Unidimensional Measurement Model Research Articles

Assessing Relationship Satisfaction with Four Items? Psychometric Evaluation of the Ultra-short German Version of the Dyadic Adjustment Scale (DAS-4)

The quality of an individual's relationship plays a central role in their personal well-being as well as their mental and physical health. Despite its great importance, there are only a few ultra-short self-report measures for the assessment of relationship quality. An exception is the four-item version of the Dyadic Adjustment Scale (DAS-4), which is gaining increasing popularity internationally. In this study, the German version of the DAS-4 was evaluated for the first time with regard to its psychometric properties in a general population sample of individuals in a romantic relationship (N=1296). In addition to satisfactory item characteristics, the unidimensional measurement model showed sufficient goodness of fit and the internal consistency was satisfactory (ω=0.80). Measurement invariance was shown for men and women based on the latent construct of the DAS-4. In line with the hypothesis, associations of the DAS-4 with gender, general life satisfaction, psychopathology and attachment styles were found, which suggests construct validity. Despite the lack of application experiences and pending psychometric analyses of the DAS-4 in relevant target groups, such as individuals in couples counselling or therapy, the four-item version can be recommended for assessing relationship satisfaction.

Ant colony optimization for parallel test assembly.

Ant colony optimization (ACO) algorithms have previously been used to compile single short scales of psychological constructs. In the present article, we showcase the versatility of the ACO to construct multiple parallel short scales that adhere to several competing and interacting criteria simultaneously. Based on an initial pool of 120 knowledge items, we assembled three 12-item tests that (a) adequately cover the construct at the domain level, (b) follow a unidimensional measurement model, (c) allow reliable and (d) precise measurement of factual knowledge, and (e) are gender-fair. Moreover, we aligned the test characteristic and test information functions of the three tests to establish the equivalence of the tests. We cross-validated the assembled short scales and investigated their association with the full scale and covariates that were not included in the optimization procedure. Finally, we discuss potential extensions to metaheuristic test assembly and the equivalence of parallel knowledge tests in general.

Equivalence of Computer- and Paper-Based Administrations of the SCHNAPP Spelling Test in German for Six-Year-Old Children

Abstract: The SCHNAPP Spelling Test is a novel screening instrument to identify at-risk children with poor spelling abilities in German at the beginning of primary school. Although originally developed as a computerized test to be administered on tablets, in school settings paper-pencil methods are often still preferred. Therefore, the present study on N = 390 children from first grades in Austrian primary schools examined the equivalence of computer and paper-pencil versions of the test. After demonstrating unidimensional measurement models in both assessment conditions, analyses of differential response functioning on the item and test level found no substantial testing mode effects. These results indicate that the SCHNAPP Spelling Test can be comparably used as a computer- or paper-based instrument in school assessments.

Studying item-effect variables and their correlation patterns with multi-construct multi-state models.

Method effects on the item level can be modeled as latent difference variables in longitudinal data. These item-effect variables represent interindividual differences associated with responses to a specific item when assessing a common construct with multi-item scales. In latent variable analyses, their inclusion substantially improves model fits in comparison to classical unidimensional measurement models. More importantly, covariations between different item-effect variables and with other constructs can provide valuable insights, for example, into the structure of the studied instrument or the response process. Therefore, we introduce a multi-construct multi-state model with item-effect variables for systematic investigations of these correlation patterns within and between constructs. The implementation of this model is demonstrated using a sample of N = 2,529 Dutch respondents that provided measures of life satisfaction and positive affect at five measurement occasions. Our results confirm non-negligible item effects in two ostensibly unidimensional scales, indicating the importance of modeling interindividual differences on the item level. The correlation pattern between constructs indicated rather specific effects for individual items and no common causes, but the correlations within a construct align with the item content and support a substantive meaning. These analyses exemplify how multi-construct multi-state models allow the systematic examination of item effects to improve substantive and psychometric research.

Accuracy of Naming Error Profiles Elicited From Adaptive Short Forms of the Philadelphia Naming Test.

