Correspondence between theory and methodology: a case study of accounting for the environment in organisational research

The two most widely investigated environmental domains concerning firms are environmental disclosure and environmental performance. This study examines how well operational variables inform constructs in these two domains. The empirical research process has two aspects: truth making and truth building. Truth making using operational variables must align with truth building with respect to constructs. Towards this aim, this article explores two research questions. First, are disclosure and performance operationally and conceptually different? Second, do the operationalised and conceptualised variables have a strong association in each domain—disclosure and performance? This study uses research data matrices available from a published journal article as an example to demonstrate analytical details. It uses the canonical correlation analysis research method for analysing matrix data to answer the research questions. The findings show that disclosure and performance are conceptually different domains. However, results show that operational variables associate differently with the construct. The findings show that selecting variables in empirical settings that reflect constructs can correspond with theoretical advancements.


Introduction
Organisations account for the environment by undertaking activities that influence performance and disclosing them to stakeholders. Performance accounts for accountability; disclosure accounts for transparency. Performance and disclosure relating to the environment are the cornerstones of accounting for the environment in organisational research. This study examines the alignment between methodological (or operational) variables and theoretical (or conceptual) variables in empirical research on accounting for the environment. Environmental concerns are at the forefront for all stakeholders. Stakeholders expect businesses to show their commitment to environmental protection (Makhdoom et al 2023).
Any individual can define the term environment. The context in which the environment is discussed has led to different sensemaking and an inability for researchers to reach a single meaning (Young 1986). Higher-order constructs, such as the environment, can carry an oversimplified meaning in day-to-day dialogues. Organisational research on the environment has investigated dimensionalising the environment to enable a more structured sense. The two most well-known dimensions are environmental disclosure and environmental performance (Doan and Sassen 2020). Gathering factual data from the field requires nominating operational variables that are assigned to these construct dimensions. Empirical research is crucial in investigating truth making through methodological approaches and truth building through theoretical approaches. The truths revealed through research endeavours become the evidence that stakeholders trust and act on (Abeysekera et al 2021, Eales 2012. This study aims to investigate analytically whether disclosure and performance have represented the higherorder construct of the environment and whether multiple operational variables representing disclosure and performance are informing the research differently. Two objectives meet these aims. First, the study rearranges matrix data from a published paper to investigate environmental disclosure and performance. Second, the study writes an SPSS syntax command and examines the matrix data using canonical correlation analysis. The study contributes to the tremendous increase in interest in empirical research related to environmental disclosure and performance issues by showing that it is vital to define constructs to ensure that the operational variables accurately reflect the intended theoretical construct through methodological use. The findings extend the understanding of an earlier study that examined constructs and the operational variables nexus (Abeysekera 2014). This study informs the findings with an ontological and epistemological basis.
Section 2 presents the background for this investigation into environmental research and briefly discusses organisational responsibilities relating to environmental performance and disclosure. Section 3 introduces the correspondence theory of truth regarding how constructs correspond with operational variables. Section 4 briefly outlines the sample article selection and discusses the chosen journal article to analyse the matrix data. It also discusses the extraction of the research data and the research method used. Two subsequent sections discuss the results of this analysed article: section 5 reports findings related to the first research question and section 6 reports findings related to the second research question. Section 7 addresses how these findings enrich the current knowledge on environmentally responsive organisational performance and disclosure.

