The Construct,Convergent and Divergent Validity,and Reliability of Three Optimism Scales among North American University Students

Abstract

The primary objective of this study is to compare the construct, convergent and divergent validity and the reliability of three optimism scales. The study relied on a nonprobability sample of 100 social work students at Western Michigan University in the United States (Seventy-nine percent of the sample were female, and 21% were male). The sample’s mean age was 26.35 years, SD = 7.70. Sixty-nine percent (69%) of the respondents self-identified as White, and 31% self-identified as African American, Hispanic/Latino, multiethnic, Native American or Asian American. The study used confirmatory factor and multiple regression analyses (CFA and MRA). The findings show that the Life Orientation Test-Revised (LOT-R) and the Personal Optimism Scale (POS) were supported by three indicators of goodness of fit, while the Brief Interactive Optimism Scale-Garcia (BIOS-G) was supported by eight. The LOT-R showed no acceptable internal consistency indicators, but the POS and the BIOS-G showed several good internal consistency indicators. Correlations of all of these scales with the Physical Well-being Scale-Garcia (PWS-G) ranged from r (100) = .303, p = .002 to r (100) = .439, p = .000. The three scales had divergent validity because their scores did not differ by gender (LOT-R: t(100) = −.885, p = .383; POS: t(100) = −.263, p = .794; BIOS-G: t(100) = −.840, p = .407). The findings suggest the advisability of recommending the BIOS-G, which is short and easy to use and understand.

Keywords

Reliability three optimism scales American university students construct validity convergent validity divergent validity

Introduction

Scientific research has long enabled us to theorize about and study human phenomena not easily detectable by our human senses (Bernard & Ritti, 1990). Testing such theories, however, requires the development and use of measurement instruments capable of detecting and validly and reliably measuring the phenomena under consideration. Therefore, the theory itself should motivate us to develop sophisticated measurement instruments. In the absence of said instruments, we can easily question the existence of the imagined phenomena. Measurement instruments should serve as a means to bridge reality and our imagined realities. In other words, according to the epistemology of Popper (2004), theories should be falsifiable; i.e., it should be possible to find empirical evidence that may be false proposals about reality.

There is a strong tradition in Latin America of accepting psychological theories and utilizing measurement instruments developed in other countries under very different psycho-sociocultural contexts (Ardila, 1972; Díaz-Guerrero, 1971; Díaz-Loving, 2006). The original creators of such theories and instruments often possess ethnocentric convictions that are rarely challenged by Latin American researchers. The latter often accept the imported theories and instruments without proper critical analysis of the imagined phenomena and the instruments intended to measure the alleged existence of said phenomena (Castro Solano, 2014; García et al., 2013a). Unfortunately, many Latin American researchers seem to lack the creativity or imagination to generate new models more pertinent to their psychological reality or to develop culturally appropriate psychological measurement instruments. Many of these researchers limit themselves to testing the validity and reliability of foreign-born instruments (Bastianello et al., 2014; Cano-García et al., 2015; Ferrando et al., 2002; Gaspar et al., 2009). Such behavior, however, involves accepting an original theory or model that was developed in a sociocultural context quite different from the one to which the model or theory is being adapted. It is worth noting that this acritical tendency is not limited to researchers from Latin America. This tendency can also be observed to a lesser extent among researchers from non-Spanish-speaking countries (Khallad, 2010; Lai & Yue, 2000).

In optimism theory, the theory of positive expectations (an orthodox dominant model that originated in the United States) has become quite prevalent in Europe. Another currently used model—interactive personality style—originated in Mexico. The Anglo-Saxon model focuses on the theory of positive expectations (Scheier & Carver, 1985), while the Mexican model focuses on interbehavioral theory (Kantor & Smith, 1975) and, more specifically, on the construct of the interactive personality style (Ribes, 2009). The main objective of this study was to compare and contrast positive expectations theory and the theory of interactive personality style while considering evidence of construct, convergent and divergent validity and the reliability of the scales developed based on these theories. This was done by applying these scales to a sample of American graduate and undergraduate students pursuing social work degrees in a public university. Hence, this study tried to determine which scale (LOT-R, POS, or BIOS-G) was most valid and reliable. The models are described as follows.