The purpose of this study was to evaluate whether a short-form computerized adaptive testing (CAT) version of the Philadelphia Naming Test (PNT) provides error profiles and model-based estimates of semantic and phonological processing that agree with the full test. Twenty-four persons with aphasia took the PNT-CAT and the full version of the PNT (hereinafter referred to as the "full PNT") at least 2 weeks apart. The PNT-CAT proceeded in two stages: (a) the PNT-CAT30, in which 30 items were selected to match the evolving ability estimate with the goal of producing a 50% error rate, and (b) the PNT-CAT60, in which an additional 30 items were selected to produce a 75% error rate. Agreement was evaluated in terms of the root-mean-square deviation of the response-type proportions and, for individual response types, in terms of agreement coefficients and bias. We also evaluated agreement and bias for estimates of semantic and phonological processing derived from the semantic-phonological interactive two-step model (SP model) of word production. The results suggested that agreement was poorest for semantic, formal, mixed, and unrelated errors, all of which were underestimated by the short forms. Better agreement was observed for correct and nonword responses. SP model weights estimated by the short forms demonstrated no substantial bias but generally inadequate agreement with the full PNT, which itself showed acceptable test-retest reliability for SP model weights and all response types except for formal errors. Results suggest that the PNT-CAT30 and the PNT-CAT60 are generally inadequate for generating naming error profiles or model-derived estimates of semantic and phonological processing ability. Post hoc analyses suggested that increasing the number of stimuli available in the CAT item bank may improve the utility of adaptive short forms for generating error profiles, but the underlying theory also suggests that there are limitations to this approach based on a unidimensional measurement model. https://doi.org/10.23641/asha.22320814.

The Reflective Functioning Questionnaire-Revised- 7 (RFQ-R-7): A new measurement model assessing hypomentalization.

Although it is a widely used questionnaire, limitations regarding the scoring procedure and the structural validity of the eight-item Reflective Functioning Questionnaire (RFQ-8) were raised. The present study aimed to examine further the latent dimensionality of the RFQ-8 and to examine linear and non-linear associations between mentalization difficulties and maladaptive psychological characteristics. Data from two separate representative samples of young adults (N = 3890; females: 51.68%; mean age: 27.06 years [SD = 4.76]) and adults (N = 1385; females: 53.20%; mean age: 41.77 years [SD = 13.08]) were used. In addition to the RFQ-8, standardized questionnaires measured the levels of impulsivity, sensation seeking, rumination, worry and well-being. Confirmatory factor analysis (CFA) was used to test the model fit of competing measurement models. CFA revealed that a revised, seven-item version of the RFQ (RFQ-R-7) with a unidimensional structure showed the most optimal levels of model fit in both samples. Impulsivity, sensation seeking, rumination and worry consistently presented significant, positive, linear associations with general mentalization difficulties in both samples. Significant quadratic associations were also identified, but these relationships closely followed the linear associations between the variables and increased only marginally the explained variance. The supported unidimensional measurement model and the associations between the general mentalization difficulties factor and maladaptive psychological characteristics indicated that the RFQ-R-7 captures a dimension of hypomentalization ranging between low and high levels of uncertainty. Increasing levels of hypomentalization can indicate a risk for less adaptive psychological functioning. Further revisions of the RFQ-8 might be warranted in the future to ensure adequate measurement for hypermentalization.

Rasch validation of the Warwick-Edinburgh Mental Well-Being Scale (WEMWBS) in community-dwelling adults

BackgroundWith the ongoing global COVID-19 pandemic and the recent political divide in the United States (US), there is an urgent need to address the soaring mental well-being problems and promote positive well-being. The Warwick-Edinburgh Mental Well-Being Scale (WEMWBS) measures the positive aspects of mental health. Previous studies confirmed its construct validity, reliability, and unidimensionality with confirmatory factor analysis. Six studies have performed a Rasch analysis on the WEMWBS, and only one evaluated young adults in the US. The goal of our study is to use Rasch analysis to validate the WEMBS in a wider age group of community-dwelling adults in the US.MethodsWe used the Rasch unidimensional measurement model 2030 software to evaluate item and person fit, targeting, person separation reliability (PSR), and differential item functioning (DIF) for sample sizes of at least 200 persons in each subgroup.ResultsAfter deleting two items, the WEMBS analyzed in our 553 community-dwelling adults (average age 51.22 ± 17.18 years; 358 women) showed an excellent PSR = 0.91 as well as person and item fit, but the items are too easy for this population (person mean location = 2.17 ± 2.00). There was no DIF for sex, mental health, or practicing breathing exercises.ConclusionsThe WEMWBS had good item and person fit but the targeting is off when used in community-dwelling adults in the US. Adding more difficult items might improve the targeting and capture a broader range of positive mental well-being.