Background considerations
As shown in figure 1, there are eight significant contemporary environmental challenges that organisations and stakeholders consider create a sustainable environment (National Research Council 2001). First, Earth has primary biological and chemical cycles in which nutrients are cycled through various places and roles within Earth's systems. Any changes to the biochemical ecosystem can affect the sources and sinks of these nutrients. An increase in global temperature can increase water levels and decrease available landmass. This change may expand living space for some species and reduce it for others, creating alterations to habitat and competition for nutrients (EPA 2011). Industrial biochemical production is rapidly growing to reduce dependence on fossil fuels for energy generation. A challenge is detecting industrial biochemicals that are economically and environmentally beneficial at their early production stage (Ögmundarso et al 2020).
Second, changes to habitat affect biological systems. Such changes can alter food chains, species behaviour, biological cycles and occurrences of various natural events (EPA 2011). Biological systems can benefit from applying circular economy principles and breaking away from linear economy principles of input of resources leads to an output of products and services. There are human-made resources and biological resources. Different set of principles are required to recycle human-made and biological products, but there is limited focus on recirculating biological-based resources into new production methods and applications (Kusumo et al 2022).
Third, the effects of human intervention and other forces on the climate system can affect the predictability of local climate patterns. For many species, the climate they live in influences their annual migration patterns and reproduction. Any changes to temperature norms can alter biotic and migratory behaviour, influence predator avoidance, and affect food availability (EPA 2011). Gaining uniform commitments of nations globally with leading-edge policies has been challenging, despite the profound adverse effect created by a lack of uniform commitment to policies among nations on agricultural and seafood production, changing the composition of waterborne and vector-borne diseases (Abbass et al 2022).
Fourth, ecological modifications can affect the hydrosphere. Changes to typical water patterns can manifest as floods, droughts, sedimentation and contamination (National Research Council 2001), which have adverse consequences for the public and for businesses. Businesses affected by floods tend to react to them by altering their investments, investment policies, cash management and executive compensation (Xiaofei and Qui 2022). Firms disclosing climate risk can lower the cost of equity and borrowing costs. Stock exchanges can consider making firms mandatorily disclose climate risk for their own good and for the good of the public (Matsumara et al 2022).
Fifth, global disease evolution and prevalence can shift with environmental changes (EPA 2011). These changes can alter the transmissibility and virulence of plant, animal and human pathogens (National Research Council 2001). Approaches to estimating disease origins and exposure levels are still evolving (Goddard et al 2020).
Sixth, human political, economic and social systems can influence resource use, extraction and restoration. For instance, world recessions, changing oil prices, unfavourable terms of trade and increased debt obligations compounded by droughts and wars have contributed to rural poverty and food shortages in Africa (Berry 1989). These systems can influence firms to become more socially responsible, and such firms are more inclined to conserve environmental resources and positively influence environmental performance (Nassani et al 2022). Countries can consider engaging businesses in environmental protection through contextually appropriate national policy approaches.
Seventh, changes to land use can affect the environment and influence water and nutrient cycling and habitats. Land-based processes and inputs can affect waterways (Smithsonian 2020). Bringing together different knowledge systems, such as those of Western and First Nations peoples, is synergetic. However, there are challenges in reaching a consensus because of differences in assumptions regarding people's value systems (Fleming et al 2022).
Finally, the materials system explains the use of materials in industrial production. The materials system can work with other information systems to ascertain whether they are potentially harming plants, animals and humans. Building a shelter requires using materials, and human construction activities consume three billion tonnes of raw material, representing 40% of global raw material use. Many building materials, such as concrete and steel, require significant energy inputs. Their manufacture consumes large amounts of power and emits carbon dioxide into the atmosphere (Eales 2012). Responsiveness of products to environmental protection begins with product design and responsiveness of products is a constant challenge because new products are continually entering the market (Delaney et al 2022).
These eight environmental challenges relating to organisations have produced fruitful empirical research to contribute to environmental sustainability. The severe effects of these changes on ecosystems, governments, stakeholders and shareholders have placed increasing expectations on organisations to meet these sustainability challenges while concurrently pursuing financial gains. Accordingly, organisations aim to contribute to one or more of the eight environmental subsystems to decrease environmental harm. Empirical research is crucial in making truth and building truth concerning these environmental concerns. These truths can then lead organisations to undertake activities towards environmental performance and disclose them to stakeholders.
It has become accepted that organisations adhere to self-imposed standards as a moral and financial obligation. They know they can otherwise face statutory compliance, monitoring and disclosure standards relating to their environmental performance. Legitimating organisational disclosure and performance with societal expectations allows firms to avoid statutory intervention (Soimakallio et al 2015).
Contextualising operational definitions can contribute to differences in relationships between environmental disclosure and performance, showing positive (Acar and Temiz 2020), negative (Patten 2002) and no association (Freeman and Wasley 1990). Contextualising the operational variables can add to understanding the construct and its dimensions. The question is whether the research studies have made disclosure and performance significantly different through the definitions they followed to develop operational variables. Meta-analysis studies can capture a wide array of studies that have differently operationalised environmental disclosure and performance and make conclusions at the aggregate level. However, this does not explain whether they are conceptually different at the study level. Studies can also differently define environmental disclosure and performance (Doan and Sassen 2020).
Using information made available by organisations and subscription-based databases, researchers have conducted studies to evaluate the success of organisational environmental performance and environmental disclosure. Studies have shown various measurement devices depicted as operational variables and have examined their association with events occurring within and outside the organisation. The investigation of these research questions emerges from existing knowledge on legitimacy, and the findings from this analysis also contribute to advancing such knowledge (Abdul Rahman andAlsayegh 2021, Luft Mombus 2005).
Some research studies choose more than one operational variable to measure a construct and provide empirical evidence. However, they do not clearly articulate how different choices of variables can enrich the construct. Moussa et al (2022) measured environmental disclosure targets using four operational variables: soft targets disclosure, semi-hard targets disclosure, hard targets disclosure and aggregated targets disclosure. Soft refers to firms making qualitative and not time-bound target disclosures, and hard refers to firms making measurable time-bound target disclosures. Because firms can make qualitative and quantitative target disclosures, Moussa et al (2022) computed an aggregate score assigning a higher ordinal score for hard target disclosure. They found a significant relationship between hard target disclosure and environmental performance only. However, the aggregated disclosure target model had a higher model explanation by R 2. , but there was an insufficient explanation for why the aggregated disclosure target was insignificant. Further, the study used Thomson Reuters Asset4 ESG data scores for the environmental performance operational variable, yet some authors show that publicly sold scores do not accurately represent the stated constructs (de Villiers et al 2022, Lee and Suh 2022).
The data source can influence the extent to which the empirical data represent the organisational reality. Data published in annual reports are likely more reliable than those published in social media outlets (Yuthas et al 2002). The accuracy of measuring data can also influence the empirical measurement and its construct representation. Interval, ordinal and categorical data can decrease data informativeness when constructing weighted averages, indices and aggregated data measures (Fontana et al 2015, Hughes et al 2001, Moussa et al 2022. It is not always feasible and practical to obtain ratio data. Differently measuring the phenomenon with empirical variables can result in studies reporting different results and conclusions (Doan and Sassen 2020). At other times, it can facilitate the construction of empirical variables. For instance, categorising firms as poor (with environmental violation records), mixed (with environmental accidents and complaints) and good environmental performers (clear of regulatory violations) can contribute to a deeper understanding of the environmental performance construct. Research projects must take the initiative to demonstrate such distinctions as theoretically founded in the research design and empirically supported or refuted by research results (Hughes et al 2001).
Diverse operational variables can enhance conceptual knowledge about environmental performance and environmental disclosure. Context bounds the real world. Some studies have used more than one operational variable for measuring environmental performance and disclosure to contextualise that real-world setting. The findings contribute to a real-life context-based understanding. However, the research community has a higherorder expectation that these operational findings will enrich higher-order knowledge of environmental performance and disclosure. Many research studies have used operational variables, not considering the theoretical constructs they represent (Abeysekera 2014).
Canonical correlation analysis is an all-encompassing technique for univariate and multivariate analysis (Zhuang et al 2020). The published papers that provide matrix correlational data help answer research questions (Zientek and Thompson 2009). Abeysekera (2014) has used the technique and applied it to two studies that had published matrix data, where environmental performance, economic performance and environmental disclosure were three different constructs. The findings showed that economic and environmental performance were two dimensions of the performance construct. The present study further extends this discussion by examining a published journal article with matrix data to validate the toxic-led environmental performance and disclosure of operational variables representing purported constructs. Additionally, it aims to locate the matrix analysis from an ontological and epistemological perspective.