Positive expectations model of optimism

This model emphasizes what a person hopes to accomplish when facing situations requiring action and a particular attitude from the individual. The model proposes that optimistic individuals believe that future events will be favorable to them and that they possess the necessary resources and skills to accomplish whatever they want. This model views optimism as a personality trait consisting of a generalized positive expectation and defines optimism as a “…generalized feeling of trust” (Carver & Scheier, 2002, p. 232). This type of optimism is personal, in that the individual is confident that he/she possesses whatever is needed for a successful future. According to Ottati and Noronha (2017), according to this theoretical approach, optimism is unidimensional and bipolar. That is, optimism may be conceptualized as a continuum, with the highest level of optimism at one end and the highest level of pessimism at the other end. According to this perspective, self-confidence and purpose are two key components of the optimism construct of positive expectations. Self-confidence is key in motivating individuals to work toward accomplishing their goals despite any obstacles they may face (Carver & Scheier, 2002). The LOT-R, developed by Scheier et al. (1994), is based on this optimism theory model. The POS, which was developed in Germany, is also based on this model (Schweizer & Koch, 2001).

Interactive personality style model of optimism

This model conceptualizes optimism as an interactive personality style (Ribes, 2009) derived from a favorable but intricate past and present interaction of persons with themselves, others and their environment. This perspective critiques and rejects the ahistorical and teleological North American model of positive expectations. According to the interactive approach, optimism is a positive way of viewing everything that surrounds us, including ourselves. We are the result of our constant, subtle and successful interactions with our surroundings. According to this perspective, optimism enables us to effectively overcome many battles. For this reason, optimism becomes a mechanism for preventing and recovering from painful, difficult and life-threatening situations. According to this model, optimists view human beings as intrinsically good. They also believe life is beautiful and generally good. In optimism, both the past and the present play equally important roles, and they are inevitably linked.

Interbehavioral theory (Kantor, 1959, 1969) proposes that optimists have developed strong stimulus-and-response function connections that influence how they perceive themselves and the surrounding world. Thus, life events serving as psychological stimuli linked to the person’s response function may lead to a favorable assessment of those events and, ultimately, to optimism.

Such stimulus-response functions are born and evolve due to the reactive biography of individuals; nevertheless, these functions eventually develop a life of their own. Based on this model, Mexican researchers have developed the BIOS-G (García et al., 2013b; García-Cadena et al., 2016, 2019).

Studies conducted in various countries have found that the LOT-R lacks reliability. These studies include Rauch et al. (2006, 2007, 2008) in Germany; Vera-Villarroel et al. (2009) in Chile; Bandeira et al. (2002) in Brazil; Ji et al. (2004) in China; García Cadena et al. (2016) in México; and Oliden Balarezo (2014) in Perú. These studies have also found that the LOT-R possesses construct, convergent and discriminant validity but lacks an acceptable level of reliability. It is very important for measurement instruments to have good internal consistency given that the lack of valid relationships between constructs may lead to erroneous interpretations of any identified associations. Additionally, lack of internal consistency may lead to patient misdiagnosis (John & Soto, 2009). The previously identified reasons demand the simultaneous study and analysis of the validity and reliability of various instruments that attempt to measure the same construct from various theoretical perspectives.

Method

Participants

Our study relied on a nonprobability sample of 100 graduate and undergraduate students in the School of Social Work at Western Michigan University in Kalamazoo, USA). Most participants were undergraduate students, and some were graduate alumni. All participants were alumni of the second author. Seventy-nine percent of the sample were female, and 21% were male. The mean age was 26.35 years (SD = 7.70); the ages of the participants ranged from 18 to 50 years. Sixty-nine percent of the study participants self-identified as White, 11% as African American, 6% as Hispanic/Latino, 4% as multiethnic, 2% as Native American, 1% as Asian, and 7% as Other. Seventy-nine of the 100 participants reported being at a medium-low or a medium-high socioeconomic level, while none reported being at a medium-medium socioeconomic level. Fifty-three percent of the sample reported having been employed at their current jobs between one and three years.

