter allows selecting the significance level (the default is 0.05) for two-tailed testing. When testing indicator weights, we follow general convention and apply two-tailed testing at a significance level of 5%.*alpha* **Following is the complete code from the previous sessions (Step 1: Convergent Validity and Step 2: Collinearity Diagnostics on evaluating formative model evaluation.****Line 27-28 is for Step 3, Assessing Indicator Weights.**

## The Code

```
library(seminr)
# Load the Data
datas <- read.csv(file = "D:\\YouTube Videos\\SEMinR\\Data.csv", header = TRUE, sep = ",")
head(datas)
# Create measurement model
simple_mm <- constructs(
composite("Vision", multi_items("VIS", 1:4), weights = mode_B),
composite("Development", multi_items("DEV", 1:7), weights = mode_B),
composite("Rewards", multi_items("RW",1:4), weights = mode_B),
composite("Collaborative Culture", multi_items("CC", 1:6)))
# Create structural model
simple_sm <- relationships(
paths(from = c("Vision","Development","Rewards"), to = "Collaborative Culture"))
# Estimate the model
simple_model <- estimate_pls(data = datas,
measurement_model = simple_mm,
structural_model = simple_sm,
missing = mean_replacement,
missing_value = "-99")
# Summarize the model results
summary_simple <- summary(simple_model)
# Bootstrap the PLS Estimated Model
boot_model <- bootstrap_model(seminr_model = simple_model, nboot = 1000, cores = parallel::detectCores(), seed = 123)
# Store the summary of the bootstrapped model
# alpha sets the specified level for significance, i.e. 0.05
summary_boot <- summary(boot_model, alpha = 0.05)
# Inspect the bootstrapping results for indicator weights
summary_boot$bootstrapped_weights
```

### Step 3: Statistical Significance and Relevance of the Indicator Weights

- The third step in assessing formatively measured constructs is examining the statistical significance and relevance (i.e., size) of the indicator weights.
- The
**indicator weights**result from regressing each formatively measured construct on its associated indicators. As such, they represent each indicator’s relative importance for forming the construct. **Significance testing**of the indicator weights relies on the bootstrapping procedure.- The bootstrapping procedure yields
*t*-values for the indicator weights (and other model parameters). - Assuming a significance level of 5%, a
*t*-value above 1.96 (two tailed test) suggests that the indicator weight is statistically significant. The critical values for significance levels of 1% (*α*= 0.01) and 10% (*α*= 0.10) probability of error are 2.576 and 1.645 (two tailed), respectively. - Inspect the
**summary_boot$bootstrapped_weights****.** - Figure shows
*t*-values for the measurement model relationships - Note that bootstrapped values are generated for all measurement model weights, but we only consider the indicators of the formative constructs.
- Recall that the critical values for significance levels of 1% (
*α*= 0.01), 5% (*α*= 0.05), and 10% (*α*= 0.10) probability of error are 2.576, 1.960, and 1.645 (two tailed), respectively.

### Indicator Weights and Factor Loadings

**Confidence intervals**are an alternative way to test for the significance of indicator weights. They represent the range within which the population parameter will fall assuming a certain level of confidence (e.g., 95%).- If a confidence interval does not include the value zero, the weight can be considered statistically significant, and the indicator can be retained.
- On the contrary, if the confidence interval of an indicator weight includes zero, this indicates the weight is not statistically significant (assuming the given significance level, e.g., 5%). In such a situation, the indicator should be considered for removal from the measurement model.
- However, if an indicator weight is not significant, it is not necessarily interpreted as evidence of poor measurement model quality.
- We recommend you also consider the
**absolute contribution**of a formative indicator to the construct (Cenfetelli & Bassellier, 2009), which is determined by the formative indicator’s loading. - At a minimum, a formative indicator’s loading should be statistically significant. Indicator loadings of 0.5 and higher suggest the indicator makes a sufficient absolute contribution to forming the construct.
- The lower boundary of the 95% confidence interval (
**2.5% CI**) is displayed in the second-to-last column, whereas the upper boundary of the confidence interval (**97.5% CI**) is shown in the last column. - We can readily use these confidence intervals for significance testing. if a confidence interval for an estimated coefficient does not include zero, the hypothesis that
*w*1 equals zero is rejected, and we assume a significant effect. - Looking at the significance levels, we find that all formative indicators are significant at a 5% level.

- Next, to assess these indicators’ absolute importance, we examine the indicator loadings by running

**summary_boot$bootstrapped_loadings****. **

- The output in Fig. (column:
**Original Est.**) shows that the indicator loadings over .70 for all the formative indicators. Furthermore, results from bootstrapping show that the*t*-values of the formative indicator loadings are clearly above 2.576, suggesting that all indicator loadings are significant even at a level of 1% (Fig). - We retain all indicators in the formatively measured constructs, even though not every indicator weight is significant. The analysis of indicator weights concludes the evaluation of the formative measurement models.

## Complete Code

```
library(seminr)
# Load the Data
datas <- read.csv(file = "D:\\YouTube Videos\\SEMinR\\Data.csv", header = TRUE, sep = ",")
head(datas)
# Create measurement model
simple_mm <- constructs(
composite("Vision", multi_items("VIS", 1:4), weights = mode_B),
composite("Development", multi_items("DEV", 1:7), weights = mode_B),
composite("Rewards", multi_items("RW",1:4), weights = mode_B),
composite("Collaborative Culture", multi_items("CC", 1:6)))
# Create structural model
simple_sm <- relationships(paths(from = c("Vision", "Development", "Rewards"), to = "Collaborative Culture"))
# Estimate the model
simple_model <- estimate_pls(data = datas, measurement_model = simple_mm, structural_model = simple_sm, missing = mean_replacement, missing_value = "-99")
# Summarize the model results
summary_simple <- summary(simple_model)
#Descriptive Stattistics Summary
summary_simple$descriptives$statistics
# Iterations to converge
summary_simple$iterations
# Collinearity analysis
summary_simple$validity$vif_items
# Bootstrap the model on the PLS Estimated Model
boot_model <- bootstrap_model(
seminr_model = simple_model,
nboot = 1000, cores = parallel::detectCores(), seed = 123)
# Store the summary of the bootstrapped model
# alpha sets the specified level for significance, i.e. 0.05
summary_boot <- summary(boot_model, alpha = 0.05)
# Inspect the bootstrapping results for indicator weights
summary_boot$bootstrapped_weights
# Inspect the bootstrapping results for indicator loadings
summary_boot$bootstrapped_loadings
```

## Reference

Hair Jr, J. F., Hult, G. T. M., Ringle, C. M., Sarstedt, M., Danks, N. P., & Ray, S. (2021). Partial Least Squares Structural Equation Modeling (PLS-SEM) Using R: A Workbook.

The tutorials on SEMinR are based on the mentioned book. The book is open source and available for download under this link.