Conceptual variables and operational variables
Concepts are the foundation of the conceptual apprehension of knowledge-ontology. As shown in figure 2, concepts are remote and distant from the practicalities of the real world. Nevertheless, they are the fountain of understanding that brings together various real-life occurrences (Doan and Sassen 2020). What is knowable from conceptual knowledge with practical consequences-the epistemology-is far closer to sensual capture. Scholarly research investigations have emphasised the research technique more to gain an epistemological understanding than to broaden the conceptual knowledge behind the constructs under study.
A debate arises regarding conceptual and operational variables, which come first in research considerations. One argument is that knowledge arises from human experiences, whereby epistemology leads to ontology through inductive reasoning. Experiences formed by real-life impressions lead to perceptions formed as ideas in the mind. Hume (2010) used the example of an apple, where taste, colour and smell are united in the fruit. Still, they make different impressions on the human experience, leading to distinct ideas about each sensory aspect. Similarly, environmental disclosure and environmental performance make different impressions on experience, presenting them as two separate ideations, even though both relate to the environment. Hume (2010) stated that human logic is valid to the extent that human experiences have allowed. When the causal reason (or effect) learned from induction does not apply to similar human experiences, this indicates that other causes are responsible for that human experience (or result). The epistemologies (knowledge gained from human experiences about environmental performance and reporting) continuously add to and refine the ontologies (the comprehensive knowledge of the imagination concerning performance and disclosure). The experiential knowledge gained about environmental performance and disclosure thus strengthens the conceptual positions. Bourdieu (1990) pointed out that human experiences become the objects of constructed knowledge through situational analysis rather than knowledge existing independently to be understood and passively recorded. The possible situational variations can make inductive learning unique, but its application to another situation can yield a degree of predictive inaccuracy. The widening of specific-sense situational understandings can lead to a general-sense or all-encompassing situational awareness or universal mental concepts.
In empirical endeavours, a universal statement is founded on the interrelationships of universal mental concepts. Empirical investigations then make hypothetical statements to apply a universal declaration to contextually specific situations (Suddaby 2010). The positivist writing before Bourdeau (1990) asserted that experiences lead to synthesised concepts and that phenomena are explained using a set of interrelated concepts.
The new positivists who strongly emphasised a theoretical framework in conducting empirical research replaced the set of interrelated synthesised concepts with conceptual statements. Empirical studies operationalise these synthesised statements by substituting testable hypothetical statements at the experiential level. Empirical research uses real-life (or objective) evidence to falsify a synthesised statement (Plus Company Updates 2020). The status quo is to accept the synthesised message as valid for now.
The synthesised concept (also known as constructs) expects that it associates with real-world events that form the objective evidence (also known as operational variables). Because each concept independently establishes a connection with the real-life event, the synthesised statements do not derive meaning from the interconnection of synthesised concepts. Instead, the purpose of the synthesised concept is to assist in interpreting the real-world event. For example, a person can analyse environmental disclosure or environmental performance because they have already conceptualised or imagined environmental disclosure or environmental performance. An alternative to this debate is the proposition that a concept already exists and sets the cognitive attitude to interpret, thereby leading to an experience (Lee 1966).
Concepts do not comprise intended meanings. The interlocking of concepts gives rise to an integrated interpretation of a real-life phenomenon, resulting in knowledge. The interlocking of concepts looks into various aspects that draw operational boundaries for the mental construct-a period in which it occurswhether it is an input, output or outcome. For instance, disclosure can include various attributes, such as quality, quantity, content and presentation. However, to conclude that a given operational feature is about environmental disclosure, there has to be an authoritative reference that differentiates it from others, such as financial disclosure. It is essential to refer to the authoritative reference in interpreting the experience; otherwise, it is an experience that has no referent. Therefore, operational variables require a conceptually referential authority to interpret an experience (Lee 1966).