An Ultra-Short Instrument to Assess Sensation Seeking: Psychometric Evaluation of the German Version of the Brief Sensation Seeking Scale (BSSS-4)

The personality trait of sensation seeking (SS) plays a prominent role in health-related risk behaviors and is associated with psychopathology, emotion regulation, and delinquency. Despite this high relevance, hardly any ultra-short self-report measures optimized for test duration exist for the assessment of SS. An exception is the Brief Sensation Seeking Scale (BSSS-4) consisting of four items, which is gaining international popularity. In this study, the German version of the BSSS-4 was psychometrically evaluated for the first time in a student sample (N=419). A unidimensional confirmatory measurement model showed adequate goodness of fit and internal consistency was in the satisfactory range (ω=0,73). As first evidence for adequate construct validity and in line with the hypotheses, associations of the BSSS-4 with male gender, self-reported risk-taking, and risk-taking behavior (operationalized via a lottery-based behavioral paradigm) but not with current depression were found. An examination of measurement invariance across men and women using multigroup CFA suggested that partial scalar measurement invariance can be assumed for the BSSS-4, when equality constraints for loadings and intercepts of Item 1 are relaxed. Considering its increasing international use, the German version of the BSSS-4 can be recommended overall: For an ultra-short instrument, it is sufficiently internally consistent and rather suitable for gender comparisons. In this regard, the facet of experience seeking may be problematic in terms of gender-dependent differences in measurement properties. In light of insufficiently rigorous tests of instruments for the assessment of SS, the results of comparisons between women and men may thus be interpreted with caution.

In Search of a Comparable Measure of Generalized Individual Religiosity in the World Values Survey

Individual religiosity measures are used by researchers to describe and compare individuals and societies. However, the cross-cultural comparability of the measures has often been questioned but rarely empirically tested. In the current study, we examined the cross-national measurement invariance properties of generalized individual religiosity in the sixth wave of the World Values Survey. For the analysis, we used multiple group confirmatory factor analysis and alignment. Our results demonstrated that a theoretically driven measurement model was not invariant across all countries. We suggested four unidimensional measurement models and four overlapping groups of countries in which these measurement models demonstrated approximate invariance. The indicators that covered praying practices, importance of religion, and confidence in its institutions were more cross-nationally invariant than other indicators.

Assessing Essential Unidimensionality of Scales and Structural Coefficient Bias.

Percentage of uncontaminated correlations (PUC), explained common variance (ECV), and omega hierarchical (ωH) have been used to assess the degree to which a scale is essentially unidimensional and to predict structural coefficient bias when a unidimensional measurement model is fit to multidimensional data. The usefulness of these indices has been investigated in the context of bifactor models with balanced structures. This study extends the examination by focusing on bifactor models with unbalanced structures. The maximum and minimum PUC values given the total number of items and factors were derived. The usefulness of PUC, ECV, and ωH in predicting structural coefficient bias was examined under a variety of structural regression models with bifactor measurement components. Results indicated that the performance of these indices in predicting structural coefficient bias depended on whether the bifactor measurement model had a balanced or unbalanced structure. PUC failed to predict structural coefficient bias when the bifactor model had an unbalanced structure. ECV performed reasonably well, but worse than ωH.

Development and initial validation of the Subjective Academic Wellbeing Measure: A new tool of youth wellbeing in school

The purpose of the current study was to investigate the preliminary development and validation of the Subjective Academic Wellbeing Measure (SAWM), which is a six-item self-report rating measure intended for use as a screening tool to assess the positive academic functioning of young people within the elementary and high school context. Exploratory factor analysis was performed with Sample 1 (N= 161), indicating that the SAWM was characterized by a unidimensional measurement model and had strong factor loadings. Results from confirmatory factor analysis, which was carried out with Sample 2 (N= 199), confirmed the measurement model by yielding good data-model fit statistics that were characterized by strong latent construct and internal reliability estimates. Further analyses showed that the scale had good convergent validity considering scores from several self-reported scales of student mental health problems and positive school functioning. Further analyses also showed that configural, metric, and scalar measurement invariance were observed across gender groups. These results provide initial evidence suggesting that the SAWM is a reliable and valid measure that can be used to assess the positive academic functioning of students within the school context. Implications are discussed, and some suggestions are provided for future research and practice

