Application of Item Response Theory (IRT)-Graded Response Model (GRM) to Entrepreneurial Ecosystem Scale

Abstract

The scale of entrepreneurial ecosystems (EE) assesses the perceptions about entrepreneurial ecosystem domains, finances, capital finances, support, support professions, policies, markets, human resources, and culture. The scales are always error-prone—these scales must possess properties that enable them it to provide maximum information and validity reliability. Convenient sampling data from (n = 474) founders, co-founders, and entrepreneurs were collected. The IRT-GRM model is used to validate and test the instrument-based on polytomous scales. IRT yields discriminating power—the level of difficulty of the items of the scale. The scale consists of 48 items. The item Pol5 (4.13) was found to have the highest discriminating value (4.13), the item mar5 had the lowest discriminating value (1.57), and all items had discriminating values greater than the threshold value of 0.60. The EE Scale showed good reliability based on McDonald’s omega and Cronbach’s alpha (0.80 and 0.88). The parallel and factor analysis showed good agreement of the one-dimesnionality of the scale. The model goodness of fit statistics based on the comparative fit index (CFI) and the Tucker–Lewis index, (TLI) and the standardized root mean square residual (SRMR) showed a satisfactory level of fit; however, the root mean square error of approximation (RMSE) showed a poor fit. The item characteristic curves showed that the all item responses were properly ordered. The items of the scale showed a satisfactory level of discrimination power and level of difficulty, and it was found to have three levels of agreement about entrepreneurial ecosystem scale. It is concluded that the EE scale possesses good psychometric properties and that it is reliable and valid instrument to measure the entrepreneurial ecosystem of the given region.

1. Introduction

The geographical regions and related conditions are essential for the economic development of any area. If favorable, these conditions lead to the clustering of innovative firms [1]. Geographical elements are termed as ecosystems, and these elements affect business innovation and job creation. These favorable regions thrive on labor markets, information, and networks [2]. The ecosystem approach encompasses entrepreneurial university ecosystems, location-based innovative clusters, social entrepreneurship ecosystems, and sustainable entrepreneurship ecosystems [3].

Conceptual attempts have been made to better understand the entrepreneurial ecosystem and why firms cluster in those regions, for example, references [4,5,6]. However, empirical measurement is still in its nascent stage and continues to evolve [3]. The perception-based scale of the entrepreneurial ecosystem was developed by reference [3], this scale has been used to collect data. Although this scale is necessary to understand the perspective of entrepreneurs and the quality of entrepreneurial ecosystem conditions in each region in terms of psychophysical behaviors may be different,. These scales are important to capture the feelings, perceptions, and behaviors that cannot be measured with one variable, the instrument or scales are always error-prone, the use of multiple items measuring the underlying latent traits or latent constructs leads to more generalized and precise research findings [4]. There is extant literature available on the theory of scales and development; however, there are incomplete scales that measure physical, mental, and behavioral attributes, which are important for science and scientific inquiry [5].

The scales can be validated using either classical test theory (CTT) or IRT; in the CTT assumes reliability is constant across all respondents, regardless of their ability levels, while in IRT, the reliability depends on the ability levels or traits of the respondents—these differences can affect the reliability and validity of the instruments or scale, and, therefore, and conclusions drawn based on the scales may not be accurate [6].

Therefore, the main aim of this research is to assess whether the EE scale possesses an acceptable level of psychometric properties, e.g., the discrimination and difficulty of the items and what items are problematic in the scale. The IRT would help to validate and assess the properties of the scale at the item level because the IRT measurement framework is extensively used in scoring scale data, such as questionnaires or scales [7].

This would be the first application of IRT on the EE scale in developing countries, such as Pakistan. The IRT measurement framework and key ideas are applied to individual items, estimating abilities or latent traits, and error measurements.

1.1. Study Motivation

This study was conducted to evaluate and validate the EE scale using IRT. The chi-square fit index was applied at the item level, and the items lacking goodness of fit were identified.

Despite the lack of empirical research on measuring the entrepreneurial ecosystem [8], no study has evaluated the reliability of the entrepreneurial ecosystem scale developed by reference [3] using IRT. Therefore, this study will highlight a few studies in other fields where IRT is applied to obtain results.

1.2. Literature Review

Researchers are concerned about the quality of the EE in different regions and countries; policy makers on the other hand want to identify policy action points within entrepreneurial ecosystems [9]. The ecosystem metaphor is borrowed from biology and it is defined as the interdependent factors and actors and their interaction effects the viability of entrepreneurial activity in a particular region [10].

The researchers focus on the strategic perspective regarding the EE and want to penetrate the complex interactions between actors and factors within an EE, which enables them to see the black box of EE—these actors work toward common goals of job creation and economic growth [11]. The EE has six domains: (1) finance, (2) policy, (3) markets, (4) human resources, (5) support, and (6) culture [3]. Policy is to what extent government supports entrepreneurial activity in terms of favorable legislation, rules, and laws; finance primarily concerns access to finance; markets is concerned with diaspora networks, distribution channels, and early adopters; human resources is concerned with access to human capital in terms of training, the technical workforce, and universities; culture deals with the values and attitudes towards innovation and business venturing; and support includes infrastructure, supporting professions, and entrepreneur-friendly programs and institutions [3].