Truth making and truth building
Truth is fundamental to people. People gain and build knowledge by forming beliefs and making statements. They utter truths as propositions, receive them as judgements and pronounce them as assertions. People also use utterances, thoughts and ideas in building knowledge. Facts, situations, events, objects and images also become the basis for truth making (BodyRutjes 2016).
Coherence theory argues that the truth of any proposition comprises its coherence, that facts have no role to play in the truth, and that there is no way to identify whether a set of propositions are true or false because of the normative position taken. The deflationary theory also takes a normative stance that any statement of assertion as truth is true. The semantic theory of truth underlines that truth is based on meaning but fits well for formal languages rather than natural language; there is no role for 'facts' and correspondence to 'facts' for truth building. Further, building truth using formal language means that formal words play a vital role, and misinterpretations can lead to unintended distortion of truth (BodyRutjes 2016).
The process of truth requires making to gain accurate knowledge that can precisely predict repetitive truth making in affairs, events and tropes. Empirical research attempts to gain experiences of truth making to develop logical truth-building knowledge (Popper 2010). The truth builders support the default truth makers because they correspond to reality. The truth makers are commonly known as 'facts'. The logic of the knowledge gained becomes a truth maker (Sangeetha 2016). In this endeavour, ontologies are truth building and truth making. The truth is embedded in the correspondence between truth building and truth making. Epistemology is correspondence between the two and is implemented in real life through methodologies. The quantitative methodologies falsify the currently built truth, appealing to new or altered truth making. The qualitative methodologies explain, interpret and describe the truth-making phenomenon being examined by using the presently available truth-building knowledge.
The correspondence theory of truth reveals that a truth builder (e.g. a statement) is true because a truth maker (e.g. a fact, evidence) corresponds. The truth maker becomes the object and the truth builder the subject; the subject corresponds with the object in various ways. The truth builder is true regardless of the label given to it because facts, in reality, are true.
The correspondence theory contrasts with the metaphysical view of reality, arguing that everything (subjects and objects) exists as ideas in the mind. The different ways of corresponding with reality to gain knowledge have led to various theories under the umbrella of the theory of correspondence. These include basic fact theory, state of affairs theory, Meinongian fact theory, mis-correspondence fact theory, logical atomism and logical subatomism. Because the truth about objects of truth making (e.g. the environment) has various properties (e.g. environmental disclosure, environmental performance), research restricts the investigation of these objects to aspects such as properties, relations and objects embedded in truth makers (i.e. facts, states of affairs). Research can conduct subatomic (very restrictive) investigations with a narrow set of properties and deduce more generalisable deductions. In that manner, knowledge codified as truth building can contain higher degrees of variability (Carneades.org 2015).
This paper uses correspondence theory to build and test the research hypotheses. The correspondence theory has been applied to examine the symmetry between two variants in crystallography (Cayron 2022) and health sciences (Custers 2019). The correspondence theory falls under the meta-theories investigating the truth as a construct. One strand of meta-theories conceives truth as the coherence explained as rational or consistent. The other strand conceives truthc as correspondence, meaning empirical validity (Custers 2019). The correspondence theory does not judge the truth-for instance, whether it is right or wrong (Marino 2006). The role of correspondence is to inquire into suspected factualities of empirical validity. The empirical validity applies to the inquiry as truth and ends with the truth it finds.
Truth-building statements and propositions are built with bounded truth makers and have room for falsification after including different and new truth makers. The truth or falsehood properties in truth making exist external to the mind and reside in truth making. Truth building occurs in the mind but with beliefs, propositions, judgements and statements. Truth-building properties, such as facts, are part of natural language. They do not follow boundaries, and can enter into causal relationships in ways that formal language cannot. The facts make the truth exist. Different facts about the truth become properties of the truth. These facts are acquired from real-world settings by investigating, observing and experiencing a phenomenon. These facts contribute to making the truth. Repetitively finding the same facts about the phenomenon helps to build a truth based on that factual property. The relationship between truth builder and truth maker is that one or more truth builder(s) can have a relationship with one or more truth maker(s). Because of this, truth buildin-such as a proposition, statement or judgement-expresses the truth condition, and facts and evidence only satisfy the requirement corresponding with truth making (Marino 2006, BodyRutjes 2016).

