Construct validation of pre-service science teacher efficacy beliefs instrument (STEBI-B): Rasch analysis technique

Confirmatory Factor Analysis of the STEBI-B Instrument

Exploratory factor analysis using principal component analysis of the revised STEBI-B scale suggests that (23) items of the instrument define two separate constructs (Bliecher, 2004; Enochs & Riggs, 1990; Morrell and Carroll, 2003). The construct validity of the two-factor model instrument was checked by confirmatory factor analysis using IBM SPSS Amos version 20. The fit statistics for the two-factor solution show that the measurement model yields reasonable fit indices (CFI = 0.98; RMSEA = 0.047; SRMR = 0.04) between the item response and the proposed measurement model (i.e. the two subscales: outcome expectancy and science teaching efficacy).

Overall Model Fit Information, Separation and Mean Logit for Outcome Expectancy items:

Table 1. Overall model fit information, separation and mean Logit for Outcome Expectancy items

Summary of 168 Measured Person
					Infit		Out fit
	Raw Score	Count	Measure	Model Error	MNSQ	ZSTD	MNSQ	ZSTD
Mean	37.7	10	0.72	0.41	1.02	-0.1	1.02	-0.1
S.D.	4.10	0.0	0.73	0.07	0.68	1.3	0.71	1.3
Max.	49.0	10	4.12	1.06	4.63	4.3	5.36	4.8
Min.	26.0	10	-0.92	0.35	0.10	-3.3	0.09	-3.1
Real RMSE	0.47	Adj. SD	0.55	Separation	1.17	Person	Reliability	0.58
Model	0.42	Adj.SD	0.59	Separation	1.41	Person	Reliability	0.67
S.E. Of Person Mean= 0.06
Summary of 10 Measured Items
					Infit		Out fit
	Raw Score	Count	Measure	Model Error	MNSQ	ZSTD	MNSQ	ZSTD
Mean	633.0	168	0.00	0.10	1.00	0.1	1.02	0.2
S.D.	95.9	0.0	0. 54	0.01	0.12	1.0	0.15	1.2
Max.	49.0	10	4.12	1.06	4.63	4.3	5.36	4.8
Min.	26.0	10	-0.92	0.35	0.10	-3.3	0.09	-3.1
Real RMSE	0.10	Adj. SD	0.53	Separation	5.10	Item	Reliability	0.96
Model RMSE 0.10 Adj.SD 0.53 Separation 5.20 Item Reliability 0.96

The separation index is an index of the spread of the person positions or item positions. For persons, the separation index is 1.17 for the data (real separation index) and the model separation is 1.41. The person reliability is 0.58 for the data and is 0.67 for the model, which is a moderate value, this value is expected due to person homogeneity in terms of the number of science method and science courses, gender, number of school science courses and self rating of their science teaching. For item separation, it is 5.1 for the data and 5.2 for the model. The item reliability is 0.96, which is high value that supports the construct validity of the scale.

Table 2. The Infit and Outfit statistics and item measure for outcome expectancy items

Item number	measure	Model S.E.	Infit		Outfit		PT Corr.
			MNSQ	ZSTD	MNSQ	ZSTD
1	-0.11	0.13	0.91	-0.6	0.90	-0.7	0.37
4	-0.36	0.11	0 .90	-0.7	0.85	-1.1	0.48
7	-0.52	0.10	1.12	1.0	1.24	1.8	0.33
9	-0.50	0.12	0.99	0.0	1.12	0.9	0.36
10	1.45	0.09	1.18	1.6	1.20	1.7	0.47
11	-0.03	0.09	0 .91	-0.8	0.91	-0.8	0.55
13	0.36	0.08	1.18	1.9	1.18	1.7	0.40
14	-0.11	0.09	0 .96	-0.4	0.93	-0.7	0.52
15	-0.02	0.11	0 .83	-1.4	0.81	-1.6	0.55
16	-0.16	0.10	1.02	0.20	1.07	0.6	0.40

The infit and outfit mean square values ( MNSQ) for the ten outcome expectancy scale items are ranged between 0.81 and 1.24, and the standardized fit values between -1.6 to = 1.9. Although there is no rule of thumb for the acceptable values for infit and outfit statistics, some considerations were suggested by researchers ( Bond & Fox, 2007; Frantom ,Green& Lam, 2002): mean square values of infit and outfit between 0.5 and 1.5, or 0.6-1.4, and 0.8-1.2; mean square values less than 1.3 for samples less than 500, 1.2 for samples 500-1000, and 1.1 for samples greater than 1000. Standardized (ZSTD) infit and outfit between -2 and +2, between -3 and +2, and less than +2. Consequently, all items of the outcome expectancy scale are within the acceptable range of fit statistics.