Instruments

Sociodemographic questionnaire

The questionnaire was composed of questions designed to gather information about the participants’ perception of their ethnic group, socioeconomic level, age, sex, labor status, and number of years at their current job.

LOT-R (Scheier et al., 1994; see Appendix 1)

This scale consists of 10 items (four filler items and six items, of which three express optimism, and three express pessimism). Three items are positively worded (optimistic), and three are negatively worded (pessimistic). The respondents were originally a large undergraduate sample (N = 2,055), 32.2% of which were women. The test is a Likert scale with five options of response: 5 = I agree a lot, 4 = I agree a little, 3 = I neither agree nor disagree, 2 = I disagree a little, and 1 = I disagree a lot. Higher scores on the scale reflect more of the construct. Studies in the United States have reported alpha values ranging from .78 to .83 (Carver & Scheier, 2002). Additionally, test-retest correlations of .56, .60, .68, and .79 were obtained; thus, the data apparently support the temporal stability of the scale (Scheier et al., 1994). In this study, a Cronbach’s alpha coefficient of .61 was found. This scale was used because it is currently the most utilized optimism scale (Huffman et al., 2019). Although there is a lack of consensus about the factorial structure of the LOT-R (Carver et al., 2010), this study adopted the recommendation of Cano-Garcia et al. (2015) to apply the one-dimensionality approach to the scale with a score resulting from adding the six items, thereby reflecting dispositional optimism.

POS (Schweizer & Koch, 2001; see Appendix 2)

This is a subscale of the Personal Optimism and Social Optimism-Extended (POSO-E). The POS consists of eight items, all answered in a four-point Likert-type scale format (1 = incorrect, 4 = completely correct), with higher scores indicating more of the construct. Schweizer and Koch (2001) reported a Cronbach’s alpha of .78. In the study reported here, the Cronbach’s alpha was .79.

BIOS-G (García-Cadena et al., 2019; see Appendix 3)

This scale consists of four items in a Likert-type format with four response options, which range from 4 (= yes of course) to 1 (= of course not); this scale also has a negative item, which is scored inversely. A higher score indicates more of the construct. This scale has shown very good internal consistency (ω = .87, ɑ = .86, ordinal ɑ = .91). In this study, the Cronbach’s alpha was .76.

PWS-G (Garcia et al., 2015; see Appendix 4)

This scale consists of four items with four response options (4 =Yes, 3 = Possibly Yes, 2 = Possibly No and 1 = No). For the negative items, the score was inverted. In this study, Cronbach’s alpha was .80, and the AVE (average variance extracted) was .52. Additionally, high goodness of fit was found, as reflected by the following indicators: X²/v (chi square/v [degrees of freedom]) ratio = 1.572; CFI (comparative fit index) = .991; NNFI (non-normed fit index) = .972; NFI (normed fit index) = .976; RMSEA (root mean square error of approximation) = .076 and SRMR (standardized root mean square residual) = .0293.

The LOT-R, POS, and BIOS-G were selected in this study because they were designed while considering the models analyzed here. Therefore, the LOT-R and POS are based on the theory of positive expectations (Scheier & Carver, 1985), while the BIOS-G is the only scale designed according to the principles of interbehavioral theory (Kantor & Smith, 1975). Moreover, these scales are recent and important instruments for measuring optimism. Hence, the LOT-R is the optimism scale most used around the world (Huffman et al., 2019), while the POS is a measurement tool that is less researched and relatively new (Bharti & Rangnekar, 2019; Kam, 2020).

Design

This study relied on a cross-sectional, ex post facto survey design.

Procedure

Prior approval to conduct this study was obtained from the Human Subjects Institutional Review Board of the North American public university where this study was conducted. All subjects who participated in this study voluntarily recorded their responses on hard-copy survey questionnaires provided by the researchers. All participants were promised anonymity and were provided only pizza and soft drinks in exchange for their participation. Survey questionnaires were administered to all participants in classrooms previously set aside for this purpose.