Research questions
As shown in figure 2, this study examines two truth-building questions using truth-making facts found in a published journal article. In relation to the knowledge domain of the environment in this study, this study hypothesises that truth built on environmental disclosure and environmental performance must correspond with their different truth-making facts. Environmental disclosure and environmental performance are conceptually two different truths. In support of the null hypothesis stated in Hypothesis 1 (H1), this study expects facts (evidence) that correspond to each of the two concepts to be statistically and significantly different. It measures the correspondence of truth building in canonical correlation analysis as a percentage of squared structure coefficients (R 2 S).
H1: Environmental disclosure and environmental performance are dimensions of the environment construct.
As shown in figure 3, when two different truths are built about the environmental performance dimension, they must correspond with different real-life facts that match each conceptual dimension. In support of the null hypothesis stated as Hypothesis 2 (H2), this study expects that facts (evidence) corresponding to the two operational environmental performance variables are statistically significantly different. In this way, we can conclude that toxic waste and recycling measured as environmental performance matrices provide substantially two different sets of information.
Additionally, the information provided must be worthy enough to pay attention. Each operational variable (toxic waste and recycling use) strongly relates to the environmental performance construct. The level of truth correspondence can be high, moderate or low. There is no strict benchmark for such categorisation (Sherry and Henson 2005). This article assumes that a truth correspondence below 5% is insignificant. The correspondence of truth building is measured in canonical correlation analysis as a percentage of squared structure coefficients (R 2 S).
H2: Environmental performance operational variables represent dimensions of the environmental performance construct.

Research methodology
4.1. Sampling frame The paper selected for this research is a study by Clarkson, Li, Richardson and Vasvari (2008). Their study included 11 predictors and used a regression model to determine the influence of environmental performance on voluntary environmental disclosure (VED). In addition, they measured the score of VED using web-based disclosures as of September 2004 by performing a content analysis using a disclosure index they devised.
There were two environmental performance proxies.
(1) The first variable measured was toxic emissions, which they measured as TRI/Sales-toxic release inventory emissions scaled by total sales revenue. The reverse sign signalled better environmental performance in their study, and large measures indicated a large effect.
(2) The second variable measured was waste recycling, which they measured as %RECYCL-the percentage of toxic waste treated, recycled or processed during production, where considerable measures signalled better environmental performance. Other variables are discussed below.
(3) The third measurement was labelled JFCOEF (the Janis-Fadner coefficient), which was a net frequency measure of news about firms' environmental performance. The coefficient was measured dichotomously, with favourable news receiving a positive sign and unfavourable information receiving a negative sign. The corporate characteristics variables included: (4) FIN-the amount of debt raised by a firm scaled by total assets of the firm; and (5) TOBIN Q-the financial performance measure of a firm. The authors measured TOBIN Q as the market value of the common stock, the book value of the preferred stock, and the book value of long-term and shortterm liabilities, divided by the book value of total assets; (6) VOLAT, the stock price volatility, was measured as the standard deviation of the market-adjusted monthly stock return; (7) ROA-return on assets, was calculated as income before extraordinary items divided by total assets; (8) LEV was the extent of leverage measured as the total debt divided by total assets; (9) SIZE was calculated as the natural logarithm of total asset value; (10) NEW was the asset newness, measured as the net value over the gross value of the plant, property and equipment; and (11) CAPIN was the capital intensity ratio of capital spending divided by total sales revenue.

