Pilot data collected during the Spring quarter (2023) on SONA students. This was piloting the CFA that will be run on Prolific participants Jan 2024.

Participants

394 undergraduate students participated for course credit in May 2023. Thirty-one participants did not complete the study and twenty-two people failed to pass attention checks so their data was not analysed. The final analysis consisted of 341 participants with ages ranging from 18 - 42 (M = 20.88, 2.7). The sample was primarily made up of females (68.3%) and people of Asian ethnicity (42.1%). See the table below for full descriptives.

gender	n	Age(mean)	Age(sd)
Man	63	21.02	2.35
No Answer	1	20.00
NonBinary	4	21.25	2.36
Other	1	19.00
TransMan	2	19.00	0.00
TransWoman	1	19.00
Woman	269	20.87	2.80

ethnoracial	n
Asian	166
Black	5
Hispanic	85
Middle Eastern	16
Mixed	24
No Answer	3
White	42

Political Ideology was scored on a 7-point Likert scale with 1 = Most Conservative and 7 = Most Liberal. The mean political ideology was 5.04(1.17), showing that this sample skewed more liberal. This is to be expected with our student sample. Family SES was scored on a 10-point ladder,with 10 being the best off, and 1 being the worst off. The mean SES was 6.3(1.72).

Method

Participants enrolled in undergraduate psychology courses signed up via SONA to participate in a short online study for course credit. They were directed to a Qualtrics survey where they were first prompted with the question “How would you define nature?”. After which they were presented with 30 CTN items. These were the CTN items selected after analysing the results from the EFA studies above. See [ADD LINK HERE] for a full list of CTN items.

Measures

Convergent Validity

Two pre-existing CTN scales were used to identify convergent validity. The Connectedenss to Nature Scale (CNS, Mayer & Frantz, 2004) and the Environmental Identity Scale revised (EID-R, Clayton et al., 2021). The CNS is a 14-item scale designed to measure the cognitive beliefs about how interneconnect one’s self is to nature. It is measured on a Likert scale ranging from 1(strongly disagree) to 5(strongly agree). The EID-R is a 14-item scale designed to measure how interneconnect one’s self is to nature. It is measured on a Likert scale ranging from 1(not at all true of me) to 7(completely true of me).

Predictive Validity

Pro-environmental behavior

Participants completed the Recurring Pro-environmental Behavior scale (Brick et al., 2017) which asks people to report how often they engage in various pro-environmental behaviors. This scale includes 20 items measured on a Likert scale ranging from 1(never) to 5(always).

Primal Beliefs

Three subscales of the primals beliefs inventory (Clifton et al., 2019) were used to identify worldviews held by participants. The About Me subscale consists of five questions asking how egocentric ones beliefs are (e.g., Whatever is happening around me often feels related to me or something I’ve done). The Hierarchical subscale consists of five questions exploring beliefs about the hierarchical nature of the world (e.g., Things are rarely equal. Most plants and animals, even people, are better or worse than one another.). The Interconnected subscale consists of four items asking how connected or atomistic one believes the world to be (e.g., Most things are basically unconnected and independent from each other [reversed]). All items are measured on a Likert scale ranging from 1(strongly disagree) to 6(strongly agree).

Covariates

Locus of Control

Participants completed a brief version of the Locus of Control Scale (Sapp & Harrod, 1993) which includes 9 items revealing how much people perceived they have internal control over events (e.g., To a great extent, my life is controlled by accidental happenings). Measured on a Likert scale from 1(strongly disagree) to 7(strongly agree).

Demographics

Participants also answered several demographics questions (age, gender, political ideology, and social economic status).

Analysis & Results

CFA Assumptions

Several assumptions need to be met before running a confirmatory factor analysis. First we checked the skewedness and kurtosis of each item to be included in the CFA. The closer to zero for both skewedness and kurtosis, the closer to a normal distribution. Any items whose distributions exhibited skewness and/or kurtosis that exceed general guidelines were considered non-normal removed from the analysis (Hair et al., 2017, p. 61). Statology Link).

Skewness

For skewedness, using the skewness function from the Moments package in R (Komsta & Novemstky, 2015), skewness was calculated for each item. Any item where the number is greater than +1 (right skewed) or lower than -1 (left skewed), this is an indication of a substantially skewed distribution. No items were heavily skewed in this dataset.