Data analysis

CFA was used to assess the construct’s goodness of fit for each scale and to determine what measurement model best accommodates the data. Maximum likelihood was the extraction method used. Values smaller than 70 were assumed to indicate multivariate normality. To test for multivariate normality, we relied on Mardia’s coefficient (Rodríguez & Ruiz, 2008). Furthermore, correlations (r) were calculated for all the scores in the various scales to measure convergent validity. Furthermore, multiple regression analyses were used to determine whether any personal and contextual variables significantly influenced the predicted variance of optimism, as measured by these three scales. SPSS version 24 and AMOS version 24 were used for all data analyses. Data goodness of fit was evaluated through nine indices: the chi square/v (degrees of freedom) ratio (X²/v), goodness of fit index (GFI), adjusted goodness of fit index (AGFI), normed fit index (NFI), non-normed fit index (NNFI), comparative fit index (CFI), standardized root mean square residual (SRMR), root mean square error of approximation (RMSEA) and average variance extracted (AVE). The following scores were viewed as indicators of good fit: X²/v ≤ 2; GFI, NFI and CFI ≥ .95; AGFI ≥ .90; and SRMR and RMSEA ≤ .05. The following scores were viewed as indicating an acceptable level of fit: X²/v ≤3, GFI, NFI, NNFI and CFI ≥.90, AGFI ≥.85, SRMR ≤.10 y RMSEA ≤.08. The equivalency of goodness of fit of both models was determined by the difference of chi squares and differential chi squares (Δχ²/Δdf) and the difference in the GFI, NFI, NNFI and CFI. P values greater than .05 for H0 (Δχ² = 0, Δχ²/Δdf >2, ΔGFI, ΔNFI, ΔNNFI and ΔCFI ≥.01) were viewed as indicating a lack of equivalency of goodness of fit of the models being compared (Byrne, 2016). Internal convergent validity was calculated through the average variance extracted (AVE) from the construct; according to Fornell and Larcker (1981), a value greater than >.50 is appropriate.

Results

The tables below show the mean, standard deviation, skewness and kurtosis of each item in each optimism scale. The tables also show how the items in each scale were correlated with each other (see Tables 1 to 3). We can see that all possible correlations of the four BIOS-G items were statistically significant (see Table 1). Concerning the LOT-R, only nine of the 15 correlations were significant (see Table 2). Finally, for the POS, 25 out of 28 correlations were statistically significant (see Table 3).

Table 1.

Factorial structure of the BIOS-G, descriptive statistics, and correlations among the items.

Items	M	SD	Sk	K	Item 1	Item 2	Item 3	Item 4
1. People are good	3.38	.581	−.319	−.678	1	–	–	–
2. Life is beautiful	3.60	.580	−1.188	.503	.211*	1	–	–
3. Life is good	3.61	.549	−1.012	.013	.348**	.848**	1	–
4. Life is ugly	3.61	.695	−1.695	2.021	.350**	.419**	.551**	1

Note: M = mean; SD = standard deviation; Sk = Skewness; K = Kurtosis; *p < .05, **p < .01

Table 2.

Factorial structure of the LOT-R, descriptive statistics, and correlations among the items.

Items	M	SD	Sk	K	Item 1	Item 2	Item 3	Item 4	Item 5	Item 6
1. Overall, I expect more good things to happen to me than bad	3.17	.911	−.756	−.467	1	–	–	–	–	–
2. If something can go wrong for me, it will	2.75	.880	−.292	−.558	.054	1	–	–	–	–
3. I hardly ever expect things to go my way	3.11	.777	−.726	.417	.301**	.119	1	–	–	–
4. I rarely count on good things happening to me	3.14	.932	−.819	−.281	.150	.037	.521**	1	–	–
5. I'm always optimistic about my future	2.87	.872	−.302	−.659	.282**	.282**	.200*	.221*	1	–
6. In uncertain times, I usually expect the best	2.95	.869	−.560	−.257	.202*	−.004	.248*	.196	.297**	1

Note: M = mean; SD = standard deviation; Sk = Skewness; K = Kurtosis; *p < .05, **p < .01

Table 3.

Factorial structure of the POS, descriptive statistics, and correlations among the items.