Research method
Although Clarkson et al (2008) examined the influence of environmental performance and control variables on environmental disclosure using a regression model, the published matrix data allow the current study to explore the proposed research questions by rearranging the matrix data. This study uses the sample article's empirical data reported as mean, standard deviation and bivariate relationships.
The first step was to create conceptual terminology to suit canonical correlation analysis. Synthetic variables are theoretical constructs of environmental disclosure and environmental performance. This paper used canonical correlation analysis as the research method. This has been used broadly across disciplines to investigate research questions relating to accounting (Abeysekera 2014), education (Zientek and Thompson 2009), health (Zhuang et al 2020) and psychology (Liu et al 2020, Sherry andHenson 2005).
Canonical correlation analysis has several advantages as an analytic technique. First, it is the 'parent' of regression techniques. Several sibling techniques of canonical correlation analysis serve specific purposes but often suffer from type one errors because they do not accommodate all possible operational variables in a single analysis. Including all possible variables and falsifying a null hypothesis (status quo as truth) is more accurate because that excludes the possibility of falsely rejecting the actual truth.
A research study can reject the current status quo because of the methodological approach adopted by one operational variable. For instance, multiple regression analysis can only include a single operationalised dependent variable. In contrast, the canonical correlation analysis research method can accommodate more than one operational variable. The capacity of canonical correlation analysis to accommodate all possible operational variables that correspond with the construct decreases the chance of falsely rejecting the current status quo because the research method allows the examination of all possible scenarios simultaneously. Further, the canonical correlation analysis research method can establish a construct after including all available facts. The construct synthesised variable represents the mentally conceptualised variable-the construct. The canonical correlation analysis technique can subsequently inform us how strongly operational variables correspond with the construct. It creates constructs, technically known as synthetic variables.
Because this research uses matrix data published in Clarkson et al's (2008) journal paper, the author wrote an SPSS syntax command to analyse the matrix data using the canonical correlation analysis research technique. The results output is obtained by running the SPSS syntax command on the matrix data. Figure 4 shows the syntax command.

First research question
H1: Environmental disclosure and environmental performance are dimensions of the environment construct.
The canonical correlation analysis model consists of an outcome construct and a predictor conceptual varialbe. The conceptual outcome variable is built by using information contained in the operational variablesdisclosure quality, environmental performance about emissions and environmental performance about recycling. The environmental disclosure construct and environmental performance construct represent different environmental dimensions. This study focused on examining the construct dimensions of disclosure and performance rather than the predictor construct in the canonical correlation analysis model.
For the first research question, the study examined the strength of the relationship of the three different outcome operational variables to the construct created by the canonical correlation analysis model. The strength of the relationship was determined by discriminant validity to conclude that environmental performance (there are two operational outcome variables) and environmental disclosure (there is one operational outcome variable only) are distinctly different. Although they all contribute to the environment construct, they contribute so differently that they are identifiable as distinct dimensions of conceptual contributions. In this way, it can be concluded that environmental disclosure is a construct dimension that is statistically different from the environmental performance construct dimension.
This study rearranged the means, standard deviations and pairwise correlations in the correlation table to examine the first research hypothesis. After that, the environmental disclosure variable (VED) and the two environmental performance variables-TRI/sales and %RECYCL-became observed criterion (outcome) variables. Other variables considered in the original study became observed predictor variables. These were JFCOEF, FIN, TOBIN Q, VOLAT, ROA, LEV, SIZE, NEW and CAPIN. The author then wrote the first syntax command in SPSS to analyse the rearranged matrix data using the canonical correlation analysis technique (Burlea and Popa 2013).
In the canonical correlation analysis, the conceptual criterion (outcome) variable is a function of operational outcome variables, VED, -TRI/sales and %RECYCL. The conceptual predictor variable is a function of operational predictor variables JFCOEF, FIN, TOBIN Q, VOLAT, ROA, LEV, SIZE, NEW and CAPIN.

Second research question
H2:Environmental performance operational variables represent dimensions of the environmental performance construct.
This study removed the environmental disclosure quality operational outcome variable for the second research question and revised the canonical correlation analysis model. This canonical correlation analysis model has two operational outcome variables of environmental performance: emissions and recycling. This canonical correlation analysis model now treats environmental performance as a construct for analysis. The study acknowledges that it is for this model only; however, overall, environmental performance is a construct dimension of the environment construct. The model still has a construct predictor variable supported by operational predictor variables. As in the first research question, the study focused on the envronment performance construct.
This study examined the toxic waste and recycling operational outcome variables of the environmental performance construct to determine whether they have sufficient discriminant validity to conclude that they are distinctly different. We also examined whether they have a statistically strong association with the environmental performance construct that requires attention.
To examine the second research question-whether environmental performance operational variables represent the environmental performance construct-this paper excluded the environmental disclosure variable and rearranged the matrix data. This article then revised the syntax command in SPSS, considering the two environmental performance variables as observed criterion (outcome) variables. The observed predictor variables remained the same as in the analysis undertaken for the first research question. The author then wrote the second syntax command in SPSS to analyse the rearranged matrix data using the canonical correlation analysis technique (StatisticsSolutions 2020).
In the canonical correlation analysis, the conceptual criterion (outcome) variable was a function of operational outcome variables -TRI/sales and %RECYCL. The conceptual predictor variable is a function of operational predictor variables JFCOEF, FIN, TOBIN Q, VOLAT, ROA, LEV, SIZE, NEW and CAPIN.

