Development of self-control in early childhood—a growth mixture modeling approach

Figures & data

Table 1. Descriptive statistics (N = 17,322)

	Variable	N	%
Gender
	Male	8,845	51.06
	Female	8,443	48.74
	Missing	34	.20
Race
	White	8,189	47.28
	Black	2,279	13.16
	Hispanic	4,372	25.24
	Asian	1,383	7.98
	Others	1,058	6.11
	Missing	41	.24
Disability
	Child without Disability	14,039	81.05
	Child with Disability	2,465	14.23
	Missing	818	4.72
Poverty
	Not Below Poverty Threshold	13,933	8.44
	Below Poverty Threshold	3,311	19.11
	Missing	78	.45
Single Parent Household
	Both parents	14,244	82.23
	Single parent	3,078	17.77
Parent Education
	Middle School or below	2,068	11.94
	High school	3,412	19.70
	Collage	4,941	28.52
	Bachler or above	4,904	28.31
	Missing	1,997	11.53
Care programs
	Nonparental arrangement	3,034	17.52
	Relative care	2,128	12.28
	Non-relative care	851	4.91
	Center-based care	8,028	46.35
	Two or more programs	347	2.00
	Missing	2,934	16.94
	Mean	SD
Parent expectation	5.18	1.46
Teacher expectation	2.85	.76
Teacher-student closeness	4.35	.64
Teacher-student conflict	1.64	.80

Table 2. Mean and standard deviation of the four scale scores at each time point (N = 17,322)

Variable	Mean	SD	Variable	Mean	SD
SC1	2.07	3.40	Interp1	2.10	3.21
SC2	3.02	1.51	Interp2	2.98	1.52
SC3	2.31	3.22	Interp3	2.39	2.93
SC4	2.97	1.84	Interp4	2.97	1.57
SC5	2.33	3.28	Interp5	2.22	3.24
SC6	3.00	1.77	Interp6	2.94	1.62
Ex1	1.27	1.94	App1	2.87	1.15
Ex2	1.56	1.11	App2	3.06	.96
Ex3	1.54	1.32	App3	3.03	.75
Ex4	1.65	1.05	App4	3.05	.93
Ex5	1.41	1.60	App5	3.03	.87
Ex6	1.66	.95	App6	3.05	.90

Note: SC, Ex, Interp, and App represent four sub-constructs of the overall self-control, namely, self-control, externalizing problem behavior, interpersonal skills, and approach to learning. 1–6 represents a total of six measurement occasions.

Table 3. Model comparison statistics for latent class analysis

	2*Log-likelihood Change	df Change	p
2-class Vs 3-class	4009.162	4	<.001
3-class Vs 4-class	1591.702	4	.24

Table 4. Growth factor estimates for each latent class

	N (Proportion)	Intercept (se)	Slope (se)	Quadratic slope (se)
High	9,161(52.89%)	7.89*** (1.14)	1.06*** (.22)	−.18*** (.04)
Medium	5,729 (33.07%)	0^a	.26 ^a	0 ^a
Low	2,432 (14.04%)	−9.31*** (1.87)	.24(.16)	−.01(.03)

Note: ^aFor the model identification purpose, the standard error of the growth factor parameters in the medium class were fixed. More details in model identification can be found in B. Muthén and Shedden (1999); *** p < .001

Figure 1. Model implied growth trajectories across three latent class

Table 5. Estimates from multinomial logistic regression

	High vs Medium		Low vs Medium		High vs Low
	Exponentiated coefficients^a	p	Exponentiated coefficients^a	p	Exponentiated coefficients^a	p
Intercept	.91	.75	.09	<.001	1.07	<.001
Child Variables
Race
Black	.73	<.001	1.45	<.001	.50	<.001
Hispanic	.91	.20	.97	.82	.93	.59
Asian	1.16	.23	1.03	.90	1.12	.64
Other	.99	.90	1.16	.40	.85	.41
Age^b	1.02	<.001	1.00	.82	1.02	.06
Gender	1.85	<.001	.63	<.001	2.93	<.001
Disability	.76	<.001	1.33	.01	.57	<.001
Family Variables
Parent Education Level
Middle School or Lower	.85	.11	1.13	.39	.75	.08
Collage	1.03	.74	1.25	.05	.82	.11
Bachelor or Higher	.98	.78	1.21	.15	.81	.14
Single Parent Household	.74	<.001	1.30	.01	.57	<.001
Poverty	1.01	.86	.92	.44	1.10	.43
Primary Nonparental Arrangements Before Kindergarten
Relative Care	1.09	.37	.79	.12	1.37	.05
Non-relative Care	.75	.02	1.05	.80	.72	.11
Center-based Care	.90	.13	.99	.96	.90	.40
Two or more Programs	.92	.62	.86	.56	1.06	.83
Parent Expectation	1.04	.07	.97	.36	1.08	.05
School Variables
Teacher Expectation	1.90	<.001	.59	<.001	3.22	<.001
Teacher-student Closeness	1.26	<.001	.99	.88	1.27	<.001
Teacher-student Conflict	.17	<.001	3.58	<.001	.05	<.001

Note:

^aExponentiated coefficients: the odds ratio of each predictors

^b Age: age of entering kindergarten centered at the average (67.4 months).

