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Examining the Invariance of a Measurement Model of Teachers’ Awareness and Exposure Levels to Nanoscience by Using the Covariance Structure Approach

Configural invariance, Factorial structure invariance, Structural covariance invariance, Measurement residual invariance, Invariance of nanotechnology scale. Abstract: The main aim of this study is to examine the measurement invariance of the structural equating model constructed on the Awareness and Exposure subscales of Nanoscience and Nanotechnology Awareness Scale (NSTAS) test for three teacher branches, three school types, and two genders by using the covariance structural analysis to test configural and metric invariances. The other aim of this study is showing how to use the IBM AMOS-24 software package with examples to address the issue of measurement invariance using the covariance structural analysis approach. Study sample was 1039 complete records gathered from science teachers with convenience sampling. Research data were collected in two stages. In the first stage, data were obtained from 624 teachers who participated to the study in the 2015-16 academic year. In the second stage, data were obtained in 2019 from 415 teachers via a link to access to the scale and all the instructions for the NSTAS in 2019. The covariance structures analysis was used to examine the measurement invariance of the scale. The comparative fit index was used to compare the measurement invariance in the measurement model. The study revealed that configural, measurement weight and structural covariance invariances were ensured for branches, school types and genders. Residual invariance was ensured only for gender. As a result, it was concluded that the NSTAS scale was not biased for teacher branches, school types or gender. NSTAS scale is recommended for the purposes of comparing branch, school type and gender groups.


INTRODUCTION
Nanoscience and nanotechnology (NSNT) are an abstract and complex topic with various applications resulting from the manipulation of atoms and molecules. Nanotechnology, one of the most promising technologies of the 21st century, utilizes devices, structures, and molecules on the scales of nanometers ranging between 1 and 100 nm (Bayda et al., 2020). The responsible development of nanotechnology that addresses the ethical, legal, and societal issues together with research, commercialization, worker education, and public engagement is assumed to two genders are determined as sub-groups to test the measurement invariances. When different groups are to be compared, the obtained scores from the scale should not be biased (Tan & Pektaş, 2020). Further investigations are necessary to explain/justify the question of whether the scale items perform similarly across subgroups, and one way to examine this question is through assessing the measurement invariance of a scale (Chung et al., 2016). There are several studies in the literature on measurement invariance for test scores (Arana et al., 2018;Camerota et al., 2018). For a measurement model to have the same structure across different groups, the factor loadings of the items in a scale, and the correlations and variances among the identified factors, should be the same (Tan & Pektaş, 2020). While examining the measurement invariance of a measurement model between groups, the model created at each stage is built on the model created in the previous stage, i.e., the models are nested. As stated by Byrne (2016, pp. 227-228), "In seeking evidence of multigroup equivalence, researchers are typically interested in finding the answer to one of five questions. First, do the items comprising a particular measuring instrument operate equivalently across different populations? In other words, is the measurement model group-invariant? Second is the factorial structure of a single instrument or of a theoretical construct equivalent across populations? Third, are certain paths in a specified causal structure equivalent across populations? Fourth are the latent means of constructs in a model different across populations? Finally, does the factorial structure of a measuring instrument replicate across independent samples drawn from the same population? This latter question addresses the issue of cross-validation." As Chung et al. (2016) stated, configural invariance is the fact that factor structures between groups are equivalent. In other words, configural invariance tests that the same pattern of itemfactor loadings exists across groups compared, which requires that the same items have nonzero loadings on the same factors. To observe whether the other steps of invariance are ensured, comparisons are made based on the configural invariance values (Cheung & Rensvold, 2002;Vandenberg & Lance, 2000). On the other hand, metric invariance refers to equivalence among factor loadings. Chung et al. (2016) emphasized metric invariance, in addition to configural invariance, requires that unstandardized factor loadings be the same across groups. The scalar invariance is based on the equivalence of factor covariances across groups. Therefore, scalar invariance, addition to configural and metric invariance, factor variances and factor covariances are the same across groups. It is a kind of invariance where factor covariances are equalized across the groups after configural and metric invariances are ensured (Cheung & Rensvold, 2002;Meredith, 1993). Strict invariance requires proof that errors do not vary by group. Strict invariance, addition to configural, metric and scalar invariance, the error variances are the same across groups. It is a type of invariance where all factor loadings, factor variances, factor covariances and error variances are constrained (Cheung & Rensvold, 2002). In the present study, the stages of identifying configural and metric measurement invariances of NSTAS were realized by using the covariance structural analysis (COVS) approach. In COVS approach of testing measurement invariances, only the variances and the covariances between paired observed variables are used as observed variables.