Items	M	SD	Sk	K	Item 1	Item 2	Item 3	Item 4	Item 5	Item 6	Item 7	Item 8
1. I anticipate that I am going to fail	3.36	.811	−.985	−.033	1	––	–	–	–	–	–	–
2. I have good or positive expectations	3.44	.701	−1.039	.502	.412**	1	–	–	–	–	–	–
3. I am worried	2.33	.995	.295	−.925	.277**	.282**	1	–	–	–	–	–
4. I am relaxed	2.62	.814	.119	−.583	.317**	.349**	.593**	1	–	–	–	–
5. I am happy with my life	3.42	.683	−.981	.576	.298**	.354**	.439**	.457**	1	–	–	–
6. I anticipate bad or negative things	2.67	.865	−.053	−.673	.456**	.339**	.501**	.464**	.270**	1	–	–
7. I am dissatisfied with life	3.66	.572	−1.483	1.252	.223*	.502**	.341**	.349**	.476**	.245*	1	–
8. I believe in success	3.74	.543	−2.404	6.841	.238*	.277**	−.008	.048	.218*	0.05	.297**	1

Note: M = mean; SD = standard deviation; Sk = Skewness; K = Kurtosis; *p < .05, **p < .01

Nine indicators of goodness of fit were selected to measure construct validity for the three optimism scales. The following are the values elicited by the three scales for the nine indicators of goodness of fit (see Table 4).

Table 4.

Indicators of goodness of fit for three optimism scales among North American university students.

Scale	N	X²/v	CFI	RMSEA	SRMR	GFI	AGFI	AVE	NNFI	NFI
LOT-R	100	2.18	.83	.11(90% CI;[.04,18])	.08	.97	.93	.24	.72	.75
POS	100	2.62	.84	.13(90% CI;[.09,17])	.09	.98	.95	.34	.77	.77
BIOS-G	100	2.99	.98	.14(90% CI;[.00,28])	.06	.99	.95	.54	.93	.97

Note: N = Sample Size; X²/v = Chi Square/Degrees of Freedom; CFI = Comparative Fit Index; RMSEA = Root Mean Square Error of Approximation; SRMR = Standardized Root Mean Square Residual; GFI = Goodness of Fit Index; AGFI = Adjusted Goodness of Fit Index; AVE = Average Variance Extracted; NNFI = Non-Normed Fit Index; NFI = Normed Fit Index.

In summary, of the nine indicators shown by both the LOT-R and the POS, two (GFI and AGFI) have a good fit, and two (X²/v and SRMR) have an acceptable level of fit, while the BIOS-G shows six indicators with a good fit (CFI, SRMR, GFI, AGFI, AVE and NFI) and two with an acceptable level of fit (X²/v and NNFI). The number of indicators of goodness of fit shown by the BIOS-G is twice the number of indicators of goodness of fit shown by the LOT-R and the POS scales (see Table 4).

Equivalence of goodness of fit of the three optimism scales

We can see the equivalence of goodness of fit for the three scales through three already identified indicators of good fit or an acceptable level of fit (see Table 5). The LOT-R was found to be equivalent to the POS and the BIOS-G in terms of ΔX²/Δv (<2), and the LOT-R and the POS are also equivalent in terms of ΔCFI and ΔGFI (<.01) (see Table 5); however, the LOT-R is not equivalent to the BIOS-G in terms of ΔCFI and ΔGFI (>.01). On the other hand, the POS and the BIOS-G are equivalent in terms of ΔX²/Δv (<2) but not for ΔCFI and ΔGFI (>.01). In summary, neither the LOT-R nor POS are equivalent to the BIOS-G in terms of ΔCFI and ΔGFI (<.01).

Table 5.

Equivalence of goodness of fit of three optimism scales based on three indicators.

	LOT-R			POS			BIOS-G
Scale	ΔX²/Δv	ΔCFI	ΔGFI	ΔX²/Δv	ΔCFI	ΔGFI	ΔX²/v	ΔCFI	ΔGFI
LOT-R	–	–	–	.44	.01	.00	.81	.15	.02
POS				–	–	–	.37	.14	.02
BIOS-G							–	–	–

Note: X²/v = Chi Square/Degrees of freedom; CFI = Comparative Fit Index; GFI = Goodness of Fit Index.