The developing countries in contrast to developed countries often lack proper support for startups, beneficial legal rules and procedures, access to human capital, adequate infrastructure, and finance, among other challenges [12]; therefore, measuring the entrepreneurial ecosystem in a certain region to identify policy action points is very important for developing countries to foster entrepreneurship and reap rewards from it.

The authors Souza et al. [13] used IRT on the entrepreneurship attitude scale developed by Souza and Lopes Jr. (2005) [14]. This scale has two dimensions: innovation and prospection, measurement and persistence. They used the graded response model to evaluate the scale. They found that their scale has two levels, the scale was able to distinguish between respondents having different ability levels.

The authors Wu et al. (2015) [15] used IRT to validate, operationalize, and conceptualize the multidimensional, as well multirole, “Entrepreneurial Behavior” scale in retailing businesses, and they found that IRT yielded robust, reliable measurements of the “ Multirole and Multidimensional construct”.

The authors Harrison et al. (2017) [16] applied IRT to psychological capacity, that is, melodic discrimination, or the ability to detect differences between two or more melodies. Their results support the application of IRTs strong construct reliability and validity. The researchers Şen and Toker (2021) [17] applied multilevel mixture IRT theory model using six different multilevel models on an eighth-grade dataset. Their results indicated that one school-level and four student-level latent classes were the best-fit models. Finally, the IRT was applied by author [12]. Using generalized partial credit model (GPCM) approach, they found the suitability of IRT on the instrument and found item difficulty levels at different grades, and 52% of students had above-average mathematical literacy.

Lemée (2019) [18] applied IRT to evaluate coping mechanisms in risky environmental situations. Their results suggest that 10 items out of 23 items were sufficient for passive and active coping willingness. Moreover, their study found that IRT can reveal the link between willingness to cope and other factors of interest. Finally, the researchers Zampetakis A. et al. (2015) [19] used IRT with the GRM to evaluate whether anticipated effect predictions conform to the questions of “what people usually do” or “what people can do”. Their findings suggest that the self-report response to the expected effect works to maximal behavior.

The authors Terman and Burke (2021) [20] used IRT to examine disability-related questions in National Health and Nutrition Examination Survey disability-related questions. Their findings showed a high degree of information that distinguished individuals with higher than mean limitations and showed zero resolution with individuals conveying lower mean activity limitations. The IRT was applied by Cordier et al. (2019) [21] on the pragmatics observational measure; their findings showed that their scale needed revision, since they observed significant covariances with a large and complex dataset.

The author Barbosa et al. (2021) [22] applied IRT to validate and assess the instrument of the “impacts of Integrated Management System”; the purpose of this instrument is to assess the effect of the integrated management system on the performance of organization. They used this scale to assess the discriminating capacity and level of difficulty of the items in the instrument, and they found that this instrument showed good discriminating ability and difficulty level for the items. Their study revealed six levels to measure impact-integrated management systems.

The author Silvia (2021) [23] evaluated the psychometric properties of the Likert item scale using the polytomous IRT. Their findings showed that the graded response model provided the best-fit model, and the threshold estimates were close to a range of one to five. To date, no such study has applied IRT to the scale of the EE scale developed by Ligouri (2019) [3].

1.3. Problem Statement

A questionnaire or instrument can be evaluated using the CTT or IRT. CTT uses simplified measures, for example, Cronbach’s alpha, while IRT provides reliability at the item level, the IRT generates item category characteristic curve (ICCC) and the test information function (TIF), ICCC and TIF show precision at different values of the theta or ability levels of the respondents. Another difference is that the CTT assumes a constant reliability and error across all respondents. On the other hand, IRT assumes that instruments are always error-prone and there is always a difference between a person’s expected and true scores. IRT calculates a probability based on item characteristics and latent trait scores. The outcome measure is based on theta in IRT. In contrast, in CTT, the outcome measure is based on the sum of the score distribution [24].

The author [19,20] have argued that CTT assumes an equal precision measurement for all respondents without considering their individual abilities, while IRT uses a precision measurement that depends on latent traits. Another advantage cited is the use of the 2PL model and GRM. These models are used to score items when computing latent trait scores and thus IRT reveals minor changes in the mental ability of individuals. IRT also facilitates the use of pre-test and post-test questions [6].

2. Methods

A cross-sectional study design was adopted for this research and respondents were surveyed using a questionnaire. The questionnaire was distributed to owners of firms and startups, and the inclusion criteria was that owners (1) should have sufficient business experience, (2) can read and understand the questionnaires, and (3) are aged 20 years or over. A total of 700 questionnaires were distributed to the participants and n = 474 responses were found to be fit for further analysis.