This result suggests the unidimensionality of the OE scale, which is a basic assumption of Rasch model. The point measure correlation for the OE scale items range between 0.33 and 0.55. This result revealed that each item contributed to define a common construct.

Moreover, Boone; Townsend and Staver (2011) suggested that instead of presenting both SE and OE items in the STEBI instrument to respondents, one is best served by presenting one set of items first (e.g., SE) and then a second set of items (OE). This would facilitate the possibility of presenting a SE rating scale that might be different from the OE rating scale, and presented in a manner that would not confuse.

Overall model fit information, separation and mean Logit for Personal science teaching efficacy items:

Table 3. The Infit and Outfit statistics and item measure for Personal science teaching efficacy items

Summary of 168 Measured Person
					Infit		Out fit
	Raw Score	Count	Measure	Model Error	MNSQ	ZSTD	MNSQ	ZSTD
Mean	46.5	13.0	0.62	0.36	1.02	-0.2	1.00	-0.2
S.D.	5.9	0.00	0.73	0.04	0.77	1.5	0.76	1.5
Max.	59.0	13.0	2.70	0.50	5.58	5.9	5.20	5.5
Min.	28.0	13.0	-1.33	0.31	0.11	-3.3	0.13	-3.2
Real RMSE	0.41	Adj. SD	0.60	Separation	1.45	Person	Reliability	0.68
Model	RMSE	0.36	Adj.SD	0.63	Separation	1.73	Reliability	0.75
S.E. Of Person Mean= 0.06
Summary of 13 Measured Items
					Infit		Out fit
	Raw Score	Count	Measure	Model Error	MNSQ	ZSTD	MNSQ	ZSTD
Mean	600.8	168	0.00	0.10	1.00	0.0	1.00	0.1
S.D.	60.7	0.0	0. 40	0.01	0.15	1.3	0.16	1.4
Max.	730.0	168.0	0.79	0.13	1.25	2.3	1.24	2.1
Min.	462.0	168.0	-0.61	0.08	0.71	-2.6	0.70	-2.7
Real RMSE	0.10	Adj. SD	0.53	Separation	5.10	Item	Reliability	0.96
S.E. Of	items	Mean=	0.12

For persons, the separation index is 1.45 for the data(real separation index) and the model separation is 1.73. The person reliability is 0.68 for the data and is 0.75 for the model, which is a moderate value; this value is expected due to person homogenity, in terms of the number of science method and college science courses, gender, number of school science courses and self rating of their science teaching. For item separation, it is 3.69 for the data and 3.79 for the model. The item reliability is 0.93, which is high value that supports the construct validity of the scale.

Table 4. The Infit and Outfit statistics and item measure for personal efficacy items

Item number	measure	Model S.E.	Infit		Outfit		PT Corr.
			MNSQ	ZSTD	MNSQ	ZSTD
2	-0.31	0.11	1.20	1.6	1.20	1.7	0.30
3	0.21	0.09	1.08	0.8	1.11	1.0	0.46
5	-0.19	0.11	1.10	1.0	1.11	0.9	0.38
6	0.00	0.11	1.04	0.4	1.04	0.4	0.53
8	-0.28	0.11	0.71	-2.6	0.70	-2.7	0.71
12	-0.28	0.11	1.00	0.0	1.00	0.1	0.47
17	0.58	0.09	0.86	-1.4	0.91	-0.9	0.61
18	-0.48	0.13	0.85	-1.2	0.87	-1.1	0.57
19	0.79	0.09	1.25	2.3	1.24	2.1	0.33
20	0.36	0.08	1.01	0.2	1.21	1.8	0.54
21	0.01	0.09	1.04	0.4	1.04	0.4	0.53
22	-0.61	0.11	0.93	-0.5	0.85	-1.2	0.51
23	0.22	0.09	0.87	-1.2	0.86	-1.2	0.60

The infit and out fit mean square values for the 13 personal efficacy scale items, as shown in table (4), are ranged between 0.71 and 1.25, and standardized fit values between -2.7 to 2.1. All items of the personal efficacy scale; except item 8 which has unacceptable in and outfit ZSTD, are within the acceptable range of fit statistics. This result revealed the unidimensionality of the PE scale, which is one of the basic assumptions of Rasch model. Moreover; the point measure correlation for the PE scale items range between 0.30 and 0.71, this result suggests that each of the items in the personal efficacy scale contributed to define a common construct.