Reliability of the three optimism scales

The POS and the BIOS-G optimism scales show three good indicators of internal consistency (ɑ, ω and mean interitem correlation [MIC]), while the LOT-R exhibits none (see Table 6).

Table 6.

Indicators of internal consistency of three optimism scales administered to North American university students.

Scale	ɑ	Ω	MIC
LOT-R	.61**	.61	.21
POS	.79**	.80	.32
BIOS-G	.76**	.80	.46

Note: ɑ = Cronbach’s alpha coefficient; ω = McDonald’s omega; MIC = Mean Inter Item Correlation.

**p <.01.

Convergent validity

We present the Pearson product-moment correlations (r) for the three optimism scales and the PWS-G. The highest correlation was found between the LOT-R and the POS (95% CI [.57, .85], r [100] = .71, p = .000, moderate size effect); similarly, the BIOS-R reveals a moderate size correlation effect with the LOT-R (95% CI [.33, .67], r [100] =.50, p = .000), and a less than moderate size effect for correlations with the POS (95% CI [.32, .66], r [100] =.49, p = .000). Finally, all correlations among the three optimism scales and the physical well-being scale have less than moderate size effects. Such values, however, were theoretically predicted to be positive (BIOS-G and PWS-G: 95% CI [.25, .62], r [100] = .43, p = .000; LOT-R and PWS-G: 95% CI [.11, .49], r [100] = .30, p = .002; POS and PWS-G: 95% CI [.26, .62], r [100] = .44, p = .000) (Ferguson, 2009).

Divergent validity

The scores of the three scales of optimism show no differences by gender (LOT-R: t(100) = −.885, p = .383; POS: t(100) = −.263, p = .794; BIOS-G: t(100) = −.840, p = .407). These results suggest that the LOT-R, POS, and BIOS-G have divergent validity (Glaesmer et al., 2012; Pan et al., 2017; Zenger et al., 2013).

Multiple regression analysis

Below are the findings of multiple regression analyses involving scores on personal and contextual variables in the three optimism scales (see Table 7). It should be highlighted that none of the three models, even when considering age, socioeconomic level, and number of years in the present job, achieve an R² (explained variance) greater than .10, thus implying that such variables do not significantly contribute to our understanding of optimism. The effect sizes (d) for the three explained variances were less than .12 (Cohen, 1992).

Table 7.

Regression of optimism on age and socioeconomic level according to the LOT-R, POS and BIOS-G optimism scales among North American university students.

	LOT-R		POS		BIOS-G
	Β	Sig.	β	Sig.	β	Sig.
Age	−.005	.961	.143	.181	−.353	.001
Socioeconomic level	.098	.350	.099	.338	.002	.985
Number of years at current job	−.084	.428	−.133	.203	−.017	.866
Adjusted R²	−.014		.004		.100

Note: β = Standardized Betas.

Factorial structure of the LOT-R in this study

The LOT-R’s goodness of fit was estimated based on the assumption it fitted into a two-factor correlated model, thereby determining the following goodness of fit indicators: X²/v = 1.508, GFI = .964, AGFI = .905, NFI = .844, NNFI = .878, CFI = 935, SRMR = .059, RMSEA = .072. The correlation between the two factors was r (100) = .59.

Discussion

The primary objective of this study was to find evidence to support whether, with respect to optimism, the theory of positive expectations has greater explanatory power than the interactive personality style theory. To achieve this objective, we analyzed and assessed the construct, convergent, and divergent validity and the reliability of the three instruments developed from the abovementioned theories. The authors are aware that determining the validity of an instrument does not fully demonstrate or establish the validity of any given theory. Nevertheless, we believe that proving the validity of the construct and the instruments that attempt to measure it are steps in the right direction.