The first step in the implementation of IRT is factor analysis; therefore, in this section, a brief introduction on factor analysis will be provided and then IRT will be discussed.

2.1. Factor Analysis

Latent variables or factors are written in the form

$$x=\mu +\mathsf{\Lambda }z+u$$

(1)

where x represents the observed (manifest) variable, u represents unique variables, Λ is regression weights, z represents common factors, and µ represents elements of the corresponding factors [25]. The Likert scale is most often treated as an interval or ordinal variable, and factor analysis is usually performed on continuous variables; however, it can be used on ordinal variables, with trial and error through IRT showing latent traits; however, comparison between FA and IRT shows the robustness of the results presented.

2.2. IRT

IRT is a latent variable model that links polytomous manifest variables to latent variables. The model used in this research is a GRM, based on the work by Samejima (1969) [26]. GRM is used because our variable scores are polytomous responses or in an ordinal form. The GRM estimates the probability of choosing a particular reaction to an item and how well an item measures the respondents’ latent traits. The following six equations for the GRM model, plot making, and parameter estimations are discussed.

$$P_i\left({\theta }_m\right)=\frac{1}{1+e^{-{\alpha }_i\left({\theta }_m-{\beta }_i\right)}}$$

(2)

$$P_{ki}^{*}\left({\theta }_m\right)=P_{ki}\left({\theta }_m\right)-P_{ki+1}\left({\theta }_m\right)$$

(3)

$${ℒ}_{\mathrm{m}}\left(\theta \right)=\log p\left(x_m;\theta \right)=\log {\displaystyle \int }p\left(x_m\mid z_m;\theta \right)p\left(z_m\right)d{z}_m$$

(4)

$$P_{5i}^{*}\left({\theta }_m\right)=P_{5i}\left({\theta }_m\right)-P_{6i}\left({\theta }_m\right)$$

(5)

$$I_i\left({\theta }_m\right)={\alpha }_i^2\times P_i\left({\theta }_m\right)\times \left(1-P_i\left({\theta }_m\right)\right)$$

(6)

Source: (Rezapour et al. (2021) [24]).

The probability of selecting the ith item is provided in Equation (2), ${\theta }_m=\left({\alpha }_i,{\beta }_i\right)$ is the ability or latent trait for individual m, ${\alpha }_i$ is the discrimination parameter for item i, location of extremity boundary for item i defined as difficulty parameter is ${\beta }_i$ (if constrained can be considered constant for all items), and ${\theta }_m$ is the ability of respondents m on various questions or items. Equation (2) can be used for 5-point Likert scale and would transfer into Equation (3), where probability $P_{ki}$ and probability $P_{ki+1}$ endorsing item i with category ki or the next higher category ki + 1, respectively. Equation (4) describes the marginal likelihood ${ℒ}_{\mathrm{m}}\left(\theta \right)$ for mth individual respondents with choice $x_m$ and ability level $z_m$; it uses an approximate integral by weighted average at already determined abscissa [27]. Equation (4) does not have a closed form and therefore Gauss–Hermite quadrature in order to approximate the value of integrals is used. Item response category characteristic curves show how the probability of responding to an item will change in response to the category, keeping in mind the latent variable trait of the individual or the ability of the individual. ICCC plots can be obtained based on 5-point Likert scale from Equation (3) for the last category, from which we derived Equation (5), and the probabilities for the lowest and highest categories are therefore 1 and 0, $P_{1i}$ $P_{6i}$ respectively.

The plotting of the ICCC curve is based on item information (I), as in Equation (6), where ${\alpha }_i$ and $P_i\left({\theta }_i\right)$ are the discrimination parameters, and the probability of endorsing an item i by individual ${\theta }_m$ and $P_i$ is derived from logistic probability, and the ICCC plot is obtained by connecting points of $P_i\left({\theta }_i\right)$ [28]. The IRT shows the relationship between an item and respondent, with the relationship having a certain level of latent traits with a probability that the respondent will endorse a particular item; this is shown in the ICCC or item characteristic curve—this curve represents the change in the probability of selecting an item as a function of three parameters, e.g., pseudo guessing (c), item difficulty (β), and discrimination (α) [29]. The differential capability of the items is represented by discrimination; in terms of item difficulty parameters, the easier items have lower (β) values, the rate of positive responses changes with an individual’s latest trait (α), and pseudo-guessing (c) is the probability of guessing a right answer [30].

The questionnaire was adopted from Ligouri (2019) [3] This questionnaire included an introduction section explaining the study’s objectives, a section on demographic profile, and questions on a 5-point Likert scale on various elements of the entrepreneurial ecosystem scale. Respondents were informed of the confidentiality of the information provided, and they were also told that they were not bound or obligated to complete the questionnaire. The following section briefly explains the study’s variables.