Aim of the Study
The very first step in nano education at any level is ensuring the awareness of the teachers (Bryan et al., 2012;Enil & Köseoğlu, 2016). The present study aimed to examine the measurement invariance of the structural equating model constructed on the Awareness and Exposure subscales of NSTAS test for three science teacher branches, three school types, and two genders by using the covariance structural analysis (COVS). In this study we also use the IBM AMOS-24 software package as illustrated with examples to address measurement invariances using the covariance structural analysis approach. This is a significant contribution to the field of science education measurement and assessing since most of the measurement invariance studies are confined purely to the measurement field.

METHOD 2.1. The Research Model
This study is a descriptive study, as it is intended to present the present situation in terms of measurement invariance of NSTAS structural model and no variable is manipulated. Details of the scale have been published elsewhere (İpek et al., 2020).

The Study Group
The sample of the study consists of 1039 complete records (without any missing records) gathered from science teachers. Research data were collected in two stages. The data in the first stage were obtained from 624 teachers in the 2015-16 academic year, used in İpek's (2017) doctoral thesis. Data in the second stage were obtained during 2019 by using a link to access the NSTAS scale and all instructions. In rare cases the scale was administered face-to-face to the respondents. Convenience sampling approach was used to form the study group. The distribution of the 1039 science teachers to the branches, school types and gender were as follows: Biology 38.5%; physics 31.5%, and chemistry 30.0%; science high school 16.3%, Anatolian high school 56.4% and vocational high school 27.3%; and male 45.4% and female 54.6%.

Data Collection Instruments
The Nanotechnology Awareness Instrument (NAI, Dyehouse et al., 2008, refer to Appendix for the instrument) was adapted into a Turkish version and named Nanoscience and Nanotechnology Awareness Scale (NSTAS, refer to Appendix for the scale); validity and reliability of the Turkish version were tested by the authors. The original scale (NAI) assessed changes in higher education student awareness, exposure, and motivation for nanotechnology, as well as factual knowledge about nanotechnology. The nanotechnology awareness subscale measures whether respondents "know something about nanotechnology" and whether they "have heard about nanotechnology and its applications". Awareness is supported by exposure, where respondents' previous exposure to nanotechnology may enhance their awareness and knowledge. NAI consisted of two parts: Items in Part A regarding awareness, exposure, and motivation subscales, and Part B regarding factual knowledge about nanotechnology (Dyehouse et al., 2008). Our version, the NSTAS, has three subscales, the Awareness (8 items) and Exposure (6 items) subscales adopted from NAI (total of 14 items), and the subscale Knowledge developed by the authors. The Awareness (8 items) and Exposure (6 items) subscales were used to perform measurement invariance analysis. The Cronbach alpha internal consistency coefficient of the Awareness (8 items) subscale was found to be .934 and Exposure subscale .845. Stratified alpha reliability coefficient for whole scale (with Awareness and Exposure, 14 items) was found to be .945.

Data Analysis
The covariance structural analysis approach was utilized to examine the measurement model invariances by sub-groups, explained above. The multivariate normal distribution assumption was tested for each subgroup. The multivariate normal distribution assumption was not met for any subgroup. Therefore, bootstrap estimation with 500 bootstrap samples was used to estimate the model parameters. In testing measurement invariances between the .01 reduction criterion the CFI value (ΔCFI) was used. Based on the conditions for ensuring measurement invariance, this has been accepted as proof for the presence of measurement invariance (Cheung & Rensvold, 2002). Also, a difference of less than .01 in the ΔCFI index supports the less parameterized model (Chung et al., 2016). During the analyses, the operations were done via the IBM AMOS-24 package program and explained as follows (Byrne, 2016): IBM AMOS-24 operations for configural invariance.
1. The groups are defined by selecting the Manage Groups function from the Analyze menu in the AMOS program. 2. Subsequently, the data files are assigned to the defined groups by selecting the Data Files function from the File menu. 3. The Emulisrel6 box is ticked by selecting Estimation from Analysis Properties in the View menu. 4. Finally, the analysis is run by selecting Calculate Estimates from the Analyze menu. IBM AMOS-24 operations for configural, factor loading, structural variances and measurement residual invariances. Until the stage of making the predictions, as an addition to the operations mentioned above, the parameters to be predicted in the model are labelled manually or automatically. For automatic labelling, 1. Multiple Group Analysis function is selected from the Analyze menu. 2. The parameters to be constrained are selected in the Multiple-Group Analysis dialog box. 3. The analysis is run by selecting Calculate Estimates from the Analyze menu.