Many studies on the factorial structure of the LOT-R identify a two-factor solution, but the factors are highly correlated, leading acceptance of the one-dimensionality of optimism (Ferrando et al., 2002; Glaesmer et al., 2012; Herzberg et al., 2006; Jovanović & Gavrilov-Jerković, 2013; Vera-Villarroel et al., 2009; Zenger et al., 2013). Hence, in this study, the score on the LOT-R was calculated while considering the six items, thereby increasing the Cronbach’s alpha coefficient. This decision was also supported because a correlation of .59 was found between the two factors (optimism and pessimism); thus, the two-factor structure has a more valid factorial solution than the one-factor structure.

Nine indicators of goodness of fit were selected to test and evaluate the three optimism scales. The findings suggest that both the LOT-R and the POS (both developed from the theory of positive expectations) comply with 44.44% of the indicators, while the BIOS-G (developed based on the theory of interactive personality style) complies with 88.88% of the indicators. This percentage of indicators is twice the number of indicators with which the LOT-R and the POS comply. More specifically, compared to the LOT-R or the POS (both of whose number of indicators with a good fit is two), the BIOS-G triples the number of indicators with a good fit (six). Additionally, the BIOS-G, the LOT-R, and the POS each have two indicators with an acceptable level of goodness of fit. A comparison of the equivalency of the three scales in terms of indicators already identified as having a good or acceptable level of fit shows that, in terms of ΔX²/Δv (<2), the ΔCFI and the ΔGFI (<.01), the LOT-R is equivalent to the POS in 50% (six) of the indicators. This finding makes sense given the theoretical foundation and origin of both scales.

These data on the scales’ goodness of fit show that the BIOS-G optimism scale enjoys greater empirical support than either the LOT-R or the POS scale. This finding suggests that interactive personality style theory (García Cadena et al., 2016; Ribes, 2009) may help us understand optimism among a sample of North American university students better than the theory of positive expectations (Scheier et al., 1994; Schweizer & Koch, 2001).

Regarding convergent validity, the strong correlation between the LOT-R and the POS scales (95% CI [.57, .85], r [100] = .71, p = < .01) is understandable given their common theoretical foundation and origin. All three scales show some level of validity and measure the optimism construct to some extent. The Mexican BIOS-G scale measures optimism just like the North American and the German scales. The correlations between the Mexican scale and the North American LOT-R scale and between the Mexican scale and the German POS scale are 95% CI [.33, .67], r [100] = .50, p = < .01; and 95% CI [.32, .66], r[100] = .49, p = < .01, respectively. These correlations suggest that given the complexity of the psychological reality, the construct of optimism can be understood using different theories and measured using different instruments. Nevertheless, the findings of this study suggest that the Mexican scale has a higher level of validity. These data suggest the advisability of developing hybrid perspectives related to psychological events and developing measurement instruments that combine items of already existing instruments, as demonstrated by García-Cadena et al. (2016), to measure the constructs of optimism, forgiveness and generosity. Additionally, the positive correlations between the three optimism scales and the physical well-being scale adds external validity to the BIOS-G optimism scale.

The three tests of internal consistency used to compare and evaluate the three optimism scales (Cronbach’s alpha, 1951; omega, McDonald, 1999; and mean inter-item correlation, Cortina, 1993) show high internal consistency for the POS and the BIOS-G but not for the LOT-R. The POS satisfies the three criteria for internal consistency despite satisfying only four of the nine indicators of goodness of fit; two (GFI and AGFI) indicate a good fit, while two (X²/v and SRMR) indicate an acceptable level of fit). It must be emphasized that an instrument’s internal consistency is highly important given that a lack of internal consistency may lead to erroneous interpretations and conclusions related to other variables (John & Soto, 2009). Additionally, it would be difficult to accept the adequacy of an instrument without construct validity even if the instrument shows good internal consistency. This difficulty would be especially true in situations where the study sample is very different from the sample used to initially validate the instrument. In relation to this study, we could erroneously conclude that the POS is an ideal scale to measure optimism among North American university students simply because the instrument met three internal consistency criteria. As previously indicated, when compared to the BIOS-G, the POS seems to have little construct validity. Consequently, it would be difficult for us to recommend the POS. The practice of accepting the adequacy of an instrument based on the identified alpha or omega may lead to errors of interpretation of the findings. In this study of three optimism scales, the BIOS-G was found to enjoy the greatest level of empirical support among the three.