Finance includes general finance infrastructure and access to capital finance, such as lending programs, the presence of a community for microloans, state facilities for finance, banks, lenders, venture capitalists, and angel investors, as well as the wealth of people in a community [3,28].

Finance has two parts: general finance (six items) and capital finance (five items). The policy variable asked respondents to what extent their national, state, and local government support and advocate entrepreneurship. This could be support of intellectual property, permissions for business, favorable regulations, taxes, and companies [29,30]. There are six items in this policy variable.

Culture is significant in stimulating business activity and innovation. It is a crucial factor in organizational performance and a vital factor in the success of the entrepreneurial ecosystem in any region. Although the acknowledgement of value and attitudes towards innovation, openness, risk-taking, and experimenting, accepting entrepreneurship as a career opportunity is primarily the result of a particular culture in each region [31,32,33]. Support has two parts: general support and support professions. These include necessary infrastructures, legal and accounting professions, supportive institutions, supportive programs, and vibrant and supportive communities [3]. General finance has seven items, and support professions has five items.

The entrepreneurial community’s access to human resources is a crucial impacting factor, and it varies from industry to industry. Although technological advances have made access to human resources easier than before, they impact small ventures in emerging economies [3,34]. The human resources category has six items. The market includes diaspora networks, distribution channels, early adopters, and testing products in a diversified market [30,35].

3. Results

The results are presented in two sections: first, factor analysis, and in the next section, IRT results are presented.

3.1. Pilot Study

The pilot study showed that respondents did not find any difficulty in the questions of the instruments, since scale was adopted and the alpha value of the pilot study was 0.908, indicating good value, which is closer to one, as recommended by reference [36].

3.2. Factor Analysis

The dimensions were assessed through factor analysis in a software statistical package for social science (SPSS) using an axis factoring method with varimax rotation on the scale of the entrepreneurial ecosystem to unearth the factor structure [37]. The original scale has six dimensions, e.g., finance, support, market, human resources, culture, and policy. The EFA performed in SPSS revealed two subdomains within finance and support, hence eight dimensions. The Kaiser–Meyer–Olkin (KMO) test and Bartlett’s sphericity test assessed (See

Table 1. KMO and Bartlett’s test of sphericity.

Dimension	Cronbach’s Alpha	McDonald’s Omega	KMO	Bartlett Test of Sphericity	Total Variance
CF	0.874	0.85	0.818	0.00	66.545
GF	0.918	0.85	0.898	0.00	71.255
HR	0.856	0.89	0.858	0.00	58.109
GS	0.882	0.92	0.890	0.00	58.843
Market	0.866	0.90	0.806	0.00	65.895
Culture	0.916	0.94	0.908	0.00	63.208
Policy	0.916	0.94	0.887	0.00	70.585
SP	0.853	0.91	0.796	0.00	63.014

) the factor loadings, and the communality of the items was assessed using a principal component matrix with the “varimax” extraction method. The reliability was assessed based on Cronbach’s alpha and McDonald’s omega to assess the reliability of the constructs (See Table 1). Parallel analysis was used to confirm the number of dimensions of the factor analysis [38].

The Kaiser–Meyer–Olkin (KMO) test of sampling adequacy shows values between 0.796 and 0.908, indicating acceptable values. Barlett’s test of sphericity for all variables was <0.05 and it is significant. McDonald’s omega coefficient (ω) tests the reliability of all variables it is interpreted in the same way Cronbach’s Alpha, and the values are greater than ≥0.70 for all constructs showing the good reliability of the instrument [36], and the total variance explained is greater than 50% of all variables.

Factor loadings of items are shown (See

Table 2. Factor loadings and communalities.

	Factor Loadings	Extraction		Factor Loadings	Extraction
Gf3	0.890	0.628	Gs3	0.797	0.535
Gf5	0.868	0.719	Gs2	0.790	0.624
Gf4	0.858	0.791	Gs6	0.783	0.636
Gf2	0.848	0.736	Gs4	0.783	0.613
Gf6	0.805	0.753	Gs5	0.779	0.607
Gf1	0.792	0.648	Gs1	0.731	0.613
			Gs7	0.701	0.491
Cf5	0.827	0.681	Sp2	0.832	0.550
Cf1	0.825	0.650	Sp4	0.811	0.692
Cf4	0.820	0.639	Sp5	0.796	0.617
Cf2	0.806	0.673	Sp3	0.786	0.657
Cf3	0.799	0.685	Sp1	0.742	0.634
Cul7	0.828	0.559	Hr2	0.781	0.573
Cul4	0.812	0.615	Hr5	0.768	0.610
Cul6	0.802	0.628	Hr4	0.763	0.552
Cul8	0.796	0.659	Hr6	0.761	0.582
Cul5	0.795	0.632	Hr1	0.757	0.590
Cul3	0.793	0.643	Hr3	0.743	0.579
Cul2	0.784	0.686	Mr3	0.881	0.653
Cul1	0.748	0.634	Mr2	0.837	0.701
Pol5	0.873	0.690	Mr1	0.808	0.776
Pol4	0.856	0.700	Mr4	0.804	0.646
Pol3	0.844	0.712	Mr5	0.720	0.518
Pol2	0.837	0.733
Pol1	0.831	0.763
Pol6	0.798	0.638

), each item strongly influences their factor and majority of factor loadings are >0.70, extraction of communalities in most cases is ≥0.50% and items contribute at least 50% of variation.

