Survival Analysis: Survival Analysis relies on hazard rate. For measures of discrete time, the hazard function is defined as:

hj=P(T=jl|T>j)

hj is the probability of experiencing an event (end of the tantrum) in time period (T)j given that it was not experienced before j. It can be calculated as the number of tantrum episodes that ended in the respective interval divided by the number of tantrum episodes that were still ongoing at the beginning of the interval in question.

Cox Regression: The transitional probabilities were used to predict tantrum cessation (i.e., the hazard) for each 60 second time window. In discrete-time survival analysis, the hazard can be related to the covariates using the logistic function shown below (Singer and Willett, 2003):

logitij= βj+ κ'zjzij+κ'xjxi…

B weights can be interpreted as the log odds of the predictor relative to the other predictors in the model. When using transitional probabilities as predictors, we will obtain a measure of the log odds of staying in the tantrum at each time point. Negative estimates decrease the probability that a child will be censored (drop out of the tantrum) while positive estimates increase the probability that a child will be censored (or drop out of the tantrum). In other words, a positive prediction weight indicates that a higher score on the predictor is associated with longer duration tantrums and a negative weight means that a higher score on the predictor is associated with shorter duration tantrums.

It Takes Two to Tango: A Unique Approach to Temper Tantrum Analysis Jennifer B. Bissona, James A. Greena, and Michael Potegalb

a.University of Connecticut b.University of Minnesota

INTRODUCTION

METHOD

CONCLUSIONS

REFERENCES

!  Tantrums are normative for children between the ages of 18-60 months (Chamberlin, 1974; Jenkins, Bax, & Hart, 1980; MacFarlane, Allen, & Honzik, 1954). ! In the past, researchers have characterized the child’s vocal and motor behavior within a tantrum episode, but less is known about how parent behavior affects the unfolding of the tantrum (Potegal & Davidson, 2003; Green, Whitney, & Potegal, 2011). ! Transitional (conditional) probabilities were created to gauge the interactions that occur between parent and child within a tantrum episode. ! These transitional probabilities were used to explore the type of parent and child interactions that affect tantrum duration.

High-fidelity audio recordings were taken from 20 videotaped tantrums of 11 toddlers (Mage = 28.45 months) and their families during home observations.

Coding Parent Speech*: Silence (N = 1258), Questions (N = 451), Commands (N = 308), or Declarative (N = 657) statements.

Coding Child Vocalizations*: silence (N = 2156), fuss (N = 327), whine (N = 993), cry (N = 356), yell (N = 212), and scream (N = 120).

*Inter-rater reliability for these codes was high (r = 0.896 – 0.975).

Transitional Probabilities: Using GSEQ, (Bakeman & Quera, 1995), parent and child vocalizations were transformed into event data and the frequency of two-behavior sequences for each dyad were computed.

probability of A|B = (frequency of BA) / (frequency of B)

(For each tantrum, 144 transitional probabilities were calculated using the proportion that one behavior followed another out of all other codes that could follow. For example, if there were 12 instances of crying and 3 were followed by questions from the parent, the transitional probability would be 3/12 or 0.25.)

Temper Tantrum Duration: Tantrum onset was operationally defined as an the first outburst of negative behavior (i.e., stiffening limbs/arching back, getting down, shouting, screaming, crying, pushing/pulling, stamping, hitting, kicking, throwing, or running away). The tantrum ended when the last of these behaviors stopped.

RESULTS & DISCUSSION !  Correlations were computed between tantrum Duration and each transitional probability.

!  Regression analyses were used to assess the predictive value of each transitional probability on tantrum Duration, holding constant other behaviors that could have followed. There were 10 regressions conducted with Duration as the dependent variable - one for each “given” code.

! Similarly, transitional probabilities were used in a survival analysis to predict the tantrum’s endpoint.

! Only significant transitional probabilities associated with parents responses are presented in Table 1.

! Results show that when a child is fussing or yelling, parent Silence predicts longer tantrums. However, when a child is crying, parent Silence reduces intensity and duration of a tantrum episode (Table 1).

! In some instances, a child’s vocal behavior alone appears to be the primary determinant of a tantrum outcome. For instance, when a child is yelling, a parent’s verbal response is not related to tantrum duration. When a child is whining, survival analyses show that all parent verbalizations shorten the tantrum (Table 1).

! Vocal exchanges between parent and child can be used to predict tantrum duration.

! Results suggest that parents have some control over their child’s tantrums. Parents might be able to shorten their child’s tantrums by responding based on their child’s vocalization.

! Survival analysis may yield additional information about behavioral responses in tantrum episodes when compared to simple regression.

Chamberlin, R. W. (1974). Management of preschool behavior problems. Pediatric Clinics of North America, 21, 33--�47. Green, J. A., Whitney, P. G., & Potegal, M. (2011). Screaming, yelling, whining, and crying: Categorical and intensity differences in vocal expressions of anger and sadness in children's tantrums. Emotion, 11(5), 1124--�1133. Jenkins, S., Bax, M., & Hart, H. (1980). Behavior problems in preschool children. The Journal of Child Psychology and Psychiatry, 21, 5–17. MacFarlane, J. W., Allen, L., Honzik, M. P. (1954). A Developmental Study of the Behavior Problems of Normal Children Between Twenty--�One Months and Fourteen Years. Berkeley, CA: University of California Press. Potegal, M., & Davidson, R. J. (2003). Temper tantrums in young children: 1. Behavioral composition. Journal Of Developmental And Behavioral Pediatrics, 24(3), 140--�147. Singer, J. D. & Willett, J. B. (2003). Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence. Oxford University Press, USA.

Correspondence should be addressed to: Jennifer.Bisson@uconn.edu

University of Minnesota

!!Table&1.&con,nued…&yell%

Ques)on!yell%

Declara)ve!Silent%

Ques)on!Ques)on%Command!

Command%Silent!

Command%Declara)ve!

!Correla)on! &r&=&0.462**&&&p&=&0.040&&

!Regression! &ß&=&0.49**&&p&=&0.020&&

&ß&=&0.49**&&&p&=&0.036&&

&ß&=&0.73**&&&p&=&0.022&&

&ß&=&<0.79**&&&p&=&0.016&&

!Survival!Analysis! &B&=&<22.56**&&&p&=&0.015&&&B&=&<25.05**&&&p&=&0.014&&

&B&=&<53.70**&&&p&=&0.011&&

&B&=&<241.52**&&&p&=&0.000&&

&B&=&<42.98**&&&p&=&0.016&&

!!Table!1.!!!Parent!“Target”!Codes!in!Rela)on!to!Tantrum!Dura)on!

fuss%!Silent!

whine%!Silent!

whine%Command!

whine%Ques)on!

whine%Declara)ve!

cry%!Silent!

yell%!Silent!

!Correla)on! &&

!Regression! &ß&=&<0.66**&&&p&=&0.034&&

!Survival!Analysis! &B&=&<54.45**&&&p&=&0.036&&

&B&=&121.44**&&&p&=&0.002&&

&B&=&197.96**&&&p&=&0.000&&

&B&=&137.10**&&&p&=&0.002&

&B&=&97.16**&&&p&=&0.007&&

&B&=&<19.29**&&&p&=&0.023&

Note.&***p&<&0.001,&**p&<&0.05&

Example of variability in transitional probabilities:

! Finally, sequences of parent behavior can be used to predict the outcome of a tantrum. A parent Command followed by Silence predicts shorter tantrums, while a Command followed by a Declarative statement characterizes longer tantrums. Similarly, parent Silence followed by a Question relates to longer tantrums (Table1).