Colombo et al. have shown that an infant's looking style which refers to an infant's duration of visual fixations to a stimulus, is an important indicator of cognitive development. Infants with short visual fixations (short looking, or SL) are cognitively advantaged over infants with longer visual fixations (long looking, or LL) (Colombo et al., 2011). However, gauging the importance of looking style has been sharply constrained for two reasons: First, looking style has only been assessed at the between-infant level, with infants classified LL or SL. In fact, looking style is a within-infant phenomenon. Second, to assess looking style has required a pretest. So the potential importance of looking style can only be assessed in settings which employ the pretest, which additionally, adds “overhead” to any setting, making subject loss more probable. These difficulties are eschewed in the model detailed here which assesses looking style at the within-infant individual-look level and without additional technology. The model could potentially unlock unrecognized information on video tapes long relegated to storage, if data were collected under the paired stimulus preference paradigm, pioneered by Fantz (1958, 1961), the setting of focus here. Thus, infant fixations show dual use: First, for assessing an infant's short or long looks on each trial, and second for addressing whatever the primary goal of the study might be. The requirements for the model implementation are a sufficient number within-infant trial replications, an issue considered later. Importantly, the model and associated procedure allows for the assessment of how looking style impacts the major variable of focus.

Historically, Beasley (1933) was probably the first researcher to recognize that individual infants displayed a variety of different looking behaviors to various visual stimulus objects. But he did not know the cognitive implications of his observations. SL infants are cognitively advanced over their LL peers on a variety of cognitive tasks (see Colombo et al., 2011 for a review). Many researchers have observed infant looking differences although the terms used to characterize the differences have varied widely (Beasley, 1933; Stechler and Latz, 1966; Cohen, 1972; Haith, 1980; Bronson, 1982, 1994; Colombo et al., 1988; Hood, 1995; Butcher et al., 2000).

The pretest procedure was developed by Colombo and his colleagues in the late 1980s and can be viewed as a two-stage procedure. First it involves partitioning infants into two groups, SL and LL based on a median split of infants' “peak” pretest looking times (Colombo et al., 1988, 1995). Various procedures may follow in the second stage. Subsequently, the pretest is used to inform the primary analysis, with the pretest acting effectively as a covariate. The general paradigm continues to be employed (Courage et al., 2004; Diaz and Bell, 2011; Cuevas and Bell, 2014).

The pretest procedure can be viewed as a simple empirical decision rule without a decision-theoretical conceptual foundation. If forces half of any sample to be classified as SL infants, an implausible outcome given different infants, tasks, and settings. The procedure could be modified so it has a decision-theoretical probabilistic basis; however, this goal is not considered here.

The larger implication may be that looking style and particularly SL is important in a much wider range of developmental processes not currently identified as being impacted by looking style differences. To investigate these possible implications means an infant's looks must be able to be assessed within the context of the ongoing study, at the within-infant trial level. Aslin has remarked that “…all looking times include a mix of active information processing and blank stares (Aslin, 2007, p. 50).” The proposed model framework illustrates how within-infant looking style can be assessed. The theory allows each looking trial response to be probabilistically specified as whether it is long or short, for each i and for each trial t.

The methodology uses mixture modeling (e.g., Everitt and Hand, 1981; Titterington et al., 1985; McLachlan and Peel, 2000) detailed in the Appendix (Supplementary Materials) but at the within-subject level, a rarity. Thus, each i has her own model and associated parameters. The key is to view the looking style problem as a latent variables problem. What is latent, that is, unobserved or unknown, is whether an infant's look on trial t is long or short.

This article has two goals: First, it illustrates how within-infant trial level inference is possible. Second, it illustrates how the information so culled can inform substantive research questions. Here the focus is on the development of preferences for faces of one's own race (also referred to as same race) vs. preference for faces of some other race. Infants were longitudinally assessed at 3, 6, and 9 months. The methodology and infant ages are similar to some other studies (e.g., Liu et al., 2015) but employs longitudinal data. Consequently, a richer set of questions can be addressed.

Briefly, the research concerning same race and other race face preferences is related to the larger literature on other race effects, but a preference paradigm is employed. Among newborns, neither same race nor other race faces have been preferred, but preference for own-race faces has been demonstrated by 3 month infants from different ethnic groups (Kelly et al., 2005, 2007; Bar-Haim et al., 2006; Liu et al., 2015). Other race face preference has been demonstrated at 9 months, but not at 6 months (Liu et al., 2015).