The parallel analysis (Figure 1) of the variance of all dimensions is 70% and that calls for the one-dimensionality of the scale, and since the variance is greater than 20%, this calls for using the unidimensional IRT model [39].

3.3. IRT Results

3.3.1. Data Description

A total of 474 responses were included in the analysis. Respondents were provided a questionnaire. They were asked to respond with their feelings on a 5-point Likert scale on various elements of the entrepreneurial ecosystem. The scale consisted of “(1) strongly disagree”, “(2) disagree”, “(3) undecided”, “(4) agree”, and “(5) strongly agree” (See

Table 3. Descriptive summary of important factors and responses.

Variable	Median	IQR	Variable	Median	IQR *
General Finance			Human Resources
Gf1	3	2	Hr1	4	1
Gf2	3	2	Hr2	3	1
Gf3	3	2	Hr3	4	1
Gf4	3	2	Hr4	3	1
Gf5	3	2	Hr5	3	1
Gf6	3	2	Hr6	3	1
Capital Finance			Support Professions
Cf1	3	2	Sp1	3	2
Cf2	3	2	Sp2	3	2
Cf3	3	1	Sp3	3	2
Cf5	3	1	Sp4	3	1
			Sp5	3	2
General Support			Culture
Gs1	3	2	Cul1	4	1
Gs2	3	2	Cul2	3	2
Gs3	3	1	Cul3	3	1
Gs4	3	2	Cul4	3	1
Gs5	3	2	Cul5	3	1
Gs6	3	2	Cul6	3	1
Gs7	3	2	Cul7	3	1
Policy			Cul8	3	1
Pol1	3	1	Market
Pol2	3	2	Mr1	3	1
Pol3	3	1	Mr2	3	1
Pol4	3	2	Mr3	3	2
Pol5	3	1	Mr4	3	2
Pol6	3	2	Mr5	3	2

* IQR = Interquartile range.

and Appendix A). The respondents had to rate elements of an entrepreneurial ecosystem, for example, general finance, capital finance, human resources, market, culture, policy, public support, and support professions. The majority of respondents rated undecided, followed by agreeing and disagreeing on various elements of the entrepreneurial ecosystem.

A total of 50% of respondents selected neutral on different items, 50% of the participants selected agree for items Hr1,H3, and Cul4, which have a median value of 4, and the IQR of all items is either 2 (some polarized opinions) or 1 (showing consensus among respondents (see Table 1)).

The scale used in this research as an instrument of the entrepreneurial ecosystem scale was developed by Ligouri (2019) [3]. This scale contains elements of the entrepreneurial ecosystem based on the model by Isenberg (2010) [40], a model of the entrepreneurial ecosystem that identified six distinct components: (a) finance, (b) support, (c) human resources, (d) market, (e) culture, and (f) policy. Furthermore, the reference [1] has identified two subdomains within finance and support, e.g., capital finance and support professions, and the scale used in this research contained 48 items distributed across eight factors. The reference [1] has identified eight factors.

Using the IRT-GRM, the value of α > 1.0, is considered highly discriminant. Difficulty values are within the range of −3 to 3 [24]. The item under the element market, that is, mar5, has the lowest discriminative value. The extremity parameters (β) show the latent score, where respondents have a 50% probability of selecting item responses. For example, respondents had a 50% probability of selecting first, second, third, and for the option of item Gf1, with extremity parameters of (−1.75), (−0.33), (0.48), and (2.32), respectively.

3.3.2. Item Category Characteristic Curve

The figures show the ICCC curve of all items in each factor in terms of latent factor (theta) (Appendix B). It is defined as a “nonlinear relationship line representing the probability of endorsing an item response category as a function of q (quantitative trait)” and values at the vertical axis are the probability of observing each response category. The probability of witnessing each response category range from one to five [41].

It is noted in the ICCC curve for all items of the scale (Appendix B) that they appear to be ordered properly; most of the items have a less than medium level of difficulty, since their probabilities of endorsing correct responses are greater than or equal to 0.5, except for items Gs1 under general support, Mr5 under market, and item Hr1 under human resources, have ICCC curve with probabilities <0.50 and flatter curve meaning they have higher levels of difficulty [42].