Statistical parameters for interpretation
The communality coefficient (h 2 ) shows the variance (or explanation) of the operational outcome variables reproduced in the construct. The structure coefficients (RS) refer to the bivariate correlation between the operational and concptual variables in the canonical correlation analysis. A squared canonical structure coefficient (R 2 S) represents the proportion of variance-that is, explanation-linearly shared by a measured or operational outcome variable with the construct. The canonical loading in the R 2 S is more valid in interpreting the canonical correlation analysis output (Dattalo 2014).
The standardised canonical function coefficients (SCFC) are the canonical weights, and canonical structure correlations are canonical loadings. Operational variables with larger SCFC mean they place greater importance or emphasis on discussing the construct. The positive and negative signs indicate the direction of the contribution.
A small SCFC weight can mean that the operational variable SCFC is not sufficiently vital in discussing its relationship with the criterion variable or is decreased because of multicollinearity. The SCFC weight can differ from sample to sample, bringing instability to a more generalised interpretation; therefore, using the SCFC requires caution (Dattalo 2014). The statistical significance does not indicate the magnitude of the relationship because the sample size influences the importance of the relationship. Hence, the next step was to examine the effect size indices to determine the practical significance of the outcome. A Wilks λ test value of 0.358 indicates the reverse effect size. The overall effect size of the model was therefore 64.2% (R 2 C = 1-0.358).

Results
Although canonical correlation analysis output produced three canonical functions, the dimension reduction analysis found only the first (Wilks λ = 0.358, F (27, 523.41) = 8.16, p = 0.000) and the second (Wilks λ = 0.745, F (16, 360) = 3.56, p = 0.000) canonical functions as statistically significant. The goal of dimension reduction is to simplify the relationship study by reducing the number of explanatory variables while retaining as much predictive information as possible within the raw data. Each canonical analysis output is independent because the second canonical correlation analysis analyses the portion (residual) unexplained by the first canonical correlation analysis (Zhou 2009). Table 1 reports the results of the first and second canonical functions. After canonical correlation analysis produced the first output-Function 1-it then analysed the remaining residual and made the second output-Function 2. Function 1 R 2 C = 51.91 and Function 2 R 2 C = 20.96.
The communality coefficient (h 2 ) suggests that the environmental disclosure variable (VED) contributed 99.9% and the %RECYCL variable contributed 99.5% to the overall canonical solution. These are the two most valuable variables for analysis in the first research hypothesis. The communality coeffect is exceptionally high for the VED variable and the %RECYCL variable. The observed variable standardised canonical function coefficients (SCFC) and structure coefficients (RS) were dissimilar. SCFCs for interpretation can be disregarded in such situations. Instead, the study can use structure coefficients (RS)-a bivariate correlation between the operational variables and constructs. The squared structure coefficients (R 2 S) are the bivariate coefficient square for interpreting results the. Table 1 reports the obtained results.
Where: SCFC is the standardised canonical function coefficient (SCFC) RS is the structure coefficient R 2 S is the squared structure coefficient h 2 is the communality coefficient R 2 C is the squared canonical function.

Canonical functions
In the first canonical function, the two environmental performance variables contributed little to explain the conceptual criterion variable in the first canonical function. The environmental disclosure variable contributed most to the conceptual criterion variable (79.96%) of the first canonical function. The environmental disclosure variable (VED) contribution was in the higher range-that is, greater than 45%. The environmental performance variables (-TRI/sales and %RECYCL) were in the lower range-less than or equal to 45%suggesting that the environmental disclosure variable expresses a construct different from the construct that the environmental performance variables represent.
In the second canonical function, the %RECYCL environmental performance variable contributed most to the conceptual criterion variable (94.29%). The -TRI/sales environmental performance variable contributed very little to the conceptual criterion variable (6.05%). The environmental disclosure variable (VED) explained little of the conceptual criterion variable (20.03%) in the second canonical function. The second canonical function also suggested that the environmental disclosure (VED) variable expressed a construct different from the environmental performance variables.
The second canonical function suggested that the %RECYCL observed variable in environmental performance differed from the -TRI/Sales variable in the environmental performance construct. However, the second canonical function found that %RECYCL was in the high contribution range and -TRI/sales was in the low contribution range. Therefore, additional evidence would help confirm whether the two environmental performance variables represent different dimensions of the environmental performance construct.
The first and second canonical functions suggest that environmental disclosure is a different construct from environmental performance. Environmental disclosure was in the high contribution range in the first canonical function, while environmental performance was in the low contribution range.

Results of the second research hypothesis
This study dropped the environmental disclosure variable in the second research question analysis and rearranged the matrix data. The author wrote a syntax command on SPSS, considering the two environmental performance variables as observed criterion variables. The observed predictor variables remained the same as in the analysis of the first research question. The canonical correlation analysis had overall statistical significance, suggesting that the overall canonical solution had statistical relevance for the analysis (Wilks λ = 0.723, F (18,360) = 3.53, p = 0.000). The overall effect size of the model was 27.7% (R 2 c = 1-0.723).
The analysis produced two canonical functions, but the dimension reduction analysis confirmed that only the first function became statistically significant (Wilks λ = 0.723, F = 3.53, 18, p = 0.000). Function R 2 C = 50.50 (see table 2).
Where: (SCFC) is the standardised canonical function coefficient RS is the structure coefficient R 2 S is the squared structure coefficient (%) R 2 C is the squared canonical function. As reported in table 2, %RECYCL contributed 98.41%, and -TRI/sales contributed 2.66% to the environmental performance construct. These two observed variables are different dimensions. The reason is that %RECYCL was at the highest end of the high range, and -TRI/sales was at the lowest end. However, the -TRI/sales contribution to the environmental performance construct was so minimal as to be considered a separate dimension. This conclusion is also consistent with the second function of the correlation analysis undertaken for the first research hypothesis, where -TRI/sales contributed 6.05% and %RECYCL contributed 94.29% to the environmental performance construct.

Conclusion
The canonical correlation analysis of the data published by Clarkson et al (2008) revealed that environmental disclosure and environmental performance variables represented substantially different constructs. The two constructs corresponded to two sets of facts from the real world: disclosure and performance. Thus, the first hypothesis was met.
The -TRI/sales (toxic waste) and %RECYCL (recycling) variables were two contrasting dimensions of the environmental performance construct, but -TRI/sales was feeble as a dimension and offered no meaningful expression. These two constructs corresponded with different facts in the real world through measured variables. However, one set of facts-%RECYCL (recycling)-was far more powerful in the knowledge or truth built regarding environmental performance. It is possible to drop the second variable (toxic waste) but retain informativeness. Thus, the second hypothesis was partially met.

Implications for research
These findings have two implications for advancing research practice. First, good research practice should ensure that the empirical variables used in research sufficiently express their intended theoretical constructs through methodological variables that establish strong correspondence between truth building and truth making. It is crucial to define constructs carefully (e.g. environmental disclosure, environmental performance) by limiting their scope (for the environment only) and the context in which the investigation is undertaken (e.g. environmental performance in the context of pollution, or environmental performance in the context of reputation).
Second, constructs that carry everyday speech labels without definitions and whose application to time and scope are not limited can acquire unintended conceptual meanings because such terms can be broadly interpreted (StatisticsSolutions 2020). Research must guard against the overloaded meaning of such constructs and must present operational definitions of environmental practices that are constructed concerning the corresponding constructs.
Third, the study highlights the importance of developing and choosing variables to express different constructs or dimensions of the same construct. A construct does not sit in isolation, and often it relates to other constructs through which it gains a logical connection. Establishing construct coherence requires demonstrating its positioning concerning other constructs that are not under investigation in the study. For instance, in this paper, 'performance' is shown to be a multidimensional construct with two dimensions comprising the environmental performance construct.
Demonstrating how truthfully an operational variable corresponds to its construct enables the reader to understand how the methodological measurements correspond to each situation's conceptual understanding. Such an orientation of scientific inquiry into actual real-world events helps to deepen the scholarly understanding of the relationships between operational variables, their constructs and theories that explain the truthfulness of their correspondence. This is because methodological applications in real-world situations involve making truths with facts. These different facts enable the research to build a body of truth. In that body of truth, there are constructs. These different constructs can be related to each other to build theories (e.g. legitimacy theory) for us to conceptualise real-world phenomena about organisational behaviour.

Implications for organisations
Empirical findings are evidence-based; consequently, they receive more trust from stakeholders such as organisations. Researchers must attempt to communicate to organisations about environmental studies that show a strong correspondence between constructs and operational variables using language that they will understand. This strong correspondence will enable organisations to invest their resources in operational activities that assist in environmental protection.

Implications for policymakers
Policymakers use constructs when making decisions and preparing policy papers. Not all operational variables in research studies correspond strongly with people's understanding of the meanings held about environmental and public policy constructs. Policymakers must carefully and consciously give importance to research findings that show that the operational variables in their studies strongly correspond with the constructs. This paper analysed matrix data obtained from one journal article and hence required no ethics agreement. The findings are not generalisable to all published articles to demonstrate the importance of paying attention to the correspondence between the methodology and theory. The paper also outlined a method for investigating new research questions using matrix data. Future research can examine various aspects of the environment by using matrix data obtained from journal article as well as raw data that finally lead to matrix data. Future studies on the environment can leverage the analytical possibilities that the canonical correlation analysis contributes to a sustainable environment-a noble gift that all beings deserve.

Data availability statement
The data that support the findings of this study will be openly available following an embargo at the following URL/DOI: https://doi.org/10.6084/m9.figshare.22337146.

Funding
This study received no external funding.

Conflicts of interest
The author declares no conflicts of interest.