## [1] "No items were heavily skewed"
## [1] skew
## <0 rows> (or 0-length row.names)

Kurtosis

For Kurtosis, using the kurtosis function from the Moments package in R (Komsta & Novemstky, 2015), kurtosis was calculated for each item. Any item were the number is greater than +3, the distribution is too peaked. Likewise, a kurtosis of less than -3 indicates a distribution that is too flat. Two items have a high kurtosis:

items	kurtosis
DEEPCTN_s_5	3.32
DEEPCTN_ex_7	3.21

Inter-item Correlation

## [1] "No items were correlated > .75"

Multivariate normality

Notes on Multivariate Normality

Quantiative test of normality: shapiro is fine for univariate normality test. But I also need to test for multivariate normality. This package is both. Use this.
Can just look at univariate for now, but REPEAT THIS with my final variables to check for multivariate normality
Sources:

A Mardia Test of multivariate normality from the MVN package in R (Korkmaz et al., 2021) indicated that this data is not normal, suggesting that a rotation-method that is robust to non-normal data should be used.

Multivariate Normality

Test	Statistic	p	Result
Mardia Skewness	7,681.36	< 0.001	NO
Mardia Kurtosis	28.32	< 0.001	NO
MVN		NA	NO

Univariate Normality

##            Test      Variable Statistic   p value Normality
## 1  Shapiro-Wilk  DEEPCTN_s_1     0.9402  <0.001      NO    
## 2  Shapiro-Wilk  DEEPCTN_s_2     0.9326  <0.001      NO    
## 3  Shapiro-Wilk  DEEPCTN_s_3     0.9175  <0.001      NO    
## 4  Shapiro-Wilk  DEEPCTN_s_4     0.9245  <0.001      NO    
## 5  Shapiro-Wilk  DEEPCTN_s_5     0.8833  <0.001      NO    
## 6  Shapiro-Wilk  DEEPCTN_s_6     0.9263  <0.001      NO    
## 7  Shapiro-Wilk DEEPCTN_ex_1     0.9230  <0.001      NO    
## 8  Shapiro-Wilk DEEPCTN_ex_2     0.9443  <0.001      NO    
## 9  Shapiro-Wilk DEEPCTN_ex_3     0.9446  <0.001      NO    
## 10 Shapiro-Wilk  DEEPCTN_s_7     0.9324  <0.001      NO    
## 11 Shapiro-Wilk  DEEPCTN_s_8     0.9402  <0.001      NO    
## 12 Shapiro-Wilk  DEEPCTN_s_9     0.9255  <0.001      NO    
## 13 Shapiro-Wilk DEEPCTN_ex_4     0.9409  <0.001      NO    
## 14 Shapiro-Wilk DEEPCTN_ex_5     0.9331  <0.001      NO    
## 15 Shapiro-Wilk DEEPCTN_ex_6     0.9256  <0.001      NO    
## 16 Shapiro-Wilk DEEPCTN_ex_7     0.8912  <0.001      NO    
## 17 Shapiro-Wilk DEEPCTN_emo_1    0.8987  <0.001      NO    
## 18 Shapiro-Wilk DEEPCTN_emo_2    0.9163  <0.001      NO    
## 19 Shapiro-Wilk DEEPCTN_emo_3    0.9262  <0.001      NO    
## 20 Shapiro-Wilk DEEPCTN_emo_4    0.8586  <0.001      NO    
## 21 Shapiro-Wilk DEEPCTN_s_10     0.9390  <0.001      NO    
## 22 Shapiro-Wilk DEEPCTN_ex_8     0.9355  <0.001      NO    
## 23 Shapiro-Wilk  DEEPCTN_m_1     0.9358  <0.001      NO    
## 24 Shapiro-Wilk  DEEPCTN_m_2     0.9380  <0.001      NO    
## 25 Shapiro-Wilk  DEEPCTN_m_3     0.9183  <0.001      NO    
## 26 Shapiro-Wilk  DEEPCTN_m_4     0.9459  <0.001      NO    
## 27 Shapiro-Wilk  DEEPCTN_m_5     0.9398  <0.001      NO    
## 28 Shapiro-Wilk  DEEPCTN_m_6     0.9329  <0.001      NO    
## 29 Shapiro-Wilk DEEPCTN_em_5     0.8499  <0.001      NO    
## 30 Shapiro-Wilk DEEPCTN_em_6     0.8968  <0.001      NO