3.3.3. Item Information Function (IIF)

The figures on the IIF and test information function (TIF) measure the reliability of latent traits at various levels; as seen in Appendix B, the curves for general finance show that information peaks at the θ = −2.0 and 2.0, and item Gf1 has lower information. Curves for capital finance show that information peaks at θ = −2.0 and 2.0, and item Cf1 has lower information values. Curves for general support show that information peaks at θ = −2.5 and 2.5, and item Gs1 has lower information across the θ continuum. Information peaks at θ = −2.5 and 2.5 for support professions, and item Sp1 has lower information. For culture, information peaks at θ = −2.0 and 2.0, and item Cul1 has lower information across the θ continuum. Information peaks at θ = −2.5 and 2.5, and item H3 has lower information. Curves for market are rather peculiar and they have multiple levels of peaks between θ = −2.5 and 2.5, and item Mr5 has lower information across θ. The curves for policy show that its information peaks at θ = −1.5 and 2.0, and item Pol6 has lower information across the latent trait.

The test information function shows how well the items estimate the ability or theta across all theta levels by aggregating the IIF of all things. This is one of the main advantages of IRT in contrast to CTT, where reliability is assumed to be constant with one index, that is, Cronbach’s alpha. The advantage of IRT is that it provides reliability with information criteria [24].

It is pertinent to note that log-likelihood can have values between -inf and +inf, and it shows the goodness of fit. Therefore, the comparison is made based on the values obtained, and the highest to lowest log-likelihood are market (−2079.6), capital finance (−2450.5), support professions (−2595.1), general finance (−2689.5), policy (−2951.6), human resources (−3184.6), general support (−3642.4), and culture (−3978.2) (See

Table 4. IRT parameter estimates.

General Finance	Log-Likelihood = −2689.5384
	α	β1	β2	β3	β4
Gf5	3.72	−1.54	−0.35	0.39	1.88
Gf4	2.78	−1.65	−0.38	0.4	2.07
Gf6	2.59	−1.7	−0.47	0.41	1.85
Gf3	2.47	−1.99	−0.44	0.37	2.34
Gf2	2.41	−1.9	−0.35	0.47	2.29
Gf1	1.97	−1.75	−0.33	0.48	2.32
Capital Finance	Log-Likelihood = −2450.4663
Cf5	2.8	−1.72	−0.58	0.81	2.66
Cf2	2.22	−2.04	−0.48	0.69	2.71
Cf4	2.03	−2.15	−0.66	0.82	2.87
Cf3	1.95	−2.27	−0.86	0.45	2.36
Cf1	1.91	−1.81	−0.63	0.77	2.66
General Support	Log-Likelihood = −3642.444
Gs3	2.52	−1.99	−0.84	0.29	2.14
Gs4	2.49	−2.07	−0.84	0.33	2.19
Gs2	2.47	−1.98	−0.6	0.43	2.23
Gs5	2.39	−2.21	−0.69	0.55	2.33
Gs6	2.34	−2.16	−0.65	0.53	2.5
Gs1	1.96	−1.81	−0.68	0.44	2.16
Gs7	1.82	−2.23	−0.62	0.7	2.68
Support Professions	Log-Likelihood = −2595.0558
Sp2	2.88	−2.12	−0.59	0.34	2.17
Sp4	2.57	−2.02	−0.58	0.51	2.31
Sp5	2.45	−2	−0.51	0.59	2.4
Sp3	2.35	−2.15	−0.61	0.53	2.59
Sp1	1.98	−2.22	−0.58	0.44	2.96
Culture	Log-Likelihood = −3978.2054
Cul7	3.21	−1.88	−0.79	0.12	1.76
Cul5	2.89	−1.81	−0.78	0.04	1.89
Cul4	2.85	−1.75	−0.78	0.03	1.61
Cul6	2.81	−1.92	−0.76	0.24	1.86
Cul8	2.78	−1.71	−0.79	0.21	1.88
Cul3	2.56	−1.92	−0.88	0.1	1.85
Cul2	2.37	−2	−0.76	0	1.88
Cul1	2.16	−2.02	−0.86	−0.02	1.97
Human Resources	Log-Likelihood = −3184.5954
Hr2	2.42	−2.01	−0.74	0.34	2.09
Hr4	2.32	−2.39	−0.86	0.35	2.14
Hr6	2.21	−2.32	−0.85	0.4	2.22
Hr5	2.19	−2.04	−0.74	0.52	2.25
Hr1	2.12	−2.11	−0.92	0.23	2.22
Hr3	2.05	−2.37	−1.2	0.07	2
Market	Log-Likelihood = −2079.6322
Mr3	3.27	−2.06	−0.82	0.42	1.82
Mr2	2.64	−2.31	−0.95	0.35	1.91
Mr1	2.5	−2.27	−1.06	0.35	2.49
Mr4	2.17	−2.25	−0.66	0.41	1.94
Mr5	1.57	−2.63	−0.72	0.49	1.93
Policy	Log-Likelihood = −2951.5784
Pol5	4.13	−1.41	−0.12	0.83	1.99
Pol4	3.55	−1.6	−0.16	0.73	2
Pol3	3.34	−1.56	−0.17	0.81	1.93
Pol2	2.95	−1.58	−0.2	0.72	2.06
Pol1	2.85	−1.6	−0.29	0.63	2.08
Pol6	2.61	−1.52	−0.19	0.8	1.87

).