This study included contextual variables to help interpret the findings. According to van de Vijver (2009), there are challenges associated with interpreting findings without considering contextual variables. The personal variables of age, socioeconomic level, and number of years in the current job were used as predictors of optimism in multiple regression analyses for each scale. We concluded that these variables do not significantly contribute to predicting optimism given that the explained variance (R²) did not exceed 12% for any of the models (Cohen, 1992).

In summary, the findings provide sufficient support for the construct validity of the BIOS-G given that the instrument meets most of the criteria recommended by John and Soto (2009). First, the confirmatory factor analysis revealed solid empirical support for the instrument’s structural validity based on the number of satisfactory indicators of goodness of fit. Second, we found evidence of convergent external validity by correlating the BIOS-G, the LOT-R and the POS and then by correlating all of these scales with the PWS-G. Third, the BIOS-G revealed good indices of internal consistency even though we have not yet tested for test-retest reliability. Future studies should focus on testing the instruments’ discriminant and face validity.

Finally, we discuss the limitations of this study. The first limitation is that responses to all three instruments relied on the subjects’ self-reports. To further assess the instruments’ reliability, it may be a good idea in the future to compare the subjects’ self-reports to responses to the same question-items provided by significant others about the study participants.

The second limitation, which is associated with the BIOS-G, is that social desirability may influence the subjects’ responses. It is always possible that the subject’s desire to project a positive image may bias the provided responses and distort the study findings. In this study, we attempted to counter this possible effect by making the survey anonymous. Researchers have no way of knowing how any particular student responded to any question, and the students were informed of this. Nevertheless, there is a possibility that students in a given group may have desired for their group to look good as a whole.

A third limitation is that the study relies on a small sample (n = 100); this reliance leads to the possibility of sampling bias, thereby restricting the generalization of the findings. A fourth limitation is that females are overrepresented in the sample. There were eight females for every two males in the sample. This overrepresentation prevents performing complementary procedures such as factorial invariance by sex to evaluate the item equivalence of a scale by comparing these two different groups (Bowen & Masa, 2015). The certainty of factorial invariance allows the interpretation of the differences between compared groups (men and women, in this case), and these differences result from the differences inherent in the evaluated construct. The lack of invariance raises the probability of measurement bias in favor of one of the groups because of the psychometric variations in the responses, thereby compromising the validity of the findings (Byrne, 2016). The fifth limitation is that university students from only one school within one university are studied. Future studies should focus on larger and more diverse samples from the United States with equal proportions of male and female students.

In conclusion, it could be said that the theory of positive expectations and interbehavioral theory are both interpretations of optimism from different approaches; however, based on current research data, it is difficult to determine which theory can better explain optimism.

Appendix 1. Life orientation Test -Revised (LOT-R; Scheier et al., 1994)

In uncertain times, I usually expect the best.

It’s easy for me to relax (Filler item).

If something can go wrong for me, it will.

I’m always optimistic about my future.

I enjoy my friends a lot (Filler item).

It’s important for me to keep busy (Filler item).

I hardly ever expect things to go my way.

I don’t get upset too easily (Filler item).

I rarely count on good things happening to me.

Overall, I expect more good things to happen to me than bad.

Appendix 2. Personal optimism scale (POS; Schweizer, & Koch, 2001)

I believe in success

I have positive expectations

I have negative expectations

I am worried

I have expectations of failure

I am not worried

I am dissatisfied with life

I am happy with life

Appendix 3. Brief interactive optimism Scale-Garcia (BIOS-G; García-Cadena et al., 2019)

Life is beautiful

Life is good

Human beings are good

Life is ugly

Appendix 4. Physical well-being Scale-Garcia (PWS-G; Garcia et al., 2015)

I enjoy good physical functioning

My health condition is good

I feel physically well

I enjoy very good health

Footnotes

Acknowledgments

The authors are grateful to the anonymous reviewers for the recommendations to their manuscript.

Article Notes

ORCID iDs

Cirilo H. Garcia Cadena

Tomas Caycho-Rodríguez

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