RESULT / FINDINGS 3.1. Measurement Model
The baseline measurement model, which is used for eight subgroups, is presented in Figure 1, below. As it seen in Figure 1, Awareness latent variable is measured with 8 items (A1 to A8) and Exposure latent variable is measured with 6 items (B1 to B6). There are covariance connections between the Awareness and Exposure latent variable and 11 covariance connections between some measurement residual variables in the baseline model. Item A5 was taken as reference for the scale of Awareness latent variable and item B3 for the scale of Exposure latent variable.

Measurement Invariance by Branch
The goodness of fit indices of the baseline measurement model used for all subgroups created within the scope of the study are presented below. Having good model fit indexes in all subgroups for the baseline measurement model is a prerequisite for invariance analysis.

Step 1: Goodness of Fit Indexes of the Baseline Measurement Model for Branch
The baseline model is presented in Figure 1. In the baseline measurement model based on the branches of teachers, the goodness of fit indexes (Schermelleh-Engel et al., 2003)  In conclusion, the baseline measurement model in Figure 1 displayed a high level of model fit for Physics, Chemistry, and Biology teachers.

Step 2: Configural invariance of the Measurement Model for Branch
As stated by Byrne (2016), to ensure configural invariance, factor loading patterns and the number of factors should be similar for each group. The measurement model based on teachers' branch has provided configural invariance with 195 2 =606.903; 2 /df=3.112; GFI=.925; CFI=.961 and RMSEA=.045. That is, in this unconstrained measurement model, the factor structure for Physics, Chemistry, and Biology Teacher groups was found to be similar. These results show that the model in Figure 1 is a valid measurement model for all subgroups. The unstandardized estimated parameters (regression weights, covariances, and variances) of three branches for configural invariance are given for each group in Tables 1a, 1b and 1c, below.  Step 3: Configural and Measurement Weights Invariance of the Measurement Model for Branch As Byrne (2016) notes, in testing the measurement, structural and measurement error invariance, the focus is on the parameters, related to the measurement model, structural components and measurement errors, being equal in all groups. The measurement model based on teachers' branch has provided configural and measurement weights invariance with 219 2 =654.437; 2 /df=2.988; GFI=.919; CFI=.959 and RMSEA=.044. For testing the significant model differences, the CFI change value that we take the criteria was found to be less than .01 (ΔCFI= .002). So, difference between configural invariance model and configural and measurement weights invariance model is not significant. In other words, the measurement model with restricted regression weights for Physics, Chemistry and Biology Teacher groups have been found to have good fit indexes with no significant CFI changes. So, measurement weights are equal for Physics, Chemistry, and Biology Teacher groups in the population. The unstandardized estimated parameters (constrained regression weights, covariances, and variances) of three branches for configural and measurement weights invariance are given for each group in Tables 2a, 2b, and 2c below.  Step

4: Configural, Measurement Weight and Structural Covariance Invariance of the Measurement Model for Branch
The measurement model based on teachers' branch has provided configural, measurement weight, and structural covariance invariance with 225 2 =667.589; 2 /df=2.967; GFI=.918; CFI=.958 and RMSEA=.044. For testing the significant model differences, the CFI change value that we take the criteria was found to be less than .01 (ΔCFI=.003). So, difference between configural invariance model and configural, measurement weight and structural covariance invariance model is not significant. In other words, the measurement model with constrained regression weights and structural covariances for Physics, Chemistry and Biology Teacher groups have good fit indexes with no significant CFI changes. So, measurement weights and structural covariances are equal for Physics, Chemistry, and Biology Teacher groups in the population. The unstandardized estimated parameters (constrained regression weights, constrained structural covariances, other covariances and variances) of three branches for Configural, Measurement Weights, and Structural Covariance Invariance model are given for each group in Tables 3a, 3b, and 3c below. In this model, since we have two structural variables (Awareness and Exposure), there is one structural covariance and two structural variances to be constrained additionally.  Step