Norm Descriptives for each item

##            Test      Variable Statistic   p value Normality
## 1  Shapiro-Wilk  DEEPCTN_s_1     0.9402  <0.001      NO    
## 2  Shapiro-Wilk  DEEPCTN_s_2     0.9326  <0.001      NO    
## 3  Shapiro-Wilk  DEEPCTN_s_3     0.9175  <0.001      NO    
## 4  Shapiro-Wilk  DEEPCTN_s_4     0.9245  <0.001      NO    
## 5  Shapiro-Wilk  DEEPCTN_s_5     0.8833  <0.001      NO    
## 6  Shapiro-Wilk  DEEPCTN_s_6     0.9263  <0.001      NO    
## 7  Shapiro-Wilk DEEPCTN_ex_1     0.9230  <0.001      NO    
## 8  Shapiro-Wilk DEEPCTN_ex_2     0.9443  <0.001      NO    
## 9  Shapiro-Wilk DEEPCTN_ex_3     0.9446  <0.001      NO    
## 10 Shapiro-Wilk  DEEPCTN_s_7     0.9324  <0.001      NO    
## 11 Shapiro-Wilk  DEEPCTN_s_8     0.9402  <0.001      NO    
## 12 Shapiro-Wilk  DEEPCTN_s_9     0.9255  <0.001      NO    
## 13 Shapiro-Wilk DEEPCTN_ex_4     0.9409  <0.001      NO    
## 14 Shapiro-Wilk DEEPCTN_ex_5     0.9331  <0.001      NO    
## 15 Shapiro-Wilk DEEPCTN_ex_6     0.9256  <0.001      NO    
## 16 Shapiro-Wilk DEEPCTN_ex_7     0.8912  <0.001      NO    
## 17 Shapiro-Wilk DEEPCTN_emo_1    0.8987  <0.001      NO    
## 18 Shapiro-Wilk DEEPCTN_emo_2    0.9163  <0.001      NO    
## 19 Shapiro-Wilk DEEPCTN_emo_3    0.9262  <0.001      NO    
## 20 Shapiro-Wilk DEEPCTN_emo_4    0.8586  <0.001      NO    
## 21 Shapiro-Wilk DEEPCTN_s_10     0.9390  <0.001      NO    
## 22 Shapiro-Wilk DEEPCTN_ex_8     0.9355  <0.001      NO    
## 23 Shapiro-Wilk  DEEPCTN_m_1     0.9358  <0.001      NO    
## 24 Shapiro-Wilk  DEEPCTN_m_2     0.9380  <0.001      NO    
## 25 Shapiro-Wilk  DEEPCTN_m_3     0.9183  <0.001      NO    
## 26 Shapiro-Wilk  DEEPCTN_m_4     0.9459  <0.001      NO    
## 27 Shapiro-Wilk  DEEPCTN_m_5     0.9398  <0.001      NO    
## 28 Shapiro-Wilk  DEEPCTN_m_6     0.9329  <0.001      NO    
## 29 Shapiro-Wilk DEEPCTN_em_5     0.8499  <0.001      NO    
## 30 Shapiro-Wilk DEEPCTN_em_6     0.8968  <0.001      NO

CFA Preparation

Only items that were decided upon during EFA pilots to be concluded

Remove items with too heavy kurtosis (see above)

All analyses going forward will only include the following items:

Code	Items
DEEPCTN_s_1	I view nature as a mother who nurtures and cares for me
DEEPCTN_s_2	Human beings and nature are connected by the same energy or Life-force
DEEPCTN_s_3	My connection to nature is something I would describe as spiritual
DEEPCTN_s_7	I think about the shared breath between myself and plants; I breathe in the oxygen released by plants, and plants use the carbon dioxide I exhale
DEEPCTN_s_10	When I eat, I feel thankful for the animals, plants, and earth for nourishing me
DEEPCTN_s_8	I often think about the fact that all life is grounded on this planet that is revolving around the sun
DEEPCTN_s_4	Every part of nature is sacred
DEEPCTN_s_6	I like the idea that, when I die, my body will return to the earth, nourishing the soil
DEEPCTN_s_9	Indoor plants are part of the family
DEEPCTN_ex_4	My favorite place is in nature
DEEPCTN_ex_5	Walking through a forest makes me forget about my daily worries
DEEPCTN_ex_6	I prefer outdoor to indoor sports
DEEPCTN_ex_8	I hike or run in nearby nature
DEEPCTN_ex_1	I like to get outdoors whenever I get the chance
DEEPCTN_ex_2	I feel uneasy if I am away from nature for too long
DEEPCTN_ex_3	I engage and participate with nature to find meaning and richness in life
DEEPCTN_m_1	I take time to watch the clouds pass by
DEEPCTN_m_2	I deliberately take time to watch stars at night
DEEPCTN_m_3	When possible I take time to watch the sunrise or the sunset without distractions
DEEPCTN_m_4	I consciously watch or listen to birds
DEEPCTN_m_5	I take time to consciously smell flowers
DEEPCTN_m_6	I pay attention to the current phase of the moon
DEEPCTN_emo_1	Seeing a cleared forest is upsetting to me
DEEPCTN_emo_2	If one of my plants died, I would blame myself
DEEPCTN_emo_3	Thinking of someone carving their initials into a tree makes me cringe
DEEPCTN_emo_4	If there is an insect, such as a fly or a spider, in my home, I try to catch and release it rather than kill it
DEEPCTN_em_6	I talk to the wild animals I encounter (e.g., birds, lizards, rabbits, squirrels)

CFA

Four Factor Hierarchical Model

Testing a structure which includes an overall Connection to Nature factor and four dimensions:

Deep: Deeply seeing the self as part of nature
Experiential: Spending more time in nature and enjoying spending time in nature
Emotional: Emotional desire to connect with nature and protect it
Presence: Engaging mindfully and consciously with nature

Items load onto their dimensions well, with the exception of 1 item (“Thinking of someone carving their initials into a tree makes me cringe”) which loaded onto the Emotion dimension at 0.33.

All dimensions loaded onto the single CTN dimension, but these loaded quite highly (especially Deep and Emotion) which suggests these might be driving the overall CTN score.

Fit Indices	df	Chi-Sqa	RMSEAb	RMSEA CI Lower	RMSEA CI Upper	SRMRc	TLId	CFIe	AICf
	320	757.665	0.064	0.058	0.07	0.058	0.887	0.897	31,855.45
aCloser to 0 indicate better fit
b(Root mean square error) 0.01 = Excellent; 0.05 = Good; 0.08 = Mediocre
c(Standardized root mean square residual) Closer to 0 indicate better fit
d(Tucker Lewis Index) Closer to 1 indicates better fit
e(Comparative fit index) Closer to 1 indicates better fit
f(Akaike’s Information Criterion) The lower the AIC, the more predictive

Four Factor Model

Testing a structure which only includes the four dimensions:

Deep: Deeply seeing the self as part of nature
Experiential: Spending more time in nature and enjoying spending time in nature
Emotional: Emotional desire to connect with nature and protect it
Presence: Engaging mindfully and consciously with nature

Items load onto their dimensions similarly well to the hierarchical model. Again, 1 item loads weakly: (“Thinking of someone carving their initials into a tree makes me cringe”) which loaded onto the Emotion dimension at 0.33.

Dimensions are intercorrelated reasonable well - not too high as to have multi-collinearity (none above .80)

Fit Indices	df	Chi-Sqa	RMSEAb	RMSEA CI Lower	RMSEA CI Upper	SRMRc	TLId	CFIe	AICf
	318	754.331	0.064	0.058	0.07	0.058	0.887	0.898	31,856.11
aCloser to 0 indicate better fit
b(Root mean square error) 0.01 = Excellent; 0.05 = Good; 0.08 = Mediocre
c(Standardized root mean square residual) Closer to 0 indicate better fit
d(Tucker Lewis Index) Closer to 1 indicates better fit
e(Comparative fit index) Closer to 1 indicates better fit
f(Akaike’s Information Criterion) The lower the AIC, the more predictive

Single Factor Model

Testing a structure which includes only a single overall Connection to Nature factor

Loadings are slightly weaker onto a single overall CTN factor. Again, 1 item loads weakly: (“Thinking of someone carving their initials into a tree makes me cringe”) which loaded onto the Emotion dimension at 0.31.