Among the issues considered here are the following: (1) Infants are provided with their own probability parameter π_io the probability of infant i being a short looker at age o (in what follows, o is often suppressed). So the change in i's looking style may be more precisely indexed than previously possible. (2) What role does looking style play in the development of same or other race face preference? (3) How are looking style changes and race-face preferences intertwined in development? Do looking style changes precede, follow, or develop concurrently with changes in race face preferences? (4) A longitudinal approach allows for better understanding of an individual infant's face preference over age which is reflected in several analyses.

i's model is:

Note that Equation (1) depends on i but does not depend on t. The subscripts short and long denoting the corresponding short and long distributions, and lettered arguments, a_i and f_i denoting the endpoints of the uniform for i. The long distribution u_long(d_it) is composed of two weighted uniform distributions u_long(d_it) = λ_iu(a_i, b_i)+(1−λ_i)u(e_i, f_i) and u_short(a_i, f_i) = u(a_i, f_i). In the notation u_mix and u_long both taking arguments d_it are mixtures of uniform distributions. The three distinct distributions, one short, and one long itself consisting of two distributions, are the mixture distribution components. The parameters a_i < b_i < 0 < e_i < f_i are component (rectangle) endpoints. The parameters λ_i denotes the proportion of responses that are negative (d_it < 0) and 1−λ_i the proportion that are positive (d_it > 0).

As noted, Figures 2, 3 give the long and short components for i 1507 and i 536 respectively. The figure captions give the estimated endpoints. Neither figure reflects the values of π^i which alters the heights of the components. For i 1507, Figure 2, π^i=0, so all d_it are estimated to have come from i's long distribution. Consequently because the π^i weight of the short component is zero the short component vanishes. For i 536, Figure 3, all responses are estimated to have come from the short component, so π^536=1 and so the long components vanish. The corresponding figure for i 2523 is not given, but his graph is similar; his data appear above. i 2523 is a mixed looker, with π^i=0.36, so most of his responses are estimated to have come from his long distribution.

What has been provided are tailor-made models for an i's individual responses. Eye-tracking methodology typically aggregates over infants and often over their responses as well, sometimes tens of thousands of them (Papageorgiou et al., 2014, Figure 1).

Equation (1) is a latent variables model because, as noted above, the knowledge of which distribution, long or short, gave rise to a particular d_it is unknown. Observations are assumed to have come from the mixture distribution or the left side of Equation (1); inference focuses on estimating the parameters on the latent right side. As noted, the central goal is to give each d_it a probabilistic interpretation as to which component distribution, long or short, d_it “came from.” The result are estimates of the form

The average of these probabilities is π^i.

The results are in three parts with subsections. Part one considers the model and data agreement. Part two provides definitions of SL and LL based on π^i and considers each infant's trajectory of change from LL to SL. Part three illustrates how the development of looking style impacts same or other race face preferences.

Looking style progresses from LL to SL, although there are large individual differences in the rate of progress; some 3-month infants display SL maturity not achieved by other infants at 9 months. Looking style and face preference were shown to be dependent, with SL well preceding changes in face preference and perhaps playing a causal role in the shift from own race to other race face preferences as the infant develops. Whether looking style changes are method (here paired stimulus array) or stimulus (here faces) dependent is unknown.

These results have shown for the first time that i's looking durations on different trials can be probabilistically assessed as to whether they are long or short, within a conventional paired preference looking paradigm which may have been thought not possible: “If one wants to document…what an infant can do on a single trial…” (Aslin, 2012, p. 128, original emphasis) eye-tracking methodology is required. Because conventional procedures were employed, as suggested earlier, the possibility of exploring old data for new insights is possible and likely with little effort or cost. While the method here is specific for paired-array settings, the general strategy should be applicable to other settings.

From a linking hypothesis perspective (Aslin, 2012) face preference is linked through i's probability distribution reflected in π^i, the weight associated with i's SL distribution: Incremental changes in π^ are associated with incremental changes in mean face preference at 3 months as Figure 6 shows. Looking style assessment is important because it appears to be a central driver in determining which face stimulus an infant prefers at 3 months, and likely during the earlier weeks in life as well. Figure 6 makes clear the magnitudes of the differences conditioned on looking style at 3 months are huge: The conditional mean differences at δ = 1/2 in Figure 6 (also Table 2 row one) are more than five standard errors apart.

To review, 3 month SL infants prefer their same race faces; LL infants prefer other race faces. When aged 6 and 9 months, the SL 3 month infants remain SL and prefer other race faces. The proportions of LL infants at 6 and 9 months dwindles, so that preferences among these remaining LL infants cannot be specified.

Broadly, the findings replicate other reports (Kelly et al., 2005, 2007; Bar-Haim et al., 2006; Liu et al., 2015). By largely replicating earlier findings, it appears that methodological variations and varying definitions of preference may not be critical. For example, Liu et al. (2015) define preference in terms of differences of ratios of looking times based on two face pairings; Bar-Haim et al. (2006) employed commonly used looking time differences based on eight face pairs; differences of 24 pairings were used here.