5: Configural, Measurement Weight, Structural Covariance, and Measurement Residual Invariance of the Measurement Model for Branch
The goodness of fit indexes for this model were found to be good with 275 2 =846.863; 2 /df=3.080; GFI=.895; CFI=.946 and RMSEA=.045. However, for testing the significant model differences, the CFI change value was higher than .01 (ΔCFI=.015). It is clear that, difference between configural invariance model and configural, measurement weight, structural covariance, and measurement residual invariance model is significant. Therefore, measurement residual estimates are not identical for Physics, Chemistry, and Biology Teacher groups in the population. Because all the model parameters are constrained equal, the unstandardized estimated parameters of the model are given in the path diagram, Figure 2, below. The main findings regarding the measurement invariance according to the branches are presented in Table 4 below. As can be observed in Table 4, according to the unconstrained (configural) model, the changes in CFI in the models obtained by constraining, in sequence, measurement weights, and structural covariances were less than .01. However, when error residuals constrained the changes, CFI was found to be more than .01. Hence, it was concluded that the measurement model has provided configural, measurement weight, and structural covariance invariance; but did not provide measurement residual invariance across three branches.

Goodness of Fit Indexes of the Baseline Measurement Model for School Type
In the baseline measurement model based on the school types, the goodness of fit indexes were found to be as follows: In conclusion, the baseline measurement model in Figure 1 displayed a high level of model fit for three school types.

Configural, Measurement Weight, Structural Covariance, and Measurement Residual Invariance of the Measurement Model for School Type
The unstandardized estimated parameters of the model are given with path diagram for school types in Figure 3, below, and the main findings regarding the measurement invariance according to the school types are presented in Table 5 below. Note: Unconstrained Model: All the parameters are predicted freely. Measurement Weights Model = All Factor loadings are constrained (equated). Structural Covariances Model = All Factor loadings + factor variances and covariances are constrained (equated). Measurement Errors Model = All Factor loadings + factor variances + factor covariances + error variances are constrained (equated).
As it seen in Table 5, according to the unconstrained (configural) model, the changes in CFI in the models obtained by constraining, in sequence, measurement weights, and structural covariances were less than .01. However, when error residuals constrained the changes in CFI was found to be more than .01. Hence, the measurement model has provided configural, measurement weight, and structural covariance invariance; but, not provided for measurement residual invariance across three school types. Note: Only 3 covariance estimates (ee5 < --> ee3=.024 with p=.226; ea7 < --> ea8=.033 with p=.054; and ea5 < --> ea2=.036 with p=.015) were not found to be significant, all the other parameters were found to be significant.

Goodness of Fit Indexes of the Baseline Measurement Model for Gender
In the baseline measurement model based on the gender, the goodness of fit indexes were found to be as follows: ✓ for male teachers 65 2 =164.122; 2 /sd=2.525; GFI=0.953; CFI=0.978 and RMSEA=.057; and ✓ for female teachers 65 2 =324.513; 2 /sd=4.993; GFI=0.927; CFI=0.957 and RMSEA=.084. In conclusion, the baseline measurement model in Figure 1 displayed a high level of model fit for the two genders.

Configural, Measurement Weight, Structural Covariance, and Measurement
Residual Invariance of the Measurement Model for Gender The unstandardized estimated parameters of the model are given with path diagram for genders in Figure 4, below, and the main findings regarding the measurement invariance according to the genders are presented in Table 6 below. Note: Only 3 covariance estimates (ee5 < --> ee3=.020 with p=.303; ea7 < --> ea8=.032 with p=.061; and ea5 < --> ea2=.035 with p=.017) were not significant, all other parameters were found to be significant. As it seen in Table 6, according to the unconstrained (configural) model, the changes in CFI in the models obtained by constraining, in sequence, measurement weights, structural covariances, and measurement residuals were less than .01. Hence, the measurement model has provided configural, measurement weight, structural covariance, and measurement residual invariance across two genders.