The discrimination parameters are found between 4.13 and 1.57. This indicates that the item response categories are powerful enough to distinguish respondents with different latent traits or knowledge with high to very high discrimination parameters for all items [43].

The polychoric parallel analysis is performed in r-studio and scree plots are shown for all variables, e.g., general finance, capital finance, human resources, market, policy, culture, general support, and support professions. In all cases the scree plot shows one factor based on eigen values >1.

3.3.4. Anchoring of Items

Table 5. Scale of degree of difficulty.

Domain	Anchor Levels
	Lower Agreement Level ≤ 0.50	Moderate Agreement Level < 0.65	Highest Agreement Level ≥ 0.65
General Finance		Gf3	Gf5
		Gf4	Gf6
		Gf2
		Gf1
Capital Finance	Cf1	Cf2	Cf3
	Cf5	Cf4
General Support		Gs1	Gs2
		Gs7	Gs3
			Gs4
			Gs5
			Gs6
Support Professions		Sp4	Sp2
		Sp3
		Sp5
		Sp1
Human Resources		Hr5	Hr3
			Hr4
			Hr2
			Hr6
			Hr1
Market			Mr1
			Mr2
			Mr3
			Mr4
			Mr5
Policy	Pol5	Pol1
	Pol3	Pol4
		Pol6
		Pol2

shows the results of the anchoring process. The IRT parameters were linearly transformed with (100 ± 10), as described by author [44] and author [45]. After the linear transformation, which showed the cumulative probability by using two parameter logistics (2PL), the (2PL)-IRT method was applied for all items, this resulted in three categories (<0.50, <0.65, and ≥0.65). These three levels show lower agreement levels, moderate agreement levels, and highest agreement levels for the items based on recommendations by Beaton and Allen (1992) [46]. The lower agreement level is on items Cf1, Cf5, Pol3, and Pol5, the moderate level agreement is on terms Gf1, Gf2, Gf3, Gf4, Cf2, Cf4, Gs1, Gs7, Sp1, Sp3, Sp4, Sp5, Hr5, Pol1, Pol2, Pol4, and Pol6, and highest level of agreement is for items Gf5, Gf5, Cf3, Gs2, Gs3, Gs4, Gs5, Gs6, Sp2, Hr1, Hr2, Hr3, Hr4, Hr6, and Mr1 to Mr5.

Table 6. Proportion of agreement.

Latent Trait	Respondents	Percentage
Lower Agreement Level	160	33.76%
Moderate Agreement Level	305	64.35%
Highest Agreement Level	9	1.90%

shows the percentage of respondents in each anchor level.

3.3.5. Item-Level Fit Assessment

The item-level fit assessment was performed on all items on observed and expected residuals using the chi-square goodness of fit. The results showed that all items had a p-value < 0.05; we expected poor goodness of fit for item Market5 under the domain “market” because of its flatter ICCC curve. However, the test did not detect a poor fit, and the model generally showed a good fit for all items.

4. Discussion

The popularity of the entrepreneurial ecosystem is gaining momentum, and there has been a continuous rise in scholarly research on measuring the entrepreneurial ecosystem to see the environment for entrepreneurs in a given region. This can provide us with policy action points to improve entrepreneurial ecosystem at the regional, state, and national levels.

The perception-based instrument of EE was developed by Ligouri (2019) [3] and expanded by reference [1]. This questionnaire has 48 items with a 5-point Likert scale, the pilot study validated the scale and reliability was found to be satisfactory. The scale was assessed through factory and parallel analysis, and it was found to be unidimensional; therefore, the multidimensional IRT model was used (see Table 1 and Table 2 and Figure 1).

With the help of IRT, it was possible to validate the scale, which enabled us to calculate the discrimination and difficulty levels for each response, regarding the level of agreement on the domains of the entrepreneurial ecosystem, e.g., general finance, capital finance, general support, support professions, human resources, culture, market, and policy, and the calculation of ability levels or (θ). The IRT results showed that items of the scale were able to differentiate respondents having different levels of abilities or (θ). The recommended value for discriminating power was based on 0.700, as recommended by Tezza et al. (2011) [47]. All items showed good discriminating power (>0.700). The highest discrimination value (4.13) was found for item pol5 (provincial and local governments have strong policies for the growth of entrepreneurship), and the lowest value was for Mr5 (1.57), although it was still greater than the recommended value (0.700). The items Mr5 and Hr4 were easiest items for the respondents at level two, while items Sp1, Cf4, and Cf2 were the most difficult at an alternative level four, thus IRT allows us to see the discrimination power and the difficulty levels of the items of the scale.