Integration of Cloud Technologies in Teaching Foreign Languages in Higher Education Institutions

This study was aimed at summarizing theoretical knowledge of students studying Economics, enhancing the educational process and training skills of independent long-term professional upgrade of students (sustainability training) through the use of an English-taught training program implemented through the use of MS Office 365 cloud services. The variational traits studied were identified: educational motivation, self-confidence, cognitive and creative skills. The study used methods that are recommended for quantitative research, namely: Rasch’s models for measuring academic motivation, methods for determining the level of academic confidence; methods of diagnosis of cognitive reflection and decision making, and a questionnaire to determine the level of creativity of thinking. The results of the diagnostic tests on academic motivation were processed using the Rasch Unidimensional Measurement Model (RUMM-2010) software, and the results of other tests were processed using SPSS 10.0.5., Statistica v. 5.5 A., MathCAD 2000 Pro. It has been found that the problem of integrating cloud technologies into the teaching foreign languages has been of interest of scholars, as the former are gradually becoming a full-fledged educational tool, allowing all institutions to create their own online spaces. In terms of language teaching methods, the used in this study teaching approach proved to create the learning environment helping to deal with the students’ communication and interaction barriers, reluctance to being engaged resulted in the enhanced students’ learning activity, their motivation for learning. This approach addressed the students’ needs in developed logical (critical) thinking and creative tactic to problem-solving, student memory (cognitive component). The integration of cloud (education) services in general proved to increase the efficiency of the learning process. https://doi.org/10.26803/ijlter.19.2.4

Qualimetric monitoring of professional competences of a teacher in the conditions of digitalization of education: problems and solutions

This article is supported by the Russian Foundation for Basic Research (project No. 19-013-00163 А “Methodology and Technology of Socio-Pedagogical Research of Family as a Subject of Creation of Individual Educational Trajectory of a Child”). The author examines the problem of monitoring of professional competences of a teacher in the conditions of digital environment. The authors propose a new technique for development of a method for assessing professional competences of a teacher based on latent variables theory, where private criteria manifest as integral with regards to indexes and indicators of professional competencies of a teacher. Qualimetric monitoring of professional competences contributes to the growth of personal growth of a teacher and improvement of the quality of his work in digital environment. The authors outline the scientific basis for qualimetric monitoring of professional competences of a teacher using the RUUM 2020 software (Rasch Unidimensional Measurement Models). The suggested approach proves that in the school digital environment can be resolved the issue of accessibility and automation of assessing professional competences of a teachers, apply Qualimetric monitoring for motivation of personal growth and self-improvement of a teacher. The new approach allows presenting the qualitative indicators in quantitative dimension. Such solution of the problem corresponds to the current level of requirements of digital environment for monitoring and scientific organization aimed at improvement of teacher’s competences.

Comprehensive ADL Outcome Measurement after Stroke: Rasch Validation of the Lucerne ICF-Based Multidisciplinary Observation Scale (LIMOS)

ObjectiveTo establish Rasch validation of the Lucerne International Classification of Functioning, Disability and Health (ICF)-based Multidisciplinary Observation Scale (LIMOS) in stroke. LIMOS measures the level of assistance in daily life activities related to motor function, communication, cognition, and domestic life. Rasch Measurement Theory (RMT) transforms an ordinal scale into an interval scale and thus the Rasch-based LIMOS scale captures a more accurate improvement of functional outcomes via Rasch-transformed scores. DesignCross-sectional study design. SettingNeurorehabilitation center, Luzerne, Switzerland. ParticipantsWe recruited participants with stroke (N=407; age=63.2±16.0y; n=157 women) through consecutive sampling. InterventionsNot applicable. Main Outcome MeasuresParticipants were assessed with LIMOS at admission and discharge of rehabilitation. We used RMT to evaluate overall model fit, response dependency, floor and ceiling effect, reliability, and differential item functioning (DIF) for sex, age, type, and time of stroke on the 4 LIMOS subscales using the Rasch Unidimensional Measurement Model (RUMM) 2030 program. ResultsThe Rasch-based LIMOS subscales fit the Rasch model after reducing and rescoring items: motor (from 20 to 18 items), communication (5 items), cognition (from 15 to 13 items), and domestic life (5 items). There was no floor or ceiling effect. Some artificial DIF was identified. Scoring at discharge was dependent on the scoring responses at admission, which means that without applying a correction factor to the discharge scores, there was an underestimation of change in scores between admission and discharge, ranging from 0.24 to 0.97 logits (10.79%-49.24%) on the different subscales. ConclusionsThe Rasch-based LIMOS scale is recommended to measure functional outcome in people with acute or chronic stages of ischemic or hemorrhagic stroke.