DISCUSSION and CONCLUSION
This study investigates the measurement invariance of the Nanoscience and Nanotechnology Awareness Scale (NSTAS) for three teacher branches, three school types, and two genders by using the covariance structural analysis to test configural and metric invariances.
There is need to plan and implement NSNT education at primary, secondary, undergraduate, and graduate levels, since teachers' knowledge and competences are the key to education. Factors affecting awareness and knowledge level of teachers/teacher trainees in NSNT should be determined and analyzed before implementing education programs (Hingant & Able, 2010;Jones et al., 2013). The NSTAS instrument was originally developed by Dyehouse et al. (2008) to promote awareness and factual knowledge among higher education students in the USA about nanotechnology uses, so students become acquainted with nanotechnology as a new field of research and innovation affecting society. The greater objective was to motivate university students to academic and career options in the field. Braeken and Blömeke (2016) pointed out, "to allow for making group comparisons in terms of correlations with external variables, the stricter requirement of equal factor loadings" across groups (i.e., metric or 'weak' invariance) needs to hold. They also pointed out that "if we wish to directly compare observed scale sum scores between groups, then additionally, the residual item variances would be required to be equal across groups, such that every item can be considered equally reliable across groups". There are some group comparisons and some educational decisions based on these comparisons regarding nanotechnology and nanoscience using NSTAS scores. In terms of objectivity features of scientific research, to test whether the structural validity or the measurement model of the NSTAS scale works in different subgroups in the same way. In other words, it is extremely important to determine whether the measurement tool provides biased group results using the measurement invariance approach. Wicherts (2016) emphasized that measurement invariance is very important for the validity of tests. In the literature, we could not find any study about measurement invariance in the field of nanotechnology. Very few studies have been found in the literature on measurement instruments used in hard sciences. Some of them are given below. Rocabado et al. (2019) performed measurement invariance testing for the configural, metric, and scalar models comparing black female students and all other students within the traditional and flipped courses for the two-factor model prescribed for the pre and posttests. Their analysis results showed that configural, metric, and scalar invariance was ensured. Maier et al. (2013) developed a preschool teachers' attitudes and beliefs toward science teaching scale. They used teacher ethnicity, education level, and experience level as subgroups. They conclude that the three factors remained invariant across each subgroup. Luo et al. (2019) presented validity evidence of scores produced from the S-STEM measurement tool, and they concluded that measurement invariance results showed that the instrument items in the surveys measured the same constructs in the same ways across gender, age groups, and races/ethnicities. Braeken and Blömeke (2016) investigated the measurement equivalence of teachers' beliefs across countries for the case of 'mathematics as-a fixed-ability'. They concluded that data provided configural and metric invariance but did not provide scaler invariance across countries. Clearly none of the measurement invariance studies cited provide indisputable explanation about the steps of invariance measurement. It is obvious that there is a deficiency in the hard science literature in terms of emphasizing the importance of measurement invariance and elaborating step by step instructions and guidance.
Having examined the measurement model invariance with respect to configural, measurement weight, and structural covariance invariance for three groups of branches, three group of school types and two groups of genders, the present study arrived at the conclusion that configural, measurement weight and structural covariance invariances were ensured for branches, school types and genders. Also, residual invariance was ensured for genders. Residual invariances are not provided for branches, and school types leading us to conclude that not every item can be considered equally reliable across those groups.
In conclusion, the results of this study provide evidence that the measurement invariance requirement for valid group comparisons for the Nanoscience and Nanotechnology Awareness Scale has been satisfied; measurement invariance can be successfully implemented in science and technology education. Casas and Blanco-Blanco (2017) acknowledged using the method for Social Cognitive Career Theory (SCCT) models in predicting mathematical/scientific interests and occupational aspirations among Colombian secondary students. Another successful application was by Caputo (2017) in science and mathematics education of 7th grade secondary students in Italy. The Measure of Acceptance of the Theory of Evolution (MATE, a single-factor instrument that assesses an individual's overall acceptance of evolutionary theory) was tested to assess how it operates differently when administered to a population of nonscience major preservice elementary teachers when compared with the reference population of in-service high school biology teachers and found to be reliable with the measurement invariance approach (Wagler & Wagler, 2013). As a result, it has been proved that the NSTAS scale will not generate biased measurements in comparing groups by teacher branches, school types and gender. Since the internal structure of NSTAS holds for different groups, NSTAS scale can be safely used to compare branch, school type and gender groups. Testing and interpreting the measurement invariance with the covariance structure approach using IBM AMOS-24, implemented with cases in this study, can be applied to all scales aimed at comparing different groups. Table A1. Nanotechnology Awareness Instrument (Dyehouse et al., 2008) For the following items, please indicate the extent to which you agree or disagree using the following scale: Strongly disagree, disagree, neutral, agree, or strongly agree. Strongly disagree Disagree Neutral Agree Strongly agree What is your awareness of nanotechnology? I can:

APPENDIX
1. Name a nanoscale-sized object.
2. Describe one way nanotechnology directly impacts my life.
3. Name a field of study that currently conducts nanotechnology research. 4. Describe one way nanotechnology may benefit society/humankind. 5. Name an application of nanotechnology.
6. Describe a process to manufacture objects at the nanoscale. 7. Name an instrument used to make measurements at the nanoscale.