Measuring Intra-Urban Inequality with Structural Equation Modeling: A Theory-Grounded Indicator

Round 1

Reviewer 1 Report

The manuscript has an appropriate structure and a clear interest in developing this quantitative methodology in the measurement of urban inequality. The design, sources and research method are explained in a correct and orderly manner. It has a finished care that is clearly manifested in the maps and graphics It is recommended to take into consideration these minor issues discussed below.

• The area of study does not appear in the title, abstract, keywords or introduction, which will make it difficult for future researchers to use it in their searches for these territories. The reference is presented in Appendix a and figure a1: the cartographic location of the area of study, as well as its characterization. The results are presented in figure 3 without the reader having some knowledge in a linear reading of the urbanistic, social, economic and localization characteristics of the area of study. This characterization prior to the presentation of results can help to better understand the scores.
• There must be an error in table 1 in the variables ent_9 and ent_10. They have the same name and different values in figure 2
• Remember to activate the link to supplementary materials
• It is recommended that self-citation 55 be avoided to refer to an issue that is much more substantial with reference 47 already present in the text.

Author Response

"Please see the attachment"

We would like to express our gratitude for the invaluable and constructive comments we have received concerning our submission. The manuscript has been revised to fully address the issues raised review process. Attached, we present in detail on how the paper has been modified.

Author Response File: Author Response.pdf

Reviewer 2 Report

The paper and the proposed methodology have good intentions but still lack consistency in some aspects, namely:

• Absence of reference to Correspondence Analysis Modeling as an alternative to Structural Equation Modeling;
• Absence of contextual information of the urban conurbation of Maringá-Sarandi-Paiçandu
• Absence of reference to the support for measuring the variables in Table 1;
• It is not clear the criteria used to select 11 of the 34 variables presented in Table 1;
• Absence of relationship between the text of lines 232-237 and figure 2;
• Absence of explanation on how to obtain the clusters in figure 2 and figure A1;
• Absence of relationship between the text of lines 245-249 and figure 3;
• Absence of relationship between the text of lines 252-258 and Figure 3.

Other detail aspects to be corrected:

• Lines 141-142: Please replace Table A1 by Table 1
• Table 1: the description of ENT_9 and ENT_10 should not be the same
• Figure 3: Please replace DOM_4 by DOM_3 and DOM_8 by DOM_7

Author Response

"Please see the attachment."

We would like to express our gratitude for the invaluable and constructive comments we have received concerning our submission. The manuscript has been revised to fully address the issues raised review process. Attached, we present in detail on how the paper has been modified.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

This second version of the article has improved significantly. The authors addressed the main gaps in the first version of the article.

However, the absence of a clear explanation about the criteria used to select the 11 variables persists. For example, we do not understand what motivated the choice of POP_3 and not the choice of POP_1 and/or POP_2. Or why is ENT_8 more relevant than ENT_7? Or even why DOM_5 and DOM_10 were not chosen when in lines 194 and 195 they are pointed out as relevant variables?

Although the explanation of the potential of CA and MCA is insufficient, additional explanations should not be required from the authors because they are not the methods used in the article.

Another detail aspect to be corrected:

• Line 275: Please replace 075 by 0.75

Author Response

We would like to express our gratitude for the invaluable and constructive comments we have received concerning our submission. In what follows, we present in detail on how the paper has been modified. The modified text is shown in blue in the revised paper, for tracking purposes.

Comments and Suggestions for Authors

Comment 1: This second version of the article has improved significantly. The authors addressed the main gaps in the first version of the article. However, the absence of a clear explanation about the criteria used to select the 11 variables persists. For example, we do not understand what motivated the choice of POP_3 and not the choice of POP_1 and/or POP_2. Or why is ENT_8 more relevant than ENT_7? Or even why DOM_5 and DOM_10 were not chosen when in lines 194 and 195 they are pointed out as relevant variables?

Response: The choice of the variables is determined by their loadings computed during the first step of the structural equation modeling. As suggested in the literature, only the variables whose loadings are greater than 0.7 are considered. This threshold ensures a high correlation with the latent variable being modeled.

Action: We have made three insertions in the manuscript to address this issue. First, we explain the criterion used to select the variables based on their factor loadings and state the threshold value used for acceptance, as suggested in the literature. Second, we have modified the first paragraph of the results section, reinforcing the reason for the selection of the eleven variables included in the model. Third, we have made a slight change in the text that precedes Figure 3 to show the loading values of the selected variables:

Line: 222

“The two-stage model was created, using the SmartPLS Software [75]. The first stage is associated with the modeling of the first-order structure in which the observed variables are selected. The criterion for selecting an observed variable is the loading factor [12]. The factor loading criterion threshold is 0.70 [49]. It implies that the most part of the observed variable variance is captured by the latent variables of the first order structure, namely Neighborhoods Inequality, Socioeconomic Inequality, and Households Inequality…”

Line: 271

“For the definition of the first-order structure that determines the creation of the latent variables representing the underlying dimensions of intra-urban inequality, 11 variables that exceeded the loading threshold of 0.70 [12] were selected. This threshold means that the latent variable explains273at least 50% of the variance of the observed variable [49].”

Line: 302

“The results of this test are illustrated in Fig. 3 that also shows the Factor Loadings of the observed variables of each latent variable and the AVE of the latent variables.”

Comment 2: Another detail aspect to be corrected: Line 275: Please replace 075 by 0.75.

Answer 2:  The typo was corrected.

Line: 268

“The upper limits of the classes were respectively: 0.25, 0.50, 0.75 and 1.00.”