Assessing learning: How can classroom-based teachers assess students’ competencies in numeracy?

ABSTRACTThis paper examines a procedure measuring student competencies in numeracy using school-based assessments, and demonstrates how the procedure informs the school system on quality improvement. The sample consisted of 7648 students, attending three different types of urban schools including government, formal private and low cost private in poor informal settlements in Kenya. The numeracy tool measures six curriculum outcome areas. Each outcome area is defined by 2–11 measured items based on the emphasis given to an area in the curriculum. Within each of the outcome areas, items are also hypothesised to measure categories of the cognitive domain of learning. Using the Rasch, we examine the item difficulties, person location and differential item functioning. The paper provides important implications to provision of evidence to inform teaching in poor urban informal settlements in Kenya and this can also be replicated in other sub-Saharan African countries.Abbreviations: APHRC: African Population and Health Research Center; CTT: Classical Test Theory; DIF: Differential Item Functioning; ICC: Item Characteristics Curve; INMS: Infit Mean Square; IRT: Item Response Theory; PASEC: Programme d’Analyse des Systèmes Educatifs de la Confemen/ The Programme for the Analysis of Education Systems; QUEST: The interactive test analysis system (software); RUMM: Rasch Unidimensional Measurement Models (software); SACMEQ: Southern and Eastern African Consortium for Monitoring Education Quality; SSA: Sub-Saharan Africa

Construct Validity of the Spanish Versions of the Memorial Symptom Assessment Scale Short Form and Condensed Form: Rasch Analysis of Responses in Oncology Outpatients

ContextThe Memorial Symptom Assessment Scale (MSAS) is a self-rating instrument for the assessment of symptom distress in cancer patients. The Spanish version of the MSAS has recently been validated. However, we lack evidence of the internal construct validity of the shorter versions (short form [MSAS-SF] and condensed form [CMSAS]). In addition, rigorous testing of these scales with modern psychometric methods is needed. ObjectivesThe aim of this study was to evaluate the internal construct validity and reliability of the Spanish versions of the MSAS-SF and CMSAS in oncology outpatients using Rasch analysis. MethodsData from a convenience sample of oncology outpatients receiving chemotherapy (n = 306; mean age 60 years; 63% women) at a university hospital were analyzed. The Rasch unidimensional measurement model was used to examine response category functioning, item hierarchy, targeting, unidimensionality, reliability, and differential item functioning by age, gender, and marital status. ResultsThe response category structure of the symptom distress items was improved by collapsing two categories. The scales were adequately targeted to the study patients, showed overall Rasch model fit (mean Infit MnSq ranged from 0.98 to 1.05), met criteria for unidimensionality, and the reliability of scores was good (person reliability > 0.80), except for the CMSAS prevalence scale. Only four items showed differential item functioning. ConclusionThe present study demonstrated that the Spanish versions of the MSAS-SF and CMSAS have adequate psychometric properties to evaluate symptom distress in oncology outpatients. Additional studies of the CMSAS are recommended.

Psychometric evaluation of the PainCAS Interference with Daily Activities, Psychological/Emotional Distress, and Pain scales.

The PainCAS is a web-based clinical tool for assessing and tracking pain and opioid risk in chronic pain patients. Despite evidence for its utility within the clinical setting, the PainCAS scales have never been subject to psychometric evaluation. The current study is the first to evaluate the psychometric properties of the PainCAS Interference with Daily Activities, Psychological/Emotional Distress, and Pain scales. Patients (N = 4797) from treatment centers and hospitals in 16 different states completed the PainCAS as part of routine clinical assessment. A subsample (n = 73) from two hospital-based treatment centers also completed comparator measures. Rasch Rating Scale Models were employed to evaluate the Interference with Daily Activities and Psychological/Emotional Distress scales, and empirical evaluation included assessment of dimensionality, discrimination, item fit, reliability, information, and person-to-item targeting. Additionally, convergent and discriminant validity were evaluated through classical test theory approaches. Convergent validity of the Pain scales was evaluated through correlations with corresponding comparator items. One Interference with Daily Activities item was removed due to poor functioning and discrimination. The retained items from the Interference with Daily Activities and Psychological/Emotional Distress scales conformed to unidimensional Rasch measurement models, yielding satisfactory item fit, reliability, precision, and coverage. Further, results provided support for the convergent and discriminant validity of these two scales. Convergent validity between the PainCAS Pain and BPI Pain items was also strong. Taken together, results provide strong psychometric support for these PainCAS Pain scales. Strengths and limitations of the current study are discussed.