Figure 2 Standard Error and information retrieved at different ability levels red curves shows the Standard Error against information obtained in blue. These figures indicate that the highest information was achieved in the range of −2.5 to +1.5, and that the perception range information is achieved at different ability levels; therefore, it validates the instrument [44,48,49].

The information and expected total score curves, Figure 2 indicate that the latent trait fits well to the cumulative model and that the information covers the different latent trait values, validating the instruments. The validations of the latent traits using this same procedure can be analyzed in the studies by author [44], author [48], and author [49].

The anchoring analysis was performed following guidelines set by Vincenzi et al. (2018) [45], and it is one of the best advantages of IRT models compared to CTT [50]. Anchoring analysis has identified three levels, namely lower, moderate, and highest levels of agreement on the domains of the entrepreneurial ecosystem, i.e., general finance, capital finance, general support, support professions, human resources, culture, market, and policy. Respondents had the lowest level of agreement for items Cf1, Cf5, Pol3, and Pol5, and the respondents had moderate levels of agreement for items Gf3, Gf4, Gf2, Gf1, Cf2, Cf4, Gs1, Gs7, Sp4, Sp3, Sp5, Sp1, Hr5, Pol1, Pol4, Pol6, and Pol2. The highest level of agreement was found for items Gf5, Gf6, Cf3, Gs2, Gs3, Gs4, Gs5, Gs6, Sp2, Hr3, Hr4, Hr2, Hr6, Hr1, Mr1, Mr2, Mr3, Mr4, and Mr5. In total, the majority level of agreement is from the lowest to moderate levels of agreement (33.76% to 64.35%) (Table 6), so it can be inferred that the level of agreement for most participants is moderate about the entrepreneurial ecosystem.

Finally, the scale is tested for goodness of fit to achieve this indices CFI, TLI, RSME and SRMR were used. The indices CFI (0.973) and TLI (0.955) values are closer to 1, indicating best fit. RSMEA (0.111) was in a lower bound (0.073 > 0.05) indicating poor fit, the upper bound was 0.152 > 0.10, indicating good fit, the p-value was 0.006 < 0.05 indicating that the fit is not close, and the SRMR was 0.026. Zero SRMR indicates a perfect fit with the threshold value at 0.08.

The validation of the scale is based on the acceptable levels for the factor analysis and the parameters of IRT, such as discriminating power and difficulty level, and it becomes possible to achieve an acceptable measurement scale with the theta or latent trait; therefore, the psychometric properties showed scale is having good properties. The factory analysis validates the latent constructs and IRT validates the discrimination power of the items [43,44].

5. Conclusions

The scale tested in the research is able to measure the level of agreement of respondents regarding the entrepreneurial ecosystem. The 48 items showed the satisfactory level of psychometric properties with a good level of discriminating power with a high to very high level of discriminating power (greater than 1.7) with respondents with different levels of knowledge, and with increasing difficulty for response alternatives, which require more abilities or latent traits. The EE scale tested and validated provides an opportunity to identify problematic items; these items need attention or rewording, e.g., item Mar5 under market has lower discrimination (1.57) and, therefore, this item should be reworded to improve its discrimination. The results from IRT have generated three levels, from a minimal level of agreement to the highest level of agreement.

The main findings of this research suggest that the EE scale possesses a satisfactory level of psychometric properties in terms of item difficulty and discrimination to measure the attitudes of respondents towards elements, e.g., policy, finance, market, human resources, culture, and support of the entrepreneurial ecosystem in a particular region, which will help policy makers to identify and prioritize policy action towards an entrepreneurial ecosystem based on the perception-based scale [3]. This research has contributed in the extant literature by providing a validated scale to measure the EE in a given region through the attitudes of the entrepreneurs, whilst many of the authors [51,52,53,54,55,56] have provided different measuring frameworks to measure the EE.

The present research has a number of limitations. First, the participants are drawn from one region of Pakistan (Sindh), and respondents from other regions, e.g., Punjab, KPK, and Baluchistan, should be included in future research because they might have different perceptions and attitudes towards specific items, therefore, establishing an invariance of the scale across different regions, ages, and gender groups, providing further evidence of the application of the scale. Another limitation is the would-be translation of the scale in local languages to assess its psychometric properties and invariance. Future studies should also use differential item functioning (DIF) using age, gender, business experience, and city of origin, which would yield more reliability for the EE scale.

6. Theoretical and Practical Implications

In this research, the authors have used IRT-GRM on the scale developed by reference [3], and this scale measures six aspects of entrepreneurial ecosystem based on D. Isenberg’s [57] model of the entrepreneurial ecosystem. The IRT-GRM model was applied to EE scale to validate the scale and to identify the problematic items, this helps EE scale to be consistent and robust to measure to assess the entrepreneurial ecosystem in a given region based on the attitudes of the entrepreneurs working in a certain region. This study further contributes towards an extent literature effort to measure entrepreneurial ecosystem.