The issue of looking style has apparently not been discussed as a potential variable in the broad literature concerned with looking responses to facial stimuli. This is likely because heretofore, looking style has been assessed only by employing a pretest, so the role of looking style was never regarded as salient. However the present findings make it clear looking style can be a critical variable to consider at least in preferential looking, and likely other settings as well, in the early weeks of life. A looking style viewpoint also allows for certain alternative explanations and raises issues never considered.

As an example, twelve 3-month infants were sampled from each of three different ethnic groups (Bar-Haim et al., 2006). The Israeli-born infants of Ethiopian origin, were presented with a Caucasian and African pair of faces. “Remarkably, [they]…showed no particular preference…(Bar-Haim et al., 2006, p. 162).” Perhaps the small insignificant preference for Caucasian faces was partly because these infants had experience with faces of both races early on. However the unknown proportion of SL infants in their sample surely would be a contributing factor. Their insignificant result parallels the unconditional insignificant findings reported here for 3 month infants. Had looking style been controlled, a different conclusion might have been rendered, as was the case here.

Recognizing the importance of looking style on infant face preferences makes clear the importance of considering the proportion of SL and LL infants when sampling, and sampling's impact on interpreting results. View sampling as a Bernoulli process, with π_osl denoting the probability of obtaining a weak SL infant at age o, and 1−π_osl the probability of a weak LL infant. To illustrate, assume SL 3 month infants prefer own faces, LL prefer other race faces and take π^3sl=0.36=21/58 (Table 2). To demonstrate, unconditionally, a significant own face preference would likely require a substantial proportion of the infants sampled be SL; likely 5 or more SL infants among a sample of 12 are needed. The probabilities are 0.45, 0.20, 0.09 of getting one, two, and three such independently drawn samples with at least 5 SL infants. This describes the sampling situation, from the current perspective, of Bar-Haim et al. (2006). The unknown proportion of SL infants actually sampled likely influenced the outcomes. This possibility presents an intriguing challenge: Separating the influence of looking style from early experience.

Liu et al. (2015) reported preferences for same or other race faces in Chinese infants aged 3, 6, and 9 months. Same race faces were preferred at 3 month, other race faces were preferred at 9 months, but no significant preference was shown at 6 months. Other race faces were preferred at 6 months in the present study. There are two alternative explanations for the Liu et al. (2015) 6 month null result. One is that what occurred in the present unconditional insignificant analysis at 3 months, occurred in their analysis at 6 months. The implications are the same as just discussed: Conditioning on looking style might lead to a different result, although this would seem unlikely if π^6sl=0.93=62/67 (Table 2) is appropriate for their sample because most infants would likely be SL. This leads to a second possibility.

Liu et al. (2015) assessed Chinese infants; the present study assessed Caucasian infants. It is quite possible that π_osl might differ for the Caucasian and Chinese infant populations. Freedman (1974) reported a myriad of behavior differences among newborns of seven different ethnic groups. Freedman and Freedman (1969) reported that Chinese-American newborns visually habituate more rapidly than European-American newborns and Japanese newborns lag behind Caucasian newborns in visual following responses (Freedman, 1974, p. 165). Consequently, it does not seem implausible to suspect that the proportions of SL infants in different racial or ethnic groups, given a fixed age, might well be importantly different.

The literature concerned with infant responses to own or other race faces views development largely as a consequence of experiential or socio-cultural learning processes (Anzures et al., 2013). The selection of and comparison with infants from different racial or ethnic groups appears to assume the infants of the same age but from different groups differ primarily in their experiences. The results presented here suggest that looking style can be a potential confounding variable, unless the corresponding population proportion of SL infants, π_osl, is near zero or one or has been controlled by, for example, conditioning on SL or LL subpopulation membership, at least early in life. Another way of measuring the impact of looking style is to note that in Figure 6, for every one tenth increase in δ units, there is roughly a 1.5 unit increase in the mean d, at least for 0 ≤ δ ≤ 1/2.

Kelly et al. (2005) reported that 3 month infants prefer same race faces, but newborns show no preference. Null findings are problematic, as they acknowledge, especially in light of earlier literature. Fantz et al. (1962) reported that infants could resolve 40 min. of visual arc with 1/8-in. stripes at 10 in. before they were a month old, and that infants can visually discriminate between patterned stimuli within 48 h after birth (Fantz, 1963). Kelly et al. (2005) note it seems likely “…newborns are able to discriminate between faces …but no group elicits a greater attraction” (Kelly et al., 2005, p. F34). One would expect some infants in the early days of life would display SL, and consequently such SL newborns might display consistent face preferences. What might be the proportion of weak SL newborns?