Appendix 1. Variable names, data source, original coding, and recoding rules

Variable Name	Definition	Data Source	Original Coding	Recoding rules
X_RACETH_R	Race and ethnicity of the child	Parent interview or FMS	1 = White, not Hispanic; 2 = Black or African American, not Hispanic; 3 = Hispanic, race specified; 4 = Hispanic, no race specified; 5 = Asian, not Hispanic; 6 = Native Hawaiian or other Pacific Islander, not Hispanic; 7 = American Indian or Alaska Native, not Hispanic; 8 = More than 1 race, not-Hispanic	Four dummy codes (white reference group): Black; Hispanic (categories 3 and 4); Asian; Other (categories 6, 7, 8); Missing (everthing else)
X1_KAGE_R	Child age in months at time of assessment; compared the child’s birthdate to completion of child direct assessment	School data and parent interview	Units = months	Continuous
X_CHSEX_R	Child’s sex	Sampling, parent interview, FMS	1 = Male;2 = Female	0 = Male; 1 = Female
X2DISABL2	Child’s disability status	Sampling, parent interview, FMS	1 = child with disability; 2 = chidl without disability	0 = chidl without disability; 1 = child with disability
X1HPARNT	Types of parents living in the household	Parent interview	1 = Two biological/adoptive parents; 2 = One biological/adoptive parent and one other parent/partner; 3 = One biological/adoptive parent only; 4 = One or more related or unrelated guardians	0 = Not single-parent (categories 1, 2); 1 = Single-parent household (categories 3, 4)
X1PAR1ED_I	Highest level of education achieved by first parent	Parent interview	1 = 8th grade or below;2 = 9th to 12th grade;3 = High school diploma/equivalent;4 = Voc/Tech program;5 = Some college;6 = Bachelor’s degree;7 = Graduate/professional school/no degree;8 = Master’s degree;9 = Doctorate or professional degree	Four dummy codes (High school/equivalent as the reference group)1 = Less than high school (categories 1, 2);2 = Some college/Voc/tech program (categories 4, 5);3 = Bachelor’s4 = Graduate school or higher (categories 7, 8, 9)
X2POVTY	Household poverty status determined by comparing household income to thresholds the U.S. Census Bureau		1 = Below the poverty threshold;2 = At or above the poverty threshold;3 = At or above the 200 percent of the poverty threshold	0 = No (categories 2, 3);1 = Yes
P1EXPECT	What degree the parent expects from the child	Parent	1 = To receive less than high school diploma;2 = To graduate from high school;3 = To attend a vocational/technical school;4 = To attend two or more years of college;5 = To finish a four or five year college degree;6 = To earn a Master’s or equivalent;	Not technically ordinal, but use 1–7 scale, everything else missing
X12PRIMPK	Primary, nonparental arrangements in which the child spent the most hours per week during the year before kindergarten	Parent questionnaire	0 = No non-parental care;1 = Relative care in child’s home;2 = Relative care in another home;3 = Relative care, location varies;4 = Non-relative care in child’s home;5 = Non-relative care in another home;6 = Non-relative care, location varies;7 = Center-based program;8 = 2 or more programs;	Four dummy codes (no non-parental care is the reference group)1 = Relative care (categories 1, 2, 3);2 = Non-relative care (categories 4, 5, 6);3 = Center-based care;4 = 2 or more programs
X2CLSNSS	Teacher-reported measures of closeness between the teacher and child	Teacher	Range from 1–5	Continuous
X2CNFLCT	Teacher-reported measures of conflict between the teacher and child	Teacher	Range from 1–5	Continuous
T4EXPECT	What degree the teacher expects from the child	Teacher	1 = To receive less than high school diploma; 2 = To graduate from high school; 3 = To attend a vocational/technical school; 4 = To attend two or more years of college; 5 = To finish a four or five year college degree; 6 = To earn a Master’s or equivalent;	Not technically ordinal, but use 1–7 scale, everything else missing

Appendix 2. Reliability of four measures for the overall self-control

Variable	Number of Items	Reliability Coefficient	Variable	Number of Items	Reliability Coefficient
SC1	4	.81	Interp1	5	.86
SC2	4	.82	Interp2	5	.87
SC3	4	.79	Interp3	5	.85
SC4	4	.81	Interp4	5	.86
SC5	4	.80	Interp5	5	.88
SC6	4	.81	Interp6	5	.85
Ex1	6	.88	App1	7	.91
Ex2	6	.89	App2	7	.91
Ex3	6	.88	App3	7	.91
Ex4	6	.86	App4	7	.91
Ex5	6	.87	App5	7	.91
Ex6	6	.88	App6	7	.91

Note: SC, Ex, Interp, and App represent four sub-constructs of the overall self-control, including self-control, externalizing problem behavior, interpersonal skills, and approach to learning, respectively. 1-6 represents a total of six measurement occasions.

Muthén, B., & Shedden, K. (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics, 55(2), 463–469. doi:10.1111/j.0006-341X.1999.00463.x

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