Fit Indices	df	Chi-Sqa	RMSEAb	RMSEA CI Lower	RMSEA CI Upper	SRMRc	TLId	CFIe	AICf
	324	1,291.895	0.095	0.089	0.1	0.075	0.754	0.773	32,381.68
aCloser to 0 indicate better fit
b(Root mean square error) 0.01 = Excellent; 0.05 = Good; 0.08 = Mediocre
c(Standardized root mean square residual) Closer to 0 indicate better fit
d(Tucker Lewis Index) Closer to 1 indicates better fit
e(Comparative fit index) Closer to 1 indicates better fit
f(Akaike’s Information Criterion) The lower the AIC, the more predictive

Comparing Fit of each Model

Comparing the fit of the three models

Sources for fit indices

Both four-factor models (flat and hierarchical) perform better than the single-factor model.

There is no difference between the hierarchical and the flat models.

Model	df	Chi-Sq	RMSEA	RMSEA CI Lower	RMSEA CI Upper	SRMR	TLI	CFI	AIC
1 Factor	324	1,291.895	0.095	0.089	0.10	0.075	0.754	0.773	32,381.68
4 Factor	318	754.331	0.064	0.058	0.07	0.058	0.887	0.898	31,856.11
4 Factor Hierarchical	320	757.665	0.064	0.058	0.07	0.058	0.887	0.897	31,855.45

## 
## Scaled Chi-Squared Difference Test (method = "satorra.bentler.2001")
## 
## lavaan NOTE:
##     The "Chisq" column contains standard test statistics, not the
##     robust test that should be reported per model. A robust difference
##     test is a function of two standard (not robust) statistics.
##  
##                   Df   AIC   BIC   Chisq Chisq diff Df diff Pr(>Chisq)    
## fit_model_hier_4 320 31855 32076  757.67                                  
## fit_model_flat   324 32382 32587 1291.90     381.09       4  < 2.2e-16 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Reduced CFA

Four Factor Hierarchical

Fit Indices	df	Chi-Sqa	RMSEAb	RMSEA CI Lower	RMSEA CI Upper	SRMRc	TLId	CFIe	AICf
	166	355.423	0.059	0.05	0.067	0.051	0.928	0.937	23,566.82
aCloser to 0 indicate better fit
b(Root mean square error) 0.01 = Excellent; 0.05 = Good; 0.08 = Mediocre
c(Standardized root mean square residual) Closer to 0 indicate better fit
d(Tucker Lewis Index) Closer to 1 indicates better fit
e(Comparative fit index) Closer to 1 indicates better fit
f(Akaike’s Information Criterion) The lower the AIC, the more predictive

Single Factor

Fit Indices	df	Chi-Sqa	RMSEAb	RMSEA CI Lower	RMSEA CI Upper	SRMRc	TLId	CFIe	AICf
	170	742.655	0.101	0.093	0.108	0.072	0.786	0.809	23,946.06
aCloser to 0 indicate better fit
b(Root mean square error) 0.01 = Excellent; 0.05 = Good; 0.08 = Mediocre
c(Standardized root mean square residual) Closer to 0 indicate better fit
d(Tucker Lewis Index) Closer to 1 indicates better fit
e(Comparative fit index) Closer to 1 indicates better fit
f(Akaike’s Information Criterion) The lower the AIC, the more predictive

Comaparing Fit

Model	df	Chi-Sqa	RMSEAb	RMSEA CI Lower	RMSEA CI Upper	SRMRc	TLId	CFIe	AICf
1 Factor	170	742.655	0.101	0.093	0.108	0.072	0.786	0.809	23,946.06
4 Factor Hierarchical	166	355.423	0.059	0.050	0.067	0.051	0.928	0.937	23,566.82
aCloser to 0 indicate better fit
b(Root mean square error) 0.01 = Excellent; 0.05 = Good; 0.08 = Mediocre
c(Standardized root mean square residual) Closer to 0 indicate better fit
d(Tucker Lewis Index) Closer to 1 indicates better fit
e(Comparative fit index) Closer to 1 indicates better fit
f(Akaike’s Information Criterion) The lower the AIC, the more predictive

DEEP CTN CFA (Pilot 4 SONA Spr23)