Beasley (1933, p. 118, Table 3, column 1) reports the proportions of his most mature white newborn visual pursuit responses among his four categorical types of pursuit: 0.21, 0.28, and 0.39, proportions at ages 1 day, 2 to 5 days, and 6 to 12 days respectively. It might be reasonable to suppose that these proportions serve as a surrogate for the proportion of weak SL newborns.

A second source for a newborn SL estimate is provided by regressing for each of the 46 infants with assessment at all three ages, their π^i3,π^i6,π^i9 against occasions o = 3, 6, 9 (with intercept estimate constrained to the interval [0,1]) then predicting i's value at 1 week of age, taken as the newborn age, and denoted π~i0.25. The mean of the π~i0.25 is 0.32 with the estimated SL proportion π^0.25sl=∑iI(π~i0.25>0.5)/46=0.28. These two estimates would imply that for Caucasian infants the proportion of SL newborns a week old π_{0.25 sl}, is around 0.25 to 0.30.

More importantly however, because π_{.25 sl} appears to be well away from zero, the actual number of SL newborns in a sample is likely to be non-negligible. Taking π^0.25sl=0.25, perhaps the expected number of roughly 12 (= 48 π^i.25 SL newborns in the Kelly et al. (2005) sample of 48 (their same vs. other race face conditions) would show consistent preferences if SL infants could have have been identified. Kelly et al. (2005) interpret the preference shown at 3 months but not at birth as due to learning occurring during the first 3 months. Such a learning explanation is difficult to falsify. An easily falsifiable explanation is that failure to find a face preference at birth or in the earliest days of life is because of the unrecognized importance of looking style differences.

A critical assumption underlies the above framework, as noted earlier, is that the difference scores of each infant are regarded as a random sample from i's population of responses which means that the difference scores are independent and identically distributed random variables within each i. Otherwise said, the responses of i are a random sample from i's own probability distribution, u_mix(d_it) in Equation (1). This assumption cannot be exactly correct, but it does not appear to be importantly wrong. It implies that the order in which the observations were made is irrelevant. This hypothesis can be tested. If the correlation between the pairs (d_it, t), t = 1, 2, 3, …, 24 within each i and at each o departs from zero, evidence would be provided that the within i random sampling assumption is wrong. Bootstrap testing one to three infants were significant, p < 0.05, at each o = 3, 6, 9 months with samples sizes 58, 67, and 62, respectively. Thus, there is no evidence, within individual infants, of the difference scores being correlated with the trial number. One reason for this lack of correlation may be the following fact. If (random variables) A (African) and T (trials) have ρ correlation, and C (Caucasian) and T also have ρ correlation, C−A = D, then D and T are zero correlated. Basing the analysis on difference scores might have mitigated certain expected trends in data.

Any implementation of the strategy proposed above requires within individual repeated measures. In the paired-stimulus setting Aslin and Fiser (2005) suggest 12 trials are typically obtained; here 24 were obtained. How many replications are needed likely depends on the task, age of infant, the observed variable, and requires study. However, a preliminary analysis suggests that if the first 12 of the 24 responses were employed, results would be little changed from those reported above. Selecting uniform probability distributions as models of infant looking responses is unique. An examination of the data drove this decision. In the absence of a rich theory some consequence of which might specify a particular family of distributions for infant responses, one simply cannot do better than to be guided by the each infant's data. Indeed, the empirical distribution function of i's own data is in fact the non-parametric maximum likelihood estimate of that infant's unknown distribution function, given certain assumptions (Owen, 2001, p. 7–8).

Individual differences remain one of the most challenging and important problems in psychology. How such differences are viewed and conceptualized, if indeed there is any interest in doing so, varies. The most common approach is to partition, at one or more places in the assumed common response distribution over individuals, then label the corresponding groups constructed as different. As noted at the outset, this is how Colombo has defined SL and LL infants (e.g., Colombo et al., 1988). This is not the approach here. Figure 1 shows the qualitative shape differences which define individual differences. Formally, infants i and j are different if and only if the distribution of i's responses is different from the distribution of j's responses. Figure 1 is, for the approach here, a call for modeling each i's response distribution; all i share the same family of response distributions, additive π-weighted uniform distributions, as in Equation (1).

This research has shown how within-infant looking style differences can inform more substantive issues without additional data collection or technical apparati. Statistical modeling alone is required. But the critical consideration in this modeling, to stress yet again, is modeling i's response distribution. Race–face preferences and looking style were shown to be dependent (Figure 6), with changes in looking style well preceding changes in race–face preference. One consequence: Without considering looking style, inferences concerning race–face preferences can be misleading at least for young infants. From a general substantive perspective, this research leads to the suggestion that looking style may be crucial for understanding a wide variety of infant behaviors never imagined to be impacted by looking style and well beyond the reach of conventional between infant looking style assessment methods.

IF designed the study, coded the data, and prepared data files. HT did the analysis, modeling and manuscript writing.