Examining the psychometric properties of a sport-related concussion survey: a Rasch measurement approach

BackgroundAwareness of sport-related concussion (SRC) is an essential step in increasing the number of athletes or parents who report on SRC. This awareness is important, as there is no established data on medical care at youth-level sports and may be limited to individuals with only first aid training. In this circumstance, aside from the coach, it is the players and their parents who need to be aware of possible signs and symptoms. The aim of this study was to examine the psychometric properties of a parent and player concussion survey intended for use before and after an education campaign regarding SRC.Methods1441 questionnaires were received from parents and 284 questionnaires from players. The responses to the sixteen-item section of the questionnaire’s ‘recognition of signs and symptoms’ were submitted to psychometric analysis using the dichotomous and polytomous Rasch model via the Rasch Unidimensional Measurement Model software RUMM2030. The Rasch model of Modern Test Theory can be considered a refinement of, or advance on, traditional analyses of an instrument’s psychometric properties.ResultsThe main finding is that these sixteen items measure two factors: items that are symptoms of concussion and items that are not symptoms of concussion. Parents and athletes were able to identify most or all of the symptoms, but were not as good at distinguishing symptoms that are not symptoms of concussion. Analyzing these responses revealed differential item functioning for parents and athletes on non-symptom items. When the DIF was resolved a significant difference was found between parents and athletes.ConclusionsThe main finding is that the items measure two ‘dimensions’ in concussion symptom recognition. The first dimension consists of those items that are symptoms of concussion and the second dimension of those items that are not symptoms of concussion. Parents and players were able to identify most or all of the symptoms of concussion, so one would not expect to pick up any positive change on these items after an education campaign. Parents and players were not as good at distinguishing symptoms that are not symptoms of concussion. It is on these items that one may possibly expect improvement to manifest, so to evaluate the effectiveness of an education campaign it would pay to look for improvement in distinguishing symptoms that are not symptoms of concussion.

Preliminary Validation of the Subjective Academic Problems Scale: A New Tool to Aid in Triaging School Mental Health Screening Results

The purpose of the present study was to investigate the preliminary structural, convergent, and incremental classification validity of responses to the Subjective Academic Problems Scale (SAPS), which is a seven-item self-report behavior rating scale intended for use as a triaging tool within secondary-level school mental health screening contexts. Findings from psychometric analyses carried out with Sample 1 ( N = 177) indicated that responses to the SAPS were characterized by a unidimensional measurement model and that scores derived from the scale had convergent validity with scores from several other self-reported measures of student wellbeing and mental health problems. Results from analyses conducted with Sample 2 ( N = 219) confirmed the unidimensionality of responses to the SAPS measurement model and demonstrated that SAPS scores had incremental validity, when used in conjunction with scores from a self-report internalizing problems screener, for identifying students with greater levels of mental health risk. Implications for future research and practice are discussed.

Georg Rasch and Benjamin Wright's Struggle With the Unidimensional Polytomous Model With Sufficient Statistics.

This article reproduces correspondence between Georg Rasch of The University of Copenhagen and Benjamin Wright of The University of Chicago in the period from January 1966 to July 1967. This correspondence reveals their struggle to operationalize a unidimensional measurement model with sufficient statistics for responses in a set of ordered categories. The article then explains the original approach taken by Rasch, Wright, and Andersen, and then how, from a different tack originating in 1961 and culminating in 1978, three distinct stages of development led to the current relatively simple and elegant form of the model. The article shows that over this period of almost two decades, the demand for sufficiency of a unidimensional parameter of the object of measurement, which enabled the separation of this parameter from the parameter of the instrument, drove the